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IRTF Crypto Forum This document defines random-access authenticated encryption (raAE), a primitive that partitions a message into an indexed sequence of segments that can be encrypted and decrypted independently and in any order. It also specifies SEAL (Segmented Encryption and Authentication Layer), a parameterized construction that defines a family of concrete raAE instantiations, one for each valid choice of an Authenticated Encryption with Associated Data (AEAD) algorithm, a key derivation function (KDF), and associated parameters. SEAL supports immutable (write-once), append-only, and mutable (in-place ciphertext rewrite) operations, each with per-segment authentication. A separately configured snapshot authenticator can additionally authenticate the complete, indexed segment set. The document also defines the security notions of raAE, specifies the requirements for conforming constructions, and analyzes SEAL against those requirements. Concrete cipher suites, serialization layouts, and test vectors for SEAL are specified in a companion document. Discussion Venues Discussion of this document takes place on the raae mailing list (raae@ietf.org), which is archived at . Source for this draft and an issue tracker can be found at .

Introduction Large encrypted content is often stored as a sequence of fixed-size segments, so that an application can read or modify any part of it without processing the whole. Encrypted backups, encrypted file formats, object stores with partial updates, and full-disk encryption over fixed-size blocks all work this way. Such a system needs to encrypt, decrypt, or re-encrypt any individual segment on its own and in arbitrary order, and to verify that the stored object as a whole is authentic and complete, without re-encrypting the segments that did not change. This document specifies the raAE primitive (), whose base interface and security notions come from Fábrega et al. (), and defines SEAL (Segmented Encryption and Authentication Layer), a parameterized construction of raAE. The base algorithms encrypt and decrypt segments in arbitrary order, so a caller can read or replace any segment on its own. On top of that base, the extended raAE interface adds in-place rewrite and a snapshot, a stored value that authenticates the segment set and count the writer recorded for it. A rewrite re-encrypts only the changed segment and updates the snapshot, leaving every other segment untouched. Appending to the end, or truncating from the end, composes the same per-segment operations, so the snapshot stays consistent without a separate algorithm. SEAL builds the primitive from a chosen AEAD algorithm, a key derivation function (KDF), and configuration parameters. Under a snapshot authenticator, it binds every segment and the count into a keyed snapshot that an adversary cannot forge without the content-derived key.

The raAE primitive and the SEAL construction

raAE separates the two authentication scopes that applications often conflate:

Per-segment authenticity:

One AEAD tag verifies under the segment index, a finality bit marking the last segment, and any caller-supplied associated data. It does not establish that the segment belongs to the current snapshot.

Snapshot integrity:

When a snapshot authenticator is configured, snapshot verification checks that the present segment set and the count are exactly what the writer recorded for that snapshot, under a content-derived key. Verification targets the whole segment set, and, where the authenticator supports it, can instead confirm that a designated subset of segments is included at their recorded positions, without reading the others (). It does not establish freshness against whole-object rollback, which a consuming protocol must supply.

raAE and SEAL are deliberately distinct layers. A consuming protocol supplies serialization, storage transactions, key management, and rollback protection, which are out of scope here. The full boundary of what raAE does not provide is . The remainder of this document presents raAE first and SEAL second. situates raAE against prior segmented authenticated-encryption (AE) constructions. fixes terminology and notation. specifies the extended raAE primitive and its snapshot operations. defines SEAL. states the target security properties an raAE construction must meet, the assumptions SEAL's components must satisfy, and the operational limits on its use, and defines the security notions. Cipher suites, serialization layouts, named instantiations, and test vectors are specified in the companion document .

Related Work CHAIN () is a segmented authenticated-encryption construction that chains state from one segment to the next. It is sequential by construction and supports neither independent random-access reads nor in-place segment rewrites. STREAM () turns a nonce-based AEAD into a segmented construction using induced nonces that encode a message nonce, the segment index, and a final-segment bit. STREAM supports random-access decryption and encryption of individual segments, but defines neither authenticated snapshots nor authenticated rewrites. SEAL's derived nonce mode () follows STREAM's counter-plus-final-bit structure and adds those operations. Tink Streaming AEAD () and OpenPGP v2 Symmetrically Encrypted and Integrity Protected Data (SEIPD) packets () are deployed STREAM-family formats. Both derive a message key and nonce prefix from a key and a salt, encrypt each chunk under an AEAD nonce carrying the chunk index, and detect truncation with a final tag over the empty string. Tink derives an AES-GCM key with the HMAC-based Key Derivation Function (HKDF) (), while v2 SEIPD selects its cipher and AEAD from packet identifiers. Each chunk is independently authenticated and can be verified locally at its boundary. Neither format defines an in-place rewrite operation or a snapshot authenticator over an updatable set of segment tags. SEAL's snapshot authenticator addresses exactly that gap. Its per-segment input is the segment leaf (), which binds the segment's content when the ciphertext digest is set. It verifies the whole segment set against the snapshot, and optionally a designated subset (). A consuming protocol that authenticates the one keyed snapshot obtains integrity over the whole segment set and its count. Where the ciphertext digest is set over a strict ordering (), the authenticated snapshot also pins each index to one ciphertext, even against holders of the content-encryption key (CEK). Tahoe-LAFS () authenticates separately encrypted pieces with a signed Merkle tree: it encrypts a mutable file in segments, builds Merkle hash trees over its erasure-coded blocks, and has the writer sign a value that includes the tree's root with an RSA key, so a reader checks one segment against the signature through the hashes on its path. A signature over an unkeyed root gives integrity and origin to a verifier that holds no decryption key. SEAL's keyed snapshot does not do that on its own. The counterpart in SEAL is the public snapshot that every strict authenticator defines, for a consuming protocol to sign (). Fábrega et al. () formalized random-access AEAD security over a raAE primitive syntax in which segment encryption and decryption may be invoked in arbitrary order, and gave a construction, FLOE (Fast Lightweight Online Encryption), proved to meet it. FLOE realizes the base interface: segments are written once, and there is no snapshot. SEAL realizes that primitive with the extension of this document, and defines the security notions used in its analysis. Each precedent covers part of the random-access AE design space. raAE is the abstract interface that generalizes the family with three capabilities none of the precedents combines: arbitrary-order encryption, in-place authenticated rewrite, and a snapshot over the whole segment set. SEAL realizes all three in one construction.

Conventions and Terminology The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here. A message segment is a unit of plaintext that is individually encrypted and authenticated. Segments need not be uniform in length. A construction MAY set a maximum segment size, and the construction or its consuming format MAY set a minimum, which applies to every segment, the final one included, unless the format exempts the final segment. A segment may be any length within those bounds. The final segment of a message is the one at its highest index, whatever that segment's length. A message is the content that one CEK and salt pair protects, the unit the primitive encrypts. An object is that message in stored form: the ciphertext segments, their metadata, and any snapshot that a storage layer holds. Each object carries one message, whose content may change through rewrite and length-changing operations. A ciphertext core is the AEAD encryption output corresponding to one message segment, excluding file-level headers and external segment metadata. An AEAD-specific split divides this output into ct_i, the encrypted segment body, and tag_i, the authentication tag. A ciphertext segment is the stored representation of one encrypted message segment. Depending on nonce_mode, it contains the ciphertext core and may also contain a stored nonce or other per-segment metadata. Segment metadata is per-segment information needed to decrypt or verify a ciphertext segment, such as a stored nonce, tag, finality status, or profile-defined values. This document writes AEAD.Encrypt and AEAD.Decrypt for the authenticated encryption and decryption operations defined in . Symbol form follows the layer a name belongs to. The abstract interface and the analysis use mathematical notation: a capital letter is an operand of that interface, either an octet string (K, N, G, T_g, A_i, M_i, C_i) or the per-message state (S). A lowercase letter is an integer index or bound (i, e, r), except the position identifier p, a pair (i, b) (). N with a lowercase letter is a size that a chosen component fixes rather than one a deployment picks: the AEAD (Nk, Nn, Nt, Nb), the KDF (Nh), the snapshot authenticator (Na), or the nonce mode (Np). Everything the construction names concretely uses lowercase snake_case, whatever its type: octet strings (salt, commitment, segment_key, ct_i), counts (n_seg, n_ep), lengths a deployment configures (segment_max, commitment_length), and identifiers, which take an _id suffix (aead_id, kdf_id, snap_id, protocol_id). Names that take arguments follow the same split. Initialisms are capitalized (LH, KDF, AEAD, and XOF, an extendable-output function), and LH is defined in . The raAE tuple is CamelCase (KeyGen, StartEnc, EncSeg, StartDec, DecSeg, RewriteSeg, SnapVerify), while the methods of a component it parameterizes over are lowercase (snapshot, verify, add, remove, and set_length of ), so a name shows which interface it belongs to. Derivations this document defines are lowercase (encode and frame in , leaf in , and nonce in ). A subscript selects one instance of a value: X_i is X for the segment at index i, as in A_i, P_i, ct_i, and tag_i, and d_e is the epoch head for epoch e (). A value written f(i), as in segment_key(i) or nonce(i), is the value that the named derivation defines for index i. Two suffixes and one prefix recur. A _label suffix is an ASCII constant that separates one derivation from another (aad_label, epoch_key_label). A _calc suffix marks a value recomputed for comparison against a stored one (d_calc(e) and leaf_calc(i) in ). An Adv_ prefix names an adversary's advantage in the analysis (Adv_snap, Adv_muPRF). The remaining terms (ikm, label, info, L, salt, CEK, protocol_id, nonce_mode, payload_info, segment_commitment, epoch_length, epoch, epoch_key, payload_key, segment_key, snap_key, and the commitment) are defined in where they first appear.

Taxonomy

raAE primitive:

The abstract random-access AE interface and security target.

Extended raAE interface:

The base interface plus snapshot maintenance and verification.

SEAL construction:

The construction specified in .

Cipher suite:

The AEAD and KDF algorithms and their sizes.

Profile:

A named set of fixed parameter choices, identified by a protocol_id, needed for interoperability.

Parameter set:

The per-object values that affect derivation and verification.

Consuming protocol:

The protocol or format that stores objects and manages keys.

Serialization:

The consuming protocol's wire or storage encoding.

Segment:

A zero-based independently encrypted plaintext unit.

Epoch:

A group of 2^epoch_length segment indices sharing one epoch key.

Keyed snapshot:

The value, computed under snap_key, that authenticates one segment set when a snapshot authenticator is configured.

Snapshot authenticator:

A pluggable SEAL component that produces and verifies the snapshot. Its abstract interface is , and its concrete instantiations are in .

Public snapshot:

The unkeyed counterpart of the keyed snapshot, which a strict snapshot authenticator defines for a verifier that holds no key: a snapshot of the same leaves, payload_info, the commitment, and the count, computed with an empty ikm in place of snap_key ().

Per-segment authenticity:

AEAD verification for one segment only.

Snapshot integrity:

Verification of the segment set, or of a designated subset or, by prefix verification, a prefix of it, against the snapshot.

Ciphertext digest:

LH(ct_i) (), the digest of one segment's ciphertext, stored in that segment's metadata and carried first in the strict authenticators' leaf when the instantiation sets it; the payload_info parameter segment_commitment selects it. It binds the segment's content, not its position (), and is distinct from the commitment, which binds the CEK, payload_info, and G.

External freshness:

Rollback protection supplied outside raAE.

Notation

I2OSP(n, w):

The w-octet big-endian encoding of the non-negative integer n, as defined in .

uint8(n), uint16(n), uint32(n), uint64(n):

Shorthand for I2OSP(n, 1), I2OSP(n, 2), I2OSP(n, 4), and I2OSP(n, 8) respectively.

||:

Octet string concatenation.

XOR:

Bitwise exclusive-or of two octet strings of equal length.

X[a:b]:

Octets a through b-1 inclusive of X (zero-based, half-open interval).

[x, y, ...]:

An ordered list of octet strings. A single-element list is written [x]. The brackets denote a list, not an optional parameter.

frame, encode:

The length-prefixed injective encoding used by SEAL, defined in . frame is total over all field lengths. The construction requires an injective framing () but does not mandate this encoding. Another profile MAY use any injective encoding that meets .

Nk:

Key size in octets for the chosen AEAD algorithm.

Nn:

Nonce size in octets for the chosen AEAD algorithm.

Np:

Presented nonce size in octets: the per-segment nonce stored in metadata. Np = Nn in random nonce mode () and Np = 0 in derived nonce mode (), where the nonce is recomputed from the key schedule.

Nh:

Hash or pseudorandom function (PRF) output size in octets for the chosen KDF.

Nt:

Authentication tag size in octets for the chosen AEAD algorithm.

Nb:

Cipher block size in octets for the chosen AEAD algorithm, defined only for an AEAD built on a block cipher. The block-size birthday limit of is expressed in Nb and does not apply to an AEAD with no block-cipher structure.

Na:

The keyed snapshot length in octets, the output size of the configured snapshot authenticator. It MAY depend on the segment count n_seg, and is 0 when none ().

n_seg:

The number of ciphertext segments in a stored message. Written n_seg (lowercase) to distinguish it from the per-message nonce N in the raAE interface ().

n_ep:

The number of epochs in a stored message, ceil(n_seg / 2^epoch_length).

The raAE Primitive

Overview Random-access authenticated encryption (raAE) partitions a message into segments, each encrypted and decrypted on its own and in any order. A reader can open one segment without the rest of the message, and a writer can encrypt one without holding the others. In the base interface , each segment is written once and thereafter only read. The extended raAE interface keeps that base and adds one capability: a segment already written may be replaced in place, without disturbing the rest. Rewriting changes the threat model. Per-segment authentication binds each segment in isolation, so it cannot tie the segments a reader assembles to a single recorded version of the object: a storage layer holding the ciphertext can roll a segment back to an older valid copy, substitute one valid same-index segment for another, or drop one, and each segment it presents still authenticates. An optional snapshot authenticates the segment set as the writer recorded it, so a reader can detect these changes. The extension () defines the snapshot and the operations that maintain it. The security notions follow the interface. raAE and its rewrites target ra-ROR (random-access real-or-random) and ra-CMT (random-access context commitment) (). Rewriting leaves the ra-CMT definition untouched, and the ra-ROR definition too in random nonce mode (), since replacing a segment there is an encryption the read-only adversary could already ask for. In derived nonce mode a rewrite is deterministic and relies on an equality-leakage relaxation of ra-ROR (), and in any nonce mode the ra-ROR bounds of do not cover it (). Snapshot authentication adds the one notion of its own, snapshot integrity ().

Interface The base raAE interface, from , is a tuple of five algorithms: KeyGen, StartEnc, EncSeg, StartDec, and DecSeg.

KeyGen:

Randomized key generation. Takes no input. Outputs a secret key K.

StartEnc(K, N, G):

Deterministic. Takes a secret key K, nonce N, and global associated data G. Outputs a ciphertext header T_g and an initial per-message encryption state S.

EncSeg(S, p, A_i, M_i):

Randomized. Takes the encryption state S, a position identifier p, per-segment associated data A_i, and message segment M_i. Outputs a ciphertext segment C_i. S is not modified. EncSeg may be called with the same S at any position, in any order, or concurrently.

StartDec(K, N, G, T_g):

Deterministic. Takes key K, nonce N, global associated data G, and ciphertext header T_g. Outputs a per-message decryption state S or an error.

DecSeg(S, p, A_i, C_i):

Deterministic. Takes the decryption state S, position identifier p, per-segment associated data A_i, and ciphertext segment C_i. Outputs message segment M_i or an error.

The position identifier p = (i, b) consists of a segment number i and a terminal bit b in {0, 1}. They impose a total ordering on segments and carry a truncation defense: a ciphertext lacking a segment with b = 1 is incomplete. The encryption state S is immutable, so EncSeg calls are order-independent and can run in parallel. The ciphertext header T_g commits to K, the nonce N, and global associated data G. A headerless scheme emits T_g = empty.

Extended Interface Replacing a segment already written, without re-encrypting the others, requires no new operation: re-encrypting a position is an ordinary EncSeg call over the immutable state. The ra-CMT definition applies to it unchanged, and so does the ra-ROR definition in random nonce mode (). A scheme that supports rewriting MAY carry a snapshot, a value over the current set of segments that a reader checks to detect tampering that per-segment authentication does not catch. A write-once scheme MAY carry one too: a single value that a consuming protocol authenticates once for the whole segment set (). Two operations, added by this document, maintain and check the snapshot. RewriteSeg replaces a segment and updates the snapshot in the same step. SnapVerify decides whether a given set of segments is one the writer recorded under the snapshot presented. The keyed snapshot is a deterministic function of the per-message state, the (index, input) set, and the count. It is not part of the immutable encryption state S. The add, remove, set_length, and snapshot() operations of update it over the writer's (index, input) set or over the authenticator's summary of that set, and the consuming protocol serializes those updates as that section requires. The verify() operation runs over the (index, input) set recomputed from the segments presented to SnapVerify, with any witness it is given.

RewriteSeg(S, p, A_i, M'_i, C_i, snapshot, witness):

Randomized. Takes the encryption state S and position identifier p, per-segment associated data A_i, the new message segment M'_i, the existing ciphertext C_i at position p, the current snapshot, and a witness for the segment set before the update. Outputs replacement ciphertext C'_i and an updated keyed snapshot, snapshot', together with the updated summary where the authenticator keeps one.

SnapVerify(S, segments, snapshot, witness):

Deterministic. Takes a per-message state S, either the encryption state from StartEnc or the decryption state from StartDec, the segments to verify as (position, ciphertext segment, A_i) triples, with A_i empty where a segment has none, the snapshot, which the caller declares complete or open (an intermediate snapshot), and a witness, which is empty for the whole-object target. The segments are either the whole current object state or, where the authenticator supports it, a designated subset of it. Outputs accept or reject.

The extension also adds an output to StartEnc. In the extended interface:

StartEnc(K, N, G):

Deterministic. As in , and additionally outputs the initial keyed snapshot, the snapshot over the empty segment set.

EncSeg retains its base signature and outputs only C_i. The caller adds C_i to the object by updating the snapshot over the new (index, input) set and count with the authenticator's operations (), in place from a summary or by recomputing. These additions define the extended raAE interface of this document: the tuple (KeyGen, StartEnc, EncSeg, StartDec, DecSeg, RewriteSeg, SnapVerify) over the keyed snapshot. Changing a message's length is a composition of these operations, not a separate algorithm in either direction. Position-addressed encryption over immutable state already permits re-encrypting a position or encrypting at a higher index (see ). A holder appends by encrypting the new segments and re-marking the old final segment with RewriteSeg, which re-encrypts its existing plaintext to clear its terminal bit. It truncates to the first m segments by dropping the segments at index m and above and re-marking segment m-1 with RewriteSeg, which re-encrypts its existing plaintext to set its terminal bit. Appending to an empty object skips the re-mark, since there is no old final segment, and truncating to zero segments yields the empty object. Each length change updates the snapshot, and gives the construction for both directions.

Witness Rules A witness is untrusted data that a subset SnapVerify reads in place of the segments it does not verify: a deterministic function of the subset presented, the (index, input) set, the count, and the snapshot key, which may include the inputs of segments not presented. The authenticator specifies its witness. Under a strict ordering () it is the count and per-segment inputs, or values derived from them, so a witness supplies the A_i of the segments it stands for (, ). A subset SnapVerify that reads a witness checks it against the keyed snapshot, so the witness adds no trust to that check. A witness is not part of the keyed snapshot. An update reads a witness for the segment set before the update: its count and, in place of the inputs the update leaves unchanged, what the authenticator needs to compute the new value. The authenticator defines that witness and how it is checked (). An authenticator's summary is state it derives from the inputs and keeps beside the object so that an update reads fewer of them; calls its stored form the aux region. A whole-object SnapVerify does not validate a stored summary: it recomputes the value from the segments and never reads the stored copy. The writer MUST NOT use a witness it has not authenticated: one it produced itself as the sole writer, or one it has checked against a verified snapshot for the same commitment and count (). Each removed input MUST be one the writer produced itself as the sole writer or be checked at its index against the same verified snapshot, unless the authenticator permits its use without that check (). An authenticator grants that permission only where an incorrect input leaves no segment set, short of a forgery, verifying against the resulting snapshot or any snapshot derived from it. It lists the permitted cases and their assumptions. When an update decrypts a stored record, the input formed from the same record bytes, under the finality bit and A_i it decrypted under, MUST match the authenticated or locally trusted input at that position. If the authenticator permits removal without checking the input, the removed input MUST instead be that record's own input, read once with the record. The update MUST fail if any required check or decryption fails. A snapshot is verified in one of two ways. It is known to be current when it comes from the locally trusted storage of a sole writer or from authentication outside the construction that carries external freshness (). Otherwise a whole-object SnapVerify that accepts the stored object verifies the stored snapshot. In an application that requires whole-object rollback resistance (), a writer MUST update only from a current verified snapshot, or it would certify a rolled-back state as the next version. Under an append-only profile () the count an append starts from MUST be current, whatever the application's rollback requirement: the writer takes n_seg from locally trusted storage or from authentication outside the construction that carries external freshness, never from the stored object alone. An append from a rolled-back count can encrypt new content at (i, b) positions the object has already used. In derived nonce mode that is the nonce reuse of , unless the AEAD provides misuse-resistant authenticated encryption (MRAE). In random nonce mode the two encryptions draw independent nonces, so AEAD-level nonce reuse occurs only by collision. Still, the pair is encrypted twice, which the hypothesis excludes regardless of nonce mode ().

The SEAL Construction SEAL is a construction for the raAE primitive of , realizing its extended interface from a KDF, an AEAD, the labels, a nonce-generation method, and an optional snapshot authenticator. Its KDF combiner () frames every derived key and input over any KDF with a two-step or one-step form. SEAL provides commitment around the AEAD, which need not itself commit. A SEAL construction MAY select any AEAD, KDF, nonce mode, commitment configuration, or snapshot authenticator that satisfies the requirements of this section. derives SEAL's bounds from the abstract properties of these components. Concrete parameter choices and interoperable suites are in . In the key hierarchy below, a CEK and per-content salt feed the payload schedule, which derives four per-message values ().

SEAL Key Hierarchy

The figure shows each segment's tag feeding the authenticator. Its actual per-segment input is the segment leaf, formed from the metadata entry ().

Construction Overview The commitment lets a reader reject a wrong key or parameter set before decrypting. The snapshot, when present, authenticates the current segment set. SEAL realizes the raAE operations of as follows: raAE operations and their SEAL realizations

raAE operation	SEAL realization
StartEnc	Derive the payload schedule from the CEK and salt, committing G (), and, under a snapshot authenticator, the snapshot over the empty set
StartDec	Re-derive the schedule and verify the stored commitment ()
EncSeg, DecSeg	EncryptSegment and DecryptSegment ()
RewriteSeg	RewriteSegment, then update the snapshot authenticator for the changed segment ()
SnapVerify	Check the index set, count, and authenticator inputs, then verify the snapshot via the authenticator ()

SEAL's salt, payload_info, and G carry the raAE per-message inputs, and the commitment stands in for the header ().

Component Suite and Parameters lists the parameters, inputs, and derived values, with what sets each and where it is defined. Parameters, inputs, and derived values

Parameter	Type or range	Set by	Defined in
AEAD	RFC 5116 algorithm	suite
KDF	KDF algorithm	suite
segment_max	power of two, at least 4096	suite
epoch_length	integer r in 0 to 63	suite
protocol_id	octet string	application
nonce_mode	"random" or "derived"	message, within the profile
aad_label	ASCII string	profile
commitment_length	integer, at least 16, default Nh	profile
Nk, Nn, Nt, Nb	sizes in octets	AEAD
Nh	size in octets	KDF
CEK	32 uniform random octets	message input
salt	32 uniform random octets	message input
payload_info	ordered element list	message input
G	octet string, empty by default	message input
commitment	commitment_length octets	derived per message
payload_key	Nk octets	derived per message
snap_key	Nh octets	derived per message
nonce_base	Nn octets, derived mode only	derived per message
epoch_key(i)	Nk octets	derived per segment
segment_key(i)	Nk octets	derived per segment
nonce(i)	Nn octets	derived per segment
segment_aad(i, is_final, A_i)	octet string	derived per segment
tag_i	Nt octets	derived per segment

SEAL fixes the segment additional authenticated data (AAD) encoding (), the commitment derivation (), and the keyed snapshot () identically across all suites. Their octet lengths still vary by suite, because Nh and Nt are suite-dependent.

Suite Choices A suite is assembled from the following choices.

AEAD:

An authenticated encryption with associated data algorithm satisfying the interface of , with Nk-octet keys, Nn-octet nonces, and Nt-octet authentication tags.

KDF:

A key derivation function supporting the abstract interface defined in .

segment_max:

A positive integer, a power of two and at least 4096 octets. Each segment carries at most this many plaintext octets. The length-dependent limits of are computed at this size.

epoch_length:

A non-negative integer r in 0 to 63. Each epoch covers 2^r consecutive segments aligned to a multiple of 2^r, so r sets the key-rotation granularity: r = 0 gives a fresh epoch key per segment and r = 63 one key for all segments (). Profiles MAY restrict r further per AEAD.

protocol_id:

An application-chosen octet string that binds all derived values to a specific protocol version. Selection guidance is in .

nonce_mode:

A payload_info element selecting one of two nonce constructions, "random" or "derived". The constructions are defined in , and the valid (nonce_mode, snap_id, segment_commitment) tuples depend on the profile.

Profile-Level Constants One constant is fixed by the profile rather than carried per message.

aad_label:

A profile-level ASCII string bound as the first element of the segment AAD encoding (). Consuming protocols MAY define their own profiles with a distinct aad_label.

Algorithm-Determined Sizes The sizes Nk, Nn, Nt, and Nh are fixed by the chosen AEAD and KDF rather than by the parameter set directly, as is Nb where it is defined. They are defined in . One configurable length defaults from Nh.

commitment_length:

A positive integer of at least 16, defaulting to Nh, the length in octets of the key commitment prefix. The collision bounds for each length are given in .

Per-Message Inputs An encrypted message is built from four input values.

CEK:

A 32-octet uniform random Content Encryption Key generated fresh for each message. The CEK is input keying material for the key schedule, not an AEAD key.

salt:

A per-content value of 32 uniformly random octets. The salt separates payload schedule outputs across messages even when the CEK is reused. and give the rules for generating and reusing it, and analyzes the consequences of reuse.

payload_info:

The committed record of the object's configuration: an ordered list of parameter set context elements covering key derivation, AEAD operations, AAD construction, and nonce construction, which the commitment () binds. The profile fixes the concrete element set and their encodings. SEAL's payload_info is specified in .

G:

An octet string of global associated data, the G input of StartEnc in the raAE primitive (), binding whole-message application context such as a name, version, or policy. G defaults to the empty octet string and is never stored: a decryptor supplies it from application context, and the commitment binds it ().

The remaining symbols in are derived values. The payload schedule computes the per-message values once from the CEK and payload_info, fixing them for the message's lifetime (). The commitment additionally binds G (). Per-segment values are defined where they are computed, in the sections cites.

The KDF Combiner The KDF combiner uses a length-prefixed encoding for all of its inputs. frame is total over every field length. A field too large to emit literally is instead prefixed by the reserved length 0xFFFF and an Nh-octet digest LH(x). LH(x), the over-large-field digest, runs the cipher suite's native KDF primitive directly on x, invoking neither encode nor frame, and returns Nh octets. The two-step and one-step classes are HPKE's: a two-step KDF () uses its extract step, and a one-step KDF () its XOF, with x carried under the label "raAE-LP-v1": Running LH through the full KDF would re-enter frame on the over-large x and recurse. The direct native call avoids that. requires the construction to justify the collision resistance of the over-large-field digest. LH's is that of the cipher suite's KDF primitive at the suite's Nh. In the two-step class LH(x) is HMAC under the fixed public key "raAE-LP-v1", so a collision in LH yields a collision in the underlying hash: with the key fixed, an HMAC collision on distinct inputs is a collision of its inner or its outer hash call. In the one-step class LH(x) is the XOF itself over a domain-separated input, so a collision in LH is a collision in the XOF at that output length. The injectivity of encode, and LH's domain separation from the literal encoding, are established in . Key material is derived through a KDF with the interface

• protocol_id: binds the output to a specific protocol version and application context.
• label: a unique ASCII string identifying the derivation role.
• ikm: input keying material, provided as a single octet string or an ordered list of octet strings.
• info: context information, provided as a single octet string or an ordered list of octet strings.
• L: the requested output length in octets.

This KDF binds protocol_id, a label, and inputs of any size into a derived value. frame reduces any over-large input to a fixed-size digest before the KDF sees it. Any protocol instantiates the combiner by supplying its own protocol_id, which domain-separates its derivations from those of every other protocol. The KDF is built from the cipher suite's hash in one of two forms. The cipher suite's kdf_id selects which one.

Two-Step KDF The notation ...x means each element of the sequence x, whether ikm or info, is a separate argument to encode. A single octet string is the one-element sequence containing it. An absent value is the empty sequence and contributes no arguments. The empty sequence and the one-element sequence whose element is the empty octet string are distinct: the first adds nothing to the encode, the second adds one zero-length field. A derivation with no info MUST use the empty sequence, not the empty octet string, so that every implementation encodes a given (protocol_id, label, ikm, info, L) tuple to the same octets. The protocol_id appears in both the Extract salt and the extract_input as a defensive measure, and binding in either position suffices for domain separation. The label appears in both Extract and Expand so that label binding is preserved even if one phase is weak in isolation. Implementations MAY amortize the Extract computation internally when deriving multiple outputs from the same protocol_id, label, and ikm.

One-Step KDF The XOF-based form frames ikm and info each as a single element of one length-prefixed encode and squeezes L octets of output. protocol_id binding is via the message-side encode prefix only. In both forms the encoded input ends with uint16(L): the two-step form places it last in expand_info and the one-step form places it last in M. Within a fixed kdf_id, distinct (protocol_id, label, ikm, info, L) tuples have distinct framed inputs, subject to the digest-collision qualification in . KDF output pseudorandomness is a separate requirement; distinct framed inputs can still produce colliding outputs. The two forms are not mutually injective: a cipher suite's kdf_id selects one form for that suite, and payload_info commits to the kdf_id (), so no derivation ever compares outputs across forms. The two-step form binds ikm in Extract and info in Expand. A multi-value ikm or info is the encode of its elements, so any number of elements is admitted.

SEAL Encodings and Labels

Payload Info Construction Element encodings for SEAL:

• aead_id: 2 octets, uint16(id), the unsigned 16-bit AEAD identifier.
• segment_max_be: 4 octets, uint32(segment_max).
• kdf_id: 2 octets, uint16(id), the unsigned 16-bit KDF identifier.
• snap_id: 2 octets, uint16(id), the snapshot authenticator identifier.
• segment_commitment: 1 octet, 0x00 when the leaf does not bind the segment's content and 0x01 when it does (). It is a choice independent of snap_id, but not every (snap_id, segment_commitment) pair is sound, so a profile selects a valid one.
• nonce_mode: 1 octet, the nonce construction: 0x00 for random, 0x01 for derived. A profile MAY select any valid (nonce_mode, snap_id, segment_commitment) tuple.
• epoch_length_u8: 1 octet, uint8(epoch_length). Implementations MUST reject epoch_length >= 64 on both encode and decode.
• salt: 32 raw octets, the per-message salt.

The aad_label is a profile-level constant for SEAL (see ) and is not carried in payload_info. The KDF () applies frame to each element of the list.

Segment AAD The segment AAD binds each segment to its context. What it must carry depends on the nonce mode: a random nonce binds neither the segment index nor the finality bit, so the AAD must, whereas a derived nonce binds both (). Segment AAD by nonce mode

	Random nonce mode	Derived nonce mode
Index i and is_final	bound in the AAD	bound in the nonce
A_i, when present	appended as a fourth encode element	the sole variable element
A_i, when empty	omitted, not a zero-length element	segment_aad is empty, with no associated-data pass

aad_label is the profile-chosen label from the parameter set, the index i is a big-endian 8-octet integer, and is_final is 1 for the last segment and 0 for all others. Because encode length-prefixes every element, omitting an empty A_i stays injective, so the index and finality bit remain authenticated. Any profile that defines a random-mode segment_aad MUST preserve injectivity and MUST authenticate the segment index and finality bit. aad_label is bound transitively through protocol_id (), so segment_aad need not repeat it for cross-profile separation. More generally, the binding of the triple (i, is_final, A_i) MUST be unambiguous under one segment key, so that no two distinct triples present the same inputs to the AEAD. In random nonce mode segment_aad alone MUST injectively bind the triple, because the nonce is an independent random draw. In derived nonce mode i and is_final are bound in the nonce and A_i, when present, in segment_aad, and the (nonce, segment_aad) pair MUST jointly determine the triple (). A_i is the caller-supplied per-segment associated data of EncSeg and DecSeg (), passed to the segment algorithms (). It MAY be empty and MAY differ per segment. Unlike a global associated data value G, which the commitment fixes at creation (), A_i rides the per-segment AEAD associated data and is rewritable: a rewrite can change a segment's A_i. The salt is not included in the AAD because it is already bound into segment_key via the payload schedule. Different messages produce different segment keys even at the same index. Transposing two segments within a message fails because the AAD at each position encodes the expected index. Because each segment binds its index and finality bit (), unauthorized truncation and extension fail per-segment authentication, which requires a decryptor to check. Authorized truncation by the CEK holder re-marks the new last segment as final, or empties the object, and updates the snapshot (). The per-segment AEAD binds a segment's index and finality, not its length, by the same means. A segment's ciphertext length is authenticated implicitly by the AEAD tag over the ciphertext: altering, truncating, or splicing a segment ciphertext is an AEAD forgery, not a parsing ambiguity. Because segments may be shorter than segment_max, the consuming format MUST convey each segment's ciphertext length to the decoder. A wrong length yields an AEAD rejection, never a silent accept.

Labels SEAL core KDF labels by role

Derivation role	Label variable	Value
Commitment	commit_label	"commit"
Payload key	payload_key_label	"payload_key"
Snapshot authenticator key	snap_key_label	"snap_key"
Nonce base	nonce_base_label	"nonce_base"
Epoch key	epoch_key_label	"epoch_key"

SEAL fixes each label to the value above. The construction formulas reference labels by variable name, so the labels are SEAL parameters rather than constants of the raAE construction. Each value is an ASCII string and is distinct from all others. These are the always-present key-schedule labels. The configured snapshot authenticator (), the plaintext-bound nonce construction (), and hedged randomness () each define their own labels.

Key Schedule and Nonce Generation A message's entire key hierarchy grows from two random values. All other keys are derived deterministically through the KDF of .

Payload Schedule Four values are derived from the CEK and per-content salt. G is the global associated data of , always the last element of the commitment info. It defaults to the empty octet string, one zero-length element, so every commitment derivation includes it. The other three derivations never take G.

Epoch Key Derivation An AEAD with a 96-bit nonce (Nn = 12) has, at a 2^(-32) collision-probability target, a random-nonce budget of about 2^32 encryptions per key. For rewritable content, this limit can be reached through repeated modifications to the same segments. Epoch keys partition the nonce space: each epoch key covers at most 2^r segment positions (initial writes plus rewrites), so the per-key invocation count is bounded regardless of the content's total size. Meeting an aggregate target also requires . When epoch_length = r is specified, the segment key for segment i is an epoch key derived from the payload key: > epoch_length return KDF(protocol_id, epoch_key_label, [payload_key], [uint64(epoch_index)], Nk) ]]> At epoch_length = 0 the shift is the identity, so each segment has its own epoch key. At a large epoch_length every segment shares one epoch key. Implementations MUST apply this derivation at every epoch_length, including 0, and MUST NOT use payload_key directly as a segment key. Epoch keys implement the parallel external rekeying pattern of , adapted for random-access patterns.

Nonce Generation Two nonce modes, random and derived, trade off AEAD flexibility, storage cost, and trust in a cryptographically secure pseudorandom number generator (CSPRNG). Derived mode needs misuse-resistant authenticated encryption (MRAE) unless the profile's writer discipline keeps every derived nonce unique. The chosen mode is part of the parameter set and MUST be consistent across all segments of a message.

The Two Nonce Modes

The two modes differ as follows: Random and derived nonce modes

Property	Random nonce mode	Derived nonce mode
Per-segment nonce stored	yes, in segment metadata	no
CSPRNG required	yes	no
AEAD requirement	any AEAD	MRAE, or any under a nonce-uniqueness discipline
Rewrite	fresh nonce each write	nonce fixed by index, reused on rewrite
Per-segment AAD	binds index and finality	empty when no A_i (index/finality in nonce)
Minimum nonce size Nn	no added constraint	at least 8 octets

Random Nonce Mode In random nonce mode (nonce_mode = "random"), each segment gets an independent random nonce: Each segment's nonce is stored in per-segment metadata and MUST be accessible to any reader that decrypts individual segments. This mode requires a functioning CSPRNG. The nonce collision probability across independently generated per-segment nonces follows the standard birthday bound. See . Two optional encryptor-side hedges harden this mode against different threats. Hedged randomness () mixes a long-term key into each draw and defends against a weak or predictable CSPRNG. The hedge's inputs are the CSPRNG output and a per-call value, tag2. If tag2 stays unique, duplicated CSPRNG state alone cannot repeat the hedged output. Duplication that also rolls back tag2's source replays the hedged output (). Only the plaintext-bound construction () defends against that, because it mixes in the plaintext. It defends only segments whose plaintext or segment AAD differ. Both hedges are implementation-local, leave the wire format unchanged, and are not separate nonce modes.

Derived Nonce Mode Derived nonce mode is intended for profiles that do not store a per-segment nonce. Nonces are derived deterministically from the payload schedule. Derived nonce mode is defined only for AEADs whose nonce size Nn is at least 8 octets. The segment index occupies the high bits of an 8-octet counter and the finality bit occupies the low bit, so the per-segment AAD need not carry either one. The XOR is applied to the last 8 octets of nonce_base, with the remaining octets unchanged: The encoded value (i << 1) | is_final MUST fit in the low 8 octets of nonce_base, so the segment index i MUST be less than 2^63. This caps an object at 2^63 segments, far beyond any reachable object. See for the resulting size limit. A derived nonce is fixed by the segment's index and finality bit, so re-encrypting a segment at the same index and finality repeats its nonce. With unchanged plaintext and associated data, the repetition reproduces the first ciphertext, because AEAD.Encrypt is a function of its inputs. With changed inputs the outcome depends on the AEAD. An MRAE AEAD tolerates the repetition, degrading to equality leakage rather than plaintext recovery, within the rewrite count its multi-user bound allows (). A non-MRAE AEAD leaks plaintext. So with a non-MRAE AEAD, derived nonce mode MUST be confined to a profile whose discipline never re-encrypts a segment with a different plaintext or associated data. Two such disciplines matter here. A write-once profile rewrites nothing and performs no length change, so no segment is re-encrypted at all. An append-only profile re-encrypts one segment per append, the re-mark that supersedes the old terminal segment, and that re-mark carries the segment's existing plaintext and changes only the finality bit, which changes the nonce (). Under either discipline, each object MUST have its own fresh salt, so its nonce base differs from every other object's. The encryptor MUST NOT perform a second encryption at any (i, is_final) pair under that salt, including after a crash (), and MUST NOT restart encryption of an incomplete object under that salt, even at pairs it has not used. Resending stored ciphertext and its metadata is not an encryption; anything else needs a fresh salt. The restart rule keeps each index to one finality form, which the terminal check of rests on. A writer interrupted after encrypting index k as the final segment that restarted under the same salt with a longer input would write a non-final segment at k beside the final one, and a holder of the old bytes could present a truncation that verifies. Because the nonce binds index and finality, an immutable, write-once profile in derived nonce mode coincides with STREAM () at the nonce-and-AEAD layer: a key-derived counter-plus-final-bit nonce over a per-segment AEAD with no associated data.

Commitment The commitment is a commitment_length-octet value the payload schedule derives from the CEK, payload_info, and the global associated data G (). A reader MUST verify the commitment before decrypting any segment, deriving the expected value from the CEK, payload_info, and G and comparing it octet-for-octet with the stored value, and MUST treat a mismatch as an authentication failure for the object. A mismatch indicates a wrong key, parameter set, or G, or a corrupted header. This is the ra-CMT context commitment for fixed per-segment A_i (). The reduction outline and bound are in . Because the commitment is fixed at creation, G is immutable: changing it invalidates the stored commitment, while segment contents stay rewritable through the snapshot authenticator (). G defaults to the empty octet string, so an application that supplies no context commits over an empty final element. A wrong G fails the commitment check () the same way a wrong CEK does ().

Snapshot Authenticator The snapshot authenticator binds the current segment set into the keyed snapshot. A SEAL profile selects one with snap_id.

Interface and Requirements A snapshot authenticator defines a per-segment input, one value per segment. It produces and checks a keyed snapshot over the (index, input) set and the count with two operations:

snapshot():

Produce the keyed snapshot over the current (index, input) set and the count n_seg.

verify(snapshot):

Recompute the keyed snapshot over the current (index, input) set and the count, reading any witness SnapVerify passes in place of the segments not presented (none for the whole-object target), and accept only if it equals the stored snapshot under a constant-time comparison.

The per-segment input is defined by the authenticator, and SEAL's strict authenticators use the segment leaf (). The AEAD tag binds the segment's index and finality bit against a party without the key, through the segment AAD in random nonce mode and through the nonce in derived nonce mode. A CEK holder can produce a valid tag for altered content at any index. Setting the ciphertext digest puts LH(ct_i) in the leaf, so changing the ciphertext changes the keyed snapshot. The commitment is therefore needed where the object is shared among CEK holders, and MAY be omitted where the CEK has a single holder. The ciphertext digest is necessary for that binding but not sufficient. An ordering is linear when a holder of the snapshot key can find a different segment set giving the same keyed snapshot below the cost of a collision, and strict when finding one is a collision problem, as the snapshot authenticators registry defines them (). An authenticator with a strict ordering defines a public snapshot and, at every count k at which the object is open, an intermediate snapshot: its keyed or public snapshot over segments 0..k-1 at count k, with segment k-1 written non-final. Both are specified in . An authenticator with a linear ordering carries no public snapshot, for the reason given there, and defines no intermediate snapshot. Every authenticator supports the whole-object target: verify the full (index, input) set and the count. An authenticator MAY additionally support a subset target: verify that a designated subset of (index, input) pairs is included at their recorded positions without presenting the other segments, reading a witness () in their place and checking it against the keyed snapshot. The keyed snapshot stays a single target-independent value of length Na, with no per-segment proof stored. To change a stored object, an authenticator updates its keyed snapshot. It MAY provide add(i, input), remove(i, input), and set_length(n) to update the value in place from the changed segment alone, or it MAY recompute the value over the changed (index, input) set. A snapshot update is not atomic against a second concurrent update, so a consuming protocol MUST serialize concurrent updates to one object. This document requires that a serialization exist and does not say how to obtain it, which remains a storage-transaction concern of the consuming protocol. Serialization is needed whether the authenticator recomputes the value or updates it in place, and only the failure differs. An authenticator that recomputes over the full set binds whatever set it read, which is neither the state before the interleaved update nor the state after. One that updates in place loses an update, when two read-modify-write cycles on the stored value interleave and the later write never observed the earlier delta. This is the concurrent case, distinct from the crash case of , where one update is interrupted rather than two interleaved. The scheme's RewriteSeg and SnapVerify () are realized from these operations. For the whole-object target, SnapVerify takes no witness and checks a stored snapshot as follows:

1. Let n_seg be the number of present segments.
2. Verify that the present segments occupy exactly the indices 0..n_seg-1, each once.
3. Call verify(snapshot) over the present (index, input) set and the count n_seg.

Where the authenticator's input carries the finality bit, as the strict authenticators' leaf does, SnapVerify binds the declared finality: it forms each input with is_final(i) for a snapshot declared complete, and with 0 at every index for one declared open. The terminal bit b of each presented position MUST agree with that declaration: b = 1 only at index n_seg-1 of a snapshot declared complete. SnapVerify rejects a set whose bits disagree. SnapVerify does not decrypt, so it does not establish that a segment opens under that finality. Segment decryption checks is_final through the segment AEAD, and rejects a present set whose highest-indexed segment does not carry is_final = 1. A duplicate or missing index is caught only by step 2, because an authenticator's verify MAY accept a malformed index multiset. An implementation MUST NOT skip the index-set check. A conforming authenticator's snapshot() MUST bind both the (index, input) set and the count n_seg, so a verifier detects any added, dropped, reordered, or re-marked segment and any changed input, and the keyed snapshot MUST be unforgeable by a party without the authenticator's key, under that authenticator's security assumption. The keyed snapshot is a fixed-length value of Na octets, with Na = 0 meaning no value. In a complete object, a segment's finality is a function of its index and the count: It is carried by that segment's input, and every segment of an intermediate snapshot carries 0. Because finality follows the count, changing n_seg moves the terminal position, so rewrite, extend, and truncate are one update over the segments whose input changes, each starting from a complete object:

1. Under the current count, remove each changed segment's current input (remove(i, input)). The current n_seg fixes which segment is terminal, so each removal carries that segment's current finality.
2. Set the length to the new count (set_length(n)).
3. Under the new count, re-encrypt each surviving changed segment under its new finality and add its new input (add(i, input)). New segments are added here. Discarded segments are not added back.
4. Call snapshot(), which recomputes the keyed snapshot over the new count and segment set.

Each operation is an instance of that shape over different segments: Rewrite, extend, and truncate

Operation	Count	Inputs removed	Inputs added	Terminal re-mark
Rewrite	unchanged	the changed segment	the changed segment	none
Extend by k	n_seg to n_seg+k	old terminal	old terminal and k new	old final, 1 to 0 (none if empty)
Truncate to m	n_seg to m	segments m to n_seg-1, and the old input at m-1	the re-marked m-1 (none if m=0)	m-1, 0 to 1 (none if m=0)

This sequence uses remove, the mutable-authenticator path. One that omits remove instead resets and re-adds the surviving segments to rebuild the value. SnapVerify detects truncation in every case but one: the truncated object is presented with the snapshot of an earlier complete version at that shorter count, and presenting it is rollback (). A snapshot at that count taken while the object was open is not that case, since such a snapshot fixes is_final = 0 at its last index, and so does not verify the shorter object declared complete.

Segment Leaf The per-segment input, leaf(i), is formed from the segment's metadata entry and its context. SEAL's strict authenticators use: LH(ct_i) is present when the ciphertext digest is set. In random nonce mode nonce_field(i) is the stored nonce(i). In derived nonce mode it is the counter from which nonce(i) is derived (), so nonce_base is never published, and once the commitment fixes the CEK and payload_info the counter fixes the nonce. The field segment_aad is the segment AAD the segment was encrypted under (), so the leaf carries A_i in both nonce modes, and a verifier needs each segment's A_i, empty or supplied, to form its leaf. The bit is_final is the finality bit the segment was encrypted under: is_final(i) above for a complete object, and 0 at every index of an intermediate snapshot. The stored metadata entry holds the leaf's leading fields, the optional ciphertext digest, the tag, and the optional stored nonce, in the same order (). The masked multiset hash uses tag_i alone as leaf(i).

Intermediate and Public Snapshots A strict authenticator produces two snapshots over the same leaves (), and either can be produced while the object is open. Keyed and public snapshots

	Keyed snapshot	Public snapshot
Computed	under snap_key ()	with an empty ikm in place of snap_key ()
Who can compute it	holders of the CEK, from which snap_key derives	anyone who holds the segments and their A_i
Who can verify it	holders of the CEK	anyone, but it is authentic only under a signature or trusted reference
Protects against	a party without the CEK altering, dropping, reordering, or truncating segments; with the ciphertext digest, a CEK holder making a fixed, externally authenticated snapshot verify a different segment set	anyone but the signer doing the same, checked by any verifier; the origin it gives is the signer's
Does not protect against	CEK holders producing new keyed snapshots for each other; rollback; staleness	a signer signing several statements; rollback; staleness; it proves neither that a segment decrypts nor which key derived the commitment

The two snapshots overlap with the commitment, which binds the CEK, payload_info, and G. A key holder checks the commitment before decrypting, so a wrong key, parameter set, or G fails there (). snap_key does not bind G, so SEAL's strict authenticators include the commitment in both snapshots, which ties each to that object's context. A verifier without the key cannot check how the commitment was derived: for it the commitment is a bound identifier, and payload_info is in the public snapshot so that the parameters are authenticated. The ciphertext digest, LH(ct_i) in the leaf, is what makes either snapshot bind ciphertext rather than tags alone. Under a strict authenticator a writer MAY produce the snapshot at a count n at which the object is open, segment n-1 written with is_final = 0 and the object not ended. It binds the (index, input) set 0..n-1 and the count n as any snapshot does, so SnapVerify over those segments with the snapshot declared open accepts, but it is not a snapshot of a complete object, and the authenticator's specification states what a reader of the prefix learns from it (). A public snapshot is an unkeyed function of payload_info, the commitment, the count, and the ordered (index, input) set. A linear ordering cannot carry one, because without a key every party is in the snap_key holder's position, and a linear ordering lets that party find a different segment set with the same value below the cost of a collision. An authenticated public snapshot binds payload_info, the commitment, the count, and each index's input in order, under the collision resistance of the functions that compute it, and it is not a hiding commitment: over inputs that are withheld it gives an offline equality test for guesses at them. A profile or consuming protocol that relies on a public snapshot MUST set the ciphertext digest: without it the public snapshot binds tags but not ciphertext, so anyone can replace a segment's ciphertext and a verifier without the key still accepts the signed public snapshot. A verifier MUST accept a public snapshot only under a signature, or an authenticated reference from a party it trusts, over a statement that names the object or stream, the count, whether the object was open at that count or complete, and the value itself, and that binds G where the verifier interprets G. From an accepted public snapshot it learns that the leaves it recomputes from the segments it holds and their A_i are those the signer authenticated, at those positions, ciphertext included. The two snapshots are computed separately and can cover different segment sets, so a CEK holder can authenticate one segment set to key holders and sign another for verifiers without the key. Where the signer signed a public snapshot, a key holder that claims the signer's origin for its segments MUST also verify the signature and recompute the public snapshot over them, which establishes agreement with the signed statement, not that the signer signed no other. A public snapshot does not replace SnapVerify for a key holder, and freshness, rollback, withholding, equivocation, and completeness are out of its scope, as for the keyed snapshot ().

None This selection configures no snapshot authenticator: no keyed snapshot is produced (Na = 0), snapshot() and verify() are no-ops, and an object rests on per-segment authentication alone. Such a profile MUST NOT produce the empty object (n_seg = 0). With no keyed snapshot to bind the zero count, a truncation that removed every segment would be indistinguishable from a legitimate empty object, so a valid object always has at least one segment.

Segment Algorithms The construction defines the per-segment subroutines EncryptSegment, DecryptSegment, and RewriteSegment. In this random-access construction, is_final is an explicit input to each subroutine. Full-message encryption derives it from the total segment count n_seg, while random-access decryption and rewrite callers supply it directly. The full-message procedures (, , ) and the rewrite procedure () compose them. Each subroutine is the cryptographic core of one operation of the base or extended raAE interface (, ), refining to the signature level. The primitive's position becomes the explicit arguments i and is_final, and its state is the payload schedule, which the segment_key(i), nonce(i), and segment_aad calls below read from context rather than take as an argument. A segment's plaintext is P_i, and its stored record is stored_i = (nonce_metadata_i, ct_i, tag_i), which names the stored values, not their order on the wire (). leaf(i) is the segment's leaf (), and new_leaf(i) the leaf of the record that replaces segment i. Segment subroutines and the primitive operations they realize

Subroutine	Realizes	Composed by
EncryptSegment	the encryption core of EncSeg	and , which add the snapshot bookkeeping
DecryptSegment	DecSeg
RewriteSegment	the encryption core of RewriteSeg	and , which add the snapshot bookkeeping

These subroutines emit ct_i and tag_i as separate fields, with ct_i of length len(P_i), at most segment_max. DecryptSegment splits stored_i using the ciphertext length the consuming format conveys (). In every subroutine, i is the segment index (a non-negative integer), is_final is 1 for the last segment and 0 for all others, A_i is the caller-supplied associated data for segment i, and P_i is the segment plaintext. The subroutines call segment_key(i) and nonce(i) as defined in , with nonce(i) following the chosen nonce_mode, and segment_aad(i, is_final, A_i) as defined in . nonce_metadata_i denotes the stored nonce metadata for segment i: nonce(i) when nonce_mode is "random", and empty when it is "derived". In random mode DecryptSegment reads its nonce from nonce_metadata_i, and in derived mode it recomputes nonce(i).

EncryptSegment AEAD.Encrypt and AEAD.Decrypt are the interfaces of Sections 2.1 and 2.2. For an AEAD whose ciphertext places the tag in its final Nt octets, ct_i is the first len(P_i) octets and C_i = ct_i || tag_i. The caller supplies the segment's leaf to the snapshot authenticator (). EncryptSegment itself does no snapshot work.

DecryptSegment DecryptSegment returns the segment plaintext, or a decryption error:

RewriteSegment RewriteSegment assumes the caller has already verified the commitment or otherwise confirmed it holds the correct CEK. A rewrite under the wrong key produces unreadable ciphertext and corrupts the snapshot authenticator's state. The error is detectable only on a subsequent read. RewriteSegment(i, is_final, A_i, new_P_i) is defined as EncryptSegment(i, is_final, A_i, new_P_i): a rewrite is a fresh encryption of the new plaintext new_P_i. The output record new_stored_i replaces the stored record for segment i. RewriteSegment produces the replacement record new_stored_i only. The caller updates the snapshot authenticator with the old and new leaves, calling remove(i, leaf(i)) then add(i, new_leaf(i)) ().

Top-level Algorithms The top-level algorithms compose the segment subroutines () over complete messages. They call the snapshot-authenticator operations of (snapshot() and verify() in every profile, add(i, input) wherever segments are written, set_length(n) at creation and on any length change, and remove(i, input) in a mutable or append-only profile) without referring to how any is computed. The profile's selected authenticator realizes those operations (). These procedures do not expose per-segment associated data, so they pass an empty A_i to each subroutine. An application that needs per-segment A_i calls the subroutines directly.

Read-Only Operations Encryption and decryption are available in every SEAL profile. They write a message once and read individual segments. Neither rewrites a stored segment. When the profile configures no snapshot authenticator, the snapshot steps below are omitted, and a reader relies on per-segment authentication alone.

Encryption Encryption runs in two phases. The first derives the per-message schedule and writes the commitment. The second encrypts each segment independently, feeds its input to the snapshot authenticator, and then calls snapshot() to bind the whole (index, input) set and the count. Because the segments are independent, the second phase may encrypt them in any order or in parallel. The snapshot calls mutate one value under a single writer, so encryption is never the concurrent case that requires a protocol to order.

Key Schedule and Segment Encryption

An application that writes a new message MUST generate a fresh, uniformly random salt. Given a CEK, that salt, a parameter set, G, and a plaintext P split into segments P_0 through P_{n_seg-1}: Under an authenticator that recomputes, the set_length and add calls collapse into one snapshot() over the (index, input) set (). A zero-length plaintext produces a single segment of length 0 with is_final = 1. A writer encrypts each segment once its content is complete and marks the last one final. A writer that does not know where its input ends holds one complete segment back until more content or the end of input arrives, so it knows whether that segment is the last when it encrypts it. Re-marking the last segment afterwards would be a re-encryption, which a write-once profile forbids and an append-only profile admits only inside an append (). Under a strict authenticator a writer may also produce the keyed snapshot at any count while the object is open ().

Decryption of Segment i Opening a segment is a local operation: check the commitment to reject a wrong key early, then AEAD-decrypt the one segment. This yields per-segment authenticity over the ciphertext core, the segment index, and the finality bit. Under a snapshot authenticator, whole-set authenticity is a separate and stronger check that requires the full present segment set. It detects any altered segment set, including same-index rollback to an older sibling (). A reader holding only one segment gets per-segment authenticity but MUST NOT claim snapshot integrity until it runs SnapVerify (). A profile with no snapshot authenticator defines no snapshot, so per-segment authenticity is the whole integrity guarantee. Given the CEK, salt, parameter set, G, segment index i, finality status, and the stored ciphertext segment for index i: Here SnapVerify is the whole-object form of : S is the decryption state derived above, segments is the full present set, each with its A_i (), the snapshot is declared complete, and no witness is passed. Whole-object SnapVerify needs the leaf of every segment (). A reader that streams segments in order can gate their release on it only by buffering those leaves first, or by using a layout that holds their leading fields in a header, completed with each segment's A_i. Two cases need less. Where the authenticator supports a subset target, a reader verifies the segments it holds against the snapshot, reading a witness () in place of the others. Where the authenticator is strict and the writer produces an intermediate snapshot at count n (), a reader that holds segments 0..n-1 verifies them, declared open, against the value for count n. It learns that they are the segments a snap_key holder recorded at those positions, and nothing about later indices or completeness (). Releasing plaintext on per-segment authenticity alone forgoes snapshot freshness for that segment (). A streaming reader cannot rule out truncation before the end of the stream. Plaintext delivered before the highest-indexed segment verifies under is_final = 1, and before SnapVerify passes where a snapshot authenticator is configured, MUST be treated as unverified with respect to completeness. A decryptor MUST reject a truncated object: one whose highest-indexed present segment carries is_final = 0 is incomplete, and the decryptor MUST fail rather than return the partial plaintext as the complete message. A streaming reader that delivered plaintext as unverified, as the preceding paragraph permits, reports that failure when the stream ends. The decryptor derives the finality each segment must carry from the segment count n_seg the application supplies (), so the last surviving segment of a truncated object, written non-final, fails verification as the final segment. The finality bit is bound per segment and unforgeable without the CEK, through the nonce or the segment AAD per the nonce mode (). Under a write-once profile no segment ever carried an earlier terminal form, so an adversary cannot present a valid is_final = 1 segment at a truncated boundary: it cannot re-mark a non-final segment, and this check detects every dropped trailing segment. An append re-marks the old terminal segment (), so under a profile that appends, a retained segment may have carried is_final = 1 under an earlier nonce. An adversary can replay that retained terminal ciphertext at the shorter count, which this check alone accepts. SnapVerify over the complete segment set then rejects the replay, except where the shorter object is an earlier complete version presented with its own snapshot, which is rollback (). The mutable profile requires a snapshot authenticator, so SnapVerify always runs there (). Authorized truncation by the CEK holder to a nonempty prefix re-marks the new last segment under is_final = 1 (), so a legitimately truncated object still ends with is_final = 1 and verifies. This check needs no snapshot authenticator. Truncation to an empty object is covered too. Without a snapshot authenticator a valid object has at least one segment, so a decryptor MUST reject one with none. With a snapshot authenticator the snapshot binds the count, making the empty object (n_seg = 0) a distinct authenticated state (). On a commitment mismatch the implementation MUST NOT proceed with decryption, SHOULD zeroize derived key material, and MUST return an error. The SnapVerify gate in the procedure above runs whenever a snapshot authenticator is configured and the full present set is available, for example a full read or an integrity audit. Decryption can fail in up to three distinguishable ways: Decryption failure conditions

Failure	Cause
Commitment mismatch	wrong key or parameters
AEAD verification failure	corrupted or tampered segment
Snapshot mismatch	segment set or count modified (snapshot authenticator only)

Implementations SHOULD report these as distinct error conditions for local diagnosis, but SHOULD return a single opaque error to untrusted callers to avoid leaking an oracle (for example, distinguishing "wrong key" from "tampered segment" over a network).

Rewritable Operations Rewriting is available only in a mutable profile, which requires a snapshot authenticator. Length change is a separate operation (), available in both directions in a mutable profile and in the append direction alone in an append-only profile (). The procedure below is written against the in-place update path (add, remove, set_length; ). Under an authenticator that recomputes instead, the remove, add, and set_length calls in this procedure collapse into a single snapshot() over the updated (index, input) set, and the operations are otherwise identical. A caller that cannot recover a re-encrypted segment's plaintext cannot perform it.

Rewriting Segment i A rewrite touches exactly one segment's ciphertext, and no other segment is decrypted. Beyond that segment, it reads only the verified snapshot and the witness its authenticator takes for the update, checked against that snapshot (). Rewrite takes the segment index i and the new plaintext new_P_i, at most segment_max octets, and keeps the segment's finality bit. Only a length change moves that bit (). The procedure is: In derived nonce mode the nonce for segment i is deterministic, so a rewrite reuses the same nonce under a key whose derivation context is identical. A mutable profile that selects derived nonce mode requires an MRAE AEAD. A rewrite is an update under the writer rule of , so the writer checks the witness and the removed input before the rewrite, as that rule requires. Otherwise a storage adversary can swap stored data for an older copy and have the writer launder it into a snapshot that verifies going forward (). Full validation is a separate operation performed with access to all tags, for example on a full read or an integrity audit.

Changing Message Length An application that holds the CEK MAY change a stored message's length in either direction: appending new segments, or truncating to a prefix. An append re-encrypts one retained segment, the old terminal one, with its existing plaintext to clear its finality bit, and none when appending to the empty object. A truncation re-encrypts one retained segment, the new terminal one, with its existing plaintext to set its finality bit, and none when truncating to the empty object; it drops the segments past the prefix. Every other changed segment is removed or added by tag, and the snapshot is updated over the new count (). Both directions are updates under the writer rule of , which the writer meets before either changes the object. Under a mutable profile, a writer that wants the start of the new content in the old terminal segment's spare capacity rewrites that segment first () and then appends the rest. Both directions reuse the existing salt: an application extending an existing message MUST reuse the salt from the object it extends. A fresh salt would change every payload schedule output and force re-encryption of the retained segments. Append takes P_new, the list of new segment plaintexts, each at most segment_max octets, and requires k = len(P_new) >= 1. Content that adds no segment is handled by a rewrite of the terminal segment under a mutable profile ().

Append 0: P_t = DecryptSegment(t, 1, empty, stored_t) (return its error on failure) new_stored_t = RewriteSegment(t, 0, empty, P_t) form leaf(t) from stored_t, is_final = 1, and an empty A_i remove(t, leaf(t)) ;; leaf of the stored_t just decrypted set_length(old_n_seg + k) if old_n_seg > 0: store new_stored_t add(t, new_leaf(t)) for j in old_n_seg .. old_n_seg+k-1: is_final = 1 if j == old_n_seg+k-1 else 0 stored_j = EncryptSegment(j, is_final, empty, P_new[j-old_n_seg]) store stored_j add(j, leaf(j)) store snapshot() ]]>

Truncate takes m < n_seg, the number of segments that survive. For m > 0 it drops segments m and above and re-marks segment m-1 as final, the reverse of the append re-mark, so the truncated object has m segments. Truncate(0) drops every segment and yields the empty object. For m = 0 it decrypts nothing, so, like RewriteSegment, it assumes the caller has already verified the commitment or otherwise confirmed it holds the correct CEK.

Truncate = old_n_seg: return an input error if m > 0: P_t = DecryptSegment(t, 0, empty, stored_t) (return its error on failure) new_stored_t = RewriteSegment(t, 1, empty, P_t) form leaf(t) from stored_t, is_final = 0, and an empty A_i remove(t, leaf(t)) ;; leaf of the stored_t just decrypted for j in m .. old_n_seg-1: form leaf(j) from stored_j, an empty A_i, and is_final = 1 only at j = old_n_seg-1 remove(j, leaf(j)) discard segments m .. old_n_seg-1 set_length(m) if m > 0: store new_stored_t add(t, new_leaf(t)) store snapshot() ]]>

Where an authenticator's input is the stored tag alone, each add and remove takes that tag, which already encodes the segment's is_final bit, so an implementation never tracks finality separately. A strict authenticator's leaf carries the bit explicitly, so each remove forms the leaf with the finality the segment was encrypted under and each add with the new one. A botched in-place update corrupts the snapshot authenticator's state silently, surfacing only at a later SnapVerify. An implementation MAY run SnapVerify over the new segment set immediately after a length change to catch this. An authenticator that recomputes rebuilds the snapshot from the per-segment leaves, formed from the stored entries, on every update, so it has no analogous silent-corruption failure mode. Both operations count against the same AEAD usage budgets as initial encryption (). An append re-encrypts the old terminal segment, except from the empty object, and a truncate re-encrypts the new terminal segment, except to the empty object (m = 0). In derived nonce mode the nonce of the segment each one encrypts is fixed by its index and finality bit. Each re-mark flips the finality bit, so its nonce differs from the segment's previous one, but a truncate's re-mark at (m-1, 1) can land on a pair the object has used, as after an earlier truncation to m, and repeated length changes in both directions can make any pair recur. Only an MRAE AEAD tolerates the resulting nonce reuse (). An append-only profile admits no truncation and appends only from the current count (), so no pair recurs and the AEAD need not be MRAE (). Applications that do not need length changes MAY forbid them. The salt-reuse requirement applies only when a length change is performed. An application that re-encrypts the entire content can generate a fresh salt and is not bound by the constraints in this section.

Appending Under an Append-Only Profile An append-only profile admits the append direction of this section () and forbids truncation. An encryptor under an append-only profile MUST NOT rewrite a segment with a different plaintext or associated data, and MUST NOT truncate (). The first rule is what lets the profile pair a derived nonce with any AEAD, including a non-MRAE one. At a fixed index and finality the key and the nonce are already fixed by the payload schedule, so the plaintext and the associated data are the only inputs that can differ, and the rule forbids exactly those. No nonce ever carries two different plaintexts, which is the condition sets for a non-MRAE AEAD. The segment an append re-encrypts keeps its existing plaintext (), so the re-encryption satisfies the first rule: it changes only the finality bit, not the plaintext or the associated data (). The second rule makes the profile append-only rather than non-rewriting. It forbids the truncate direction, so a stored object can only grow. Provided each append starts from the current count (), an index the object has spent is never freed for a later append to fill with different content. After an interrupted append, the writer follows the crash rule of . An append re-encrypts one retained segment, so each segment is encrypted at most twice, and an epoch key covers at most 2^(epoch_length + 1) segment encryptions (). An append keeps the re-encrypted segment's length (), and this profile cannot rewrite that segment first. So an append to an object whose terminal segment is short leaves a short interior segment, which a layout with uniformly sized interior segments cannot represent. A consuming protocol using this profile supplies a serialization that conveys each segment's ciphertext length ().

Security Analysis The formal proofs are not reproduced here. The ra-ROR and ra-CMT notions are taken unchanged from , which proved them for a construction that instantiates the same component contracts other than the snapshot authenticator () and that never re-encrypts a position (). Snapshot integrity is the one notion this document defines. The configured authenticator argues its bound (), and a combined proof is deferred to . The limits of are operational deployment bounds, not proof obligations.

Security Notions raAE has two security tiers. The base tier comprises the notions of : ra-ROR, ra-CMT, and its position-choosing variant ra-CMT-p. The extension tier adds one notion, snapshot integrity, defined by this document. A construction MAY provide the base tier only.

ra-ROR ra-ROR (random-access real-or-random) is the joint confidentiality and authenticity notion for raAE in a multi-user, nonce-respecting setting. An adversary with adaptive encryption and decryption access across many key instances, sessions, and arbitrary positions cannot distinguish real ciphertexts and headers from random, and cannot make an out-of-context ciphertext segment decrypt. The game is defined in . The encryption core of the extension operations is ordinary EncSeg. A RewriteSeg produces its replacement ciphertext as a repeated EncSeg at the same index. Appending is EncSeg at the positions past the current end plus one RewriteSeg of the old final segment, and truncating to a nonempty prefix is one RewriteSeg of the new final segment. Under a mutable profile the positions either one writes need not be fresh, since a truncate's re-mark can encrypt at a pair the object has used and repeated length changes in both directions can make any (index, finality bit) pair recur (). In random nonce mode these draw fresh nonces, which repeat only by collision. For an append whose positions are new, the ra-ROR bound charges that collision, in Adv_muROR$ for directly drawn nonces and in Adv_nonce_coll under a nonce hedge (). A rewrite in place still re-encrypts a position, and so can a length change under a mutable profile. Either falls outside the ra-ROR bound in any nonce mode, since that bound assumes a position-respecting adversary (). The ra-ROR bounds do not carry over in any nonce mode: Theorems 4 and 6 of assume an adversary that never queries EncSeg twice at the same key instance, session, and position. Re-encrypting a position falls outside them and needs an extended analysis, deferred to . In derived nonce mode the analysis turns on whether the profile permits a rewrite in place. Where it does, a rewrite repeats the position's derived nonce with new content. In derived nonce mode EncSeg at a position is deterministic, so one repeated query separates the real and random ra-ROR games. That is a deliberate nonce-repeating query, and the underlying MRAE AEAD handles it under the equality-leakage relaxation documented for derived nonce mode (), not the unmodified nonce-respecting game. Where it does not, no query repeats a position with new content. The write-once profile re-encrypts nothing. The append-only profile re-encrypts only at the append's RewriteSeg, which flips the finality bit and so writes a position the initial write did not use. A writer recovering from a crash may resend saved ciphertext without another EncSeg call. Both profiles use each position at most once in encryption (, ), so both meet the hypothesis that no position is encrypted twice, each derived nonce is used once, and neither needs an MRAE AEAD. The keyed snapshot these operations maintain is outside the syntax and is governed by snapshot integrity (), not by ra-ROR.

ra-CMT ra-CMT (random-access context commitment) is the segment-level commitment notion: no single ciphertext segment decrypts successfully under two different decryption contexts (key, nonce, global associated data, and per-segment associated data). In this position-matched notion the two contexts share a position. Because the scheme is random access, committing one segment's context commits the full ciphertext's context. The external commitment in this construction establishes the position-matched claim only for fixed per-segment associated data A_i: both openings use the same A_i at the shared position. The full notion also permits differing A_i, which the external commitment does not bind. That case requires a separate AEAD AAD-commitment assumption and is outside the claim established here (). ra-CMT is distinct from the per-AEAD notions CMT-1 and CMT-4 of : a scheme can achieve ra-CMT through an external commitment mechanism even when its underlying AEAD commits to nothing. The Invisible Salamanders attacks () show what a non-committing AEAD permits, and frames it as a key-commitment failure with fixes.

ra-CMT-p ra-CMT-p is the position-choosing variant of ra-CMT: the two decryption contexts need not share a position, so the adversary binds a segment's content to a position of its choice. Under honest keys a construction inherits ra-CMT-p from the underlying AEAD's commitment. Against a holder of the CEK it does not follow from per-segment AEAD alone, and SEAL's snapshot authenticators give at most the weaker per-index binding of , under the conditions stated there (, ).

Snapshot Authentication Per-segment AEAD authenticates a segment at its position, but it does not authenticate the current object snapshot: which set of segments belongs to the current stored object state. An adversary with write access to stored segments can silently substitute an old valid same-index segment or delete a segment, and per-segment AEAD verification at each presented segment still passes. (A segment moved to a different index fails its AEAD check through the index binding of .) Snapshot integrity is the notion that covers that set. Its interface is in and its bound in . SEAL provides it under a snapshot authenticator and omits it otherwise ().

Relations to Other Notions

AEAD ():

raAE generalizes AEAD to multi-segment content with arbitrary-order encryption. A single-segment raAE is an AEAD.

nOAE2 ():

nOAE2 is the nonce-based online authenticated encryption notion for schemes that encrypt in order and support random-access decryption. Hoang and Shen introduced nOAE2 in their analysis of Tink Streaming AEAD (), where they also show STREAM satisfies it. ra-ROR is strictly stronger: every ra-ROR-secure scheme is nOAE2-secure when used in order, but nOAE2-secure schemes can fail when encryption order is arbitrary ().

Commitment ():

CMT-1 and CMT-4 () are per-AEAD commitment notions. ra-CMT is the corresponding notion for segmented random-access schemes. See .

Rewrite safety and extension safety need no notions beyond ra-ROR and snapshot integrity. Replacing a segment in place is an EncSeg at an already-used position together with a snapshot update (). In derived nonce mode it repeats the segment nonce, so it MUST use an MRAE AEAD (). Each rewrite also counts against the AEAD usage budgets (). Appending and truncating likewise add no algorithm () and no notion. An adversary's ability to add, drop, reorder, or re-mark a terminal segment is exactly the snapshot integrity adversary of , and detection follows from the index and finality binding of together with snapshot verification. Rollback of the whole object to an earlier honest (state, snapshot) after truncation is the freshness case that snapshot integrity excludes ().

Adversary Model and Assumptions The adversary model is that of the ra-ROR game (, ). In the construction's terms: the adversary can observe all ciphertexts and content metadata, tamper with individual segments or their ordering, replace the keyed snapshot, and attempt decryption with chosen keys. The per-content salt is public metadata available to the adversary, and the arguments need it fresh and uniform, not secret. The confidentiality and integrity bounds assume the CEK is secret and uniform, the single-owner regime: an application MUST supply a CEK that is either generated uniformly at random or derived so that it is computationally indistinguishable from uniform, such as the output of a KDF keyed by a secret. When multiple messages share a CEK, the per-content salt separates payload schedule outputs across messages under the PRF assumption (). The commitment notions ra-CMT and ra-CMT-p () also cover a shared-CEK regime, where the adversary holds the CEK and so can decrypt and forge segment tags at will. One binding can still hold against a CEK holder, under three conditions that each close a distinct gap. The keyed snapshot MUST be authenticated outside the construction, because a CEK holder derives snap_key and can otherwise forge any keyed snapshot directly. The ciphertext digest MUST be set: without it a segment's leaf binds its ciphertext only through the AEAD tag, which a CEK holder forges for altered content. The authenticator's ordering MUST be strict: under a linear ordering a snap_key holder can present a different segment set with the same keyed snapshot even when every leaf commits to its content, and only a strict ordering makes finding one a collision problem. A snapshot meeting all three is the basis of the per-index binding of . The persistent state of an raAE object, and the party that owns each item, is:

CEK:

Secret key-management state. It is the root secret for the object.

salt:

Public stored object metadata. It separates objects under one CEK.

parameter set:

Profile or object metadata. It fixes suite, maximum segment size, and epoch policy.

commitment:

Stored object metadata. It rejects wrong key or parameter context before decryption.

segment metadata:

Storage-format state. It holds AEAD tags, the per-segment nonces in random nonce mode, and, when set, each segment's ciphertext digest ().

snapshot:

Stored object metadata. It authenticates the segment set and segment count.

external freshness state:

Consuming-protocol state. It detects whole-object rollback.

The security argument relies on three distinct assumptions about the KDF. For derivations whose input keying material is secret and uniformly random, including payload_key, snap_key, nonce_base, epoch_key, and the snapshot authenticator's keyed derivations, the KDF is assumed to be a multi-user PRF with domain separation by protocol_id and label. For commitment, the function is additionally assumed to be collision resistant over adversarially chosen tuples (CEK, payload_info, G), with G empty by default. PRF security alone is not sufficient for this property, because the commitment adversary may choose the CEK and context values. For the plaintext-bound nonce construction, the plaintext digest step targets collision resistance, not PRF security.

raAE Construction Requirements The bounds below rely on the KDF framing and the snapshot authenticator. Their requirements are obligations on the raAE construction, not part of the raAE primitive of . A profile selects the concrete framing for every derivation surface: the KDF input assembly (), the payload_info construction (), the segment AAD (), and the snapshot authenticator's keyed inputs (). Any such framing MUST meet the following contract. SEAL is one such framing (, ).

Pseudorandomness:

KDF outputs MUST be computationally indistinguishable from random to an adversary that does not know the ikm, assuming the underlying hash or PRF is a secure pseudorandom function.

Injectivity:

A construction encodes the tuple (protocol_id, label, ikm, info, L) into the underlying primitive input, and that encoding MUST be injective: distinct tuples map to distinct primitive inputs. This is a requirement on the encoding, not on the KDF, which need not itself be injective. ikm and info MUST be unambiguously separable in the encoded input, whatever the number of elements each contains. The two-step form binds ikm and info in its separate Extract and Expand inputs. The one-step form frames ikm and info each as a single encode element. Where the encoding admits inputs too large to encode literally, it MAY substitute a fixed-length digest of the over-large field. The encoding is then injective only up to the collision resistance of that digest, which the construction MUST justify and domain-separate from the literal encoding ().

Label uniqueness:

Each derivation role, including commitment, payload key, snapshot authenticator key, nonce base, epoch key, segment nonce, hedged key, and the authenticator's internal roles, MUST use a distinct label string within each protocol version.

Protocol binding:

The protocol_id MUST appear as a distinct component of the KDF primitive input. Different application protocols using the same AEAD and KDF MUST use different protocol_id values.

Output length commitment:

The requested output length L MUST be part of the KDF primitive input, so a truncated longer output cannot pass as a shorter one.

Cross-role isolation:

Cross-role isolation follows from label uniqueness and PRF security of the underlying primitive: a KDF output for one derivation role, such as payload_key, is computationally independent of the output for any other role, such as snap_key, even when derived from the same CEK and payload_info.

Snapshot authenticator:

When a snapshot authenticator is configured, the construction MUST bind the current (index, input) set and the segment count into a keyed snapshot that an adversary without the authenticator's secret key cannot forge for a modified (index, input) set or count, even after observing keyed snapshots and their deltas across rewrites. How the value is computed, and whether a single-segment change updates it in place or rebuilds it, is the authenticator's choice. SEAL's snapshot authenticators are in .

SEAL's construction () satisfies these requirements. Its KDF (), keyed by the CEK, is modeled as a pseudorandom function. Its encode framing () is injective, up to LH collision resistance for over-large fields, and places protocol_id and the output length L in the primitive input, so injectivity, protocol binding, and output-length commitment hold. SEAL's labels (, each configured snapshot authenticator's own labels, the plaintext-bound construction's labels in , and the hedged-randomness label in ) are distinct, giving label uniqueness and, with PRF security, cross-role isolation. Each configured snapshot authenticator satisfies the snapshot authenticator requirement, with its forgery argument accounted in . Of SEAL's fields only the caller-supplied G () and A_i, and a strict authenticator's leaf, which carries A_i, can exceed 0xFFFE octets and so take the LH digest path. Cross-protocol separation comes from protocol_id in the KDF inputs and from aad_label in the segment AAD, not from LH ().

Segment Confidentiality and Integrity The construction targets ra-ROR security (). The advantage bound, its adversary parameters, and the per-term analysis are in . Ciphertext cores are indistinguishable from random under the ra-ROR definition, up to the public length leakage and public metadata exposed by the consuming format (file-level headers, stored nonces in random mode, the salt, and the commitment). Re-encrypting a position is outside that bound in either nonce mode. Under a derived nonce and an MRAE AEAD it also reveals whether the new plaintext and associated data equal the old (). Each segment AEAD ciphertext binds the segment to its own index and finality bit (through segment_aad in random nonce mode and through the nonce in derived nonce mode) so an adversary cannot modify or substitute a segment under a given index, or flip its finality bit, without causing an AEAD verification failure on that segment. Three quadratic floors bound the multi-message advantage: In derived nonce mode the salt-collision floor is the only one for the 256-bit-key suites. The 128-bit-key suite also has the epoch-key collision floor, which dominates (). In random nonce mode, with or without the plaintext-bound hedge, the nonce-collision floor applies, summed over keys (). Here q is the number of segment encryptions under one key, and Nn is the nonce length in octets. The block-size birthday term is derived in . Segment size enters the analysis only through the forgery and block-size terms, both bounded in . A segment's length is authenticated implicitly by its AEAD tag, not through segment_aad or the nonce, so the analysis assumes the consuming format conveys each segment's true ciphertext length. Segments shorter than segment_max consume no more than their share of the per-key budget and need no separate accounting.

Commitment Security raAE's commitment target here is ra-CMT for fixed per-segment A_i (), not the per-AEAD CMT-1 (): the commitment binds the CEK and payload_info, which together carry the full parameter context affecting key derivation, AEAD operation, and AAD and nonce construction. For fixed A_i, ra-CMT relies on collision resistance of the derivation map over the tuple (protocol_id, "commit", CEK, payload_info, G, commitment_length), with G empty by default (). SEAL sets commitment_length = Nh, so the commitment offers about 2^128 collision-search work at Nh = 32 and about 2^256 at Nh = 64. The reduction outline and the collision quantities for a general commitment_length are in . The commitment bounds ra-CMT where the positions and A_i match (). It does not bind the segment position. Position binding for the ra-CMT-p variant is inherited from the underlying AEAD's commitment level. Because the SEAL AEADs are not relied upon to provide it, position confusion under an adversarially chosen key is out of scope, consistent with . A malicious encryptor that controls the CEK can craft a single ciphertext segment that opens at two positions, and the per-segment AEAD tag does not prevent it. A strict authenticator with the ciphertext digest set pins each index to one ciphertext even against a CEK holder, where a profile selects it and a consuming protocol authenticates the one keyed snapshot outside the construction (, ). Where that snapshot also binds the commitment, as SEAL's strict authenticators do, each index accepts one opening: one (CEK, nonce, plaintext) under which the commitment verifies and the stored ciphertext and tag at that index decrypt under that index's segment AAD. In random nonce mode the nonce field is the nonce. In derived nonce mode it is the counter, which fixes the nonce once the commitment fixes the CEK, so the binding holds for a decryptor that verifies the commitment. It holds in both nonce modes for every suite, for any A_i, and at the last index of an intermediate snapshot, where the leaf fixes is_final = 0. Per-index binding is weaker than the ra-CMT-p of , which also rules out one ciphertext opening at two positions. The object's author can store one ciphertext at two indices whose epoch keys both accept it, and the snapshot then accepts it at both. For example, at epoch_length 10, indices 0 and 1024 fall under different epoch keys, and an AES-GCM ciphertext valid under both keys costs no search (). Under ChaCha20-Poly1305 and AES-256-GCM-SIV the two indices need not fall under different epoch keys, since each index's nonce gives it its own authentication key (). The per-segment associated data A_i is likewise outside the commitment: SEAL binds A_i through segment_aad and the AEAD tag for that segment, so contexts that differ only in A_i fall outside the ra-CMT claim (). A_i is also rewritable. The strict authenticators' leaf carries segment_aad, so an authenticated strict snapshot binds each index's A_i. A snapshot under a linear ordering does not, and an application that needs A_i bound under one MUST bind it externally. A deployment that must defend against a malicious encryptor who controls the CEK can close the adversarial-key position gap by one of two changes, neither of which SEAL adds to the base construction. They are optional because only the object's author, who holds the CEK, can make one ciphertext open at two positions, which gains it nothing it could not already write, and the gap matters only to a system that identifies content by ciphertext independent of position, such as deduplication or content addressing.

• A context-committing AEAD, so that each segment ciphertext commits to its full decryption context rather than relying on the external commitment over (CEK, payload_info, G).
• A per-segment collision-resistant commitment over the segment's position and ciphertext, on the order of 16 to 64 octets per segment, bound alongside the segment so that no segment opens at two positions.

A strict authenticator with the ciphertext digest set narrows the gap without closing it, giving at most the per-index binding above (). None of the SEAL AEADs is relied upon to provide CMT-1 or CMT-4 (). In particular AES-256-GCM-SIV is not key-committing, with known attacks such as partitioning oracles. With commitment_length = Nh and Nt = 16, ra-CMT for fixed A_i is bounded by commitment collision resistance, and ra-CMT-p for fixed A_i adds the AEAD position-commitment term (). Under honestly generated keys the idealized per-pair tag-forgery floor is 2^(-128) because Nt = 16, and concrete per-AEAD authenticity bounds degrade with segment length ().

Snapshot Authenticator Security What each layer guarantees

Guarantee	Established by	Scope	Provided by
Segment confidentiality and integrity, index and finality bound	AEAD decrypt, per segment	segment	this construction
Segment-set integrity: per-segment input, position, count	SnapVerify over the keyed snapshot	whole object	this construction
Segment-set integrity for a designated subset: per-segment input, position	SnapVerify with a witness	designated subset	this construction, under an authenticator that supports the subset target
Segment-set integrity for a prefix (prefix verification): per-segment input, position, count	SnapVerify over a snapshot the writer produced at that count	prefix 0..n-1	this construction, under a strict authenticator
Sender attribution, third-party verifiability	signature over the keyed snapshot, or over a public snapshot for a verifier without the CEK	whole object, or prefix 0..n-1 under an intermediate snapshot	consuming protocol, not provided
Freshness, whole-object rollback protection	external version or freshness state	whole object	consuming protocol, not provided

Snapshot integrity is keyed by snap_key and protects the writer's current segment set against a storage or write adversary that does not hold snap_key. A verifier who holds snap_key, hence the CEK from which it is derived, detects any alteration of the segment set (). The value gives no protection among parties that share the CEK, which can recompute snap_key, and it is not a third-party-verifiable commitment to a segment set. Whether a fixed, externally authenticated keyed snapshot binds segment content against key holders depends on the authenticator (). An application that needs sender attribution or third-party verifiability MUST add a signing layer, over the keyed snapshot for a verifier that holds the CEK, or over a public snapshot for one that does not, where the authenticator defines one (). A profile MUST keep each of an authenticator's KDF labels inside the injective encode frame () so distinct roles cannot collide on the primitive input. snap_key is derived per message from the CEK and salt and is not exposed through the interface.

Capacity and Usage Limits These usage limits are organized around independent limit classes, not around named suites. The accounting unit is one segment encryption under one epoch key (). The budgets depend on the AEAD's nonce, key, tag, and cipher block sizes (Nn, Nk, Nt, Nb), on the AEAD's own published confidentiality and integrity analysis, on the KDF's output size Nh and its mu-PRF security (), and on the suite's segment_max. A suite that fixes those works out every figure below. The mu-PRF security allows epoch keys to be treated as independent random keys, subject to its distinguishing cost. The length-dependent limits in this section are computed at the suite's segment_max, the largest plaintext one segment encryption carries. Independent of these per-key budgets, a segment-encryption procedure MUST respect each underlying AEAD's per-invocation input limits.

Accounting Model One segment encryption consumes one write from a segment-encryption key's budget. Initial writes and rewrites are both segment encryptions. The write budget belongs to the epoch key, not the CEK. A derived-nonce MRAE AEAD's data-volume term is the exception: absent an allocation it is counted in accounted blocks across all of the object's epoch keys ().

epoch-key budget:

the segment encryptions allowed under one epoch key.

write (initial write):

the first encryption of a segment.

rewrite:

a later encryption of the same segment.

epoch_length (r):

the base-2 log of the number of segments that share one epoch key.

n_blk:

the most AAD-plus-plaintext blocks one segment encryption processes, for a block-cipher AEAD: about segment_max / Nb when the segment AAD is short.

advantage target:

the bound a budget is solved against. The numerical confidentiality figures in this section use 2^-32 for one of these scopes: one indicated term under one key; the derived-nonce data-volume term over one object; one term across the aggregate scope; or the stated isolated workload. The exception is AES-GCM with random nonces, whose own specification caps it at 2^32 encryptions per key, here the epoch key, rewrites included ( Section 8.3). A budget quoted from an AEAD's own analysis holds at the target that analysis states ().

Aggregate Security Accounting The scope of an aggregate target includes all objects and epoch keys available to the adversary. Only the consuming protocol can see that scope, so it allocates the target among the terms of , and the sum of these allocations stays within the target. For a workload that re-encrypts a position, which the ra-ROR bound does not cover, these terms are AEAD-level operating limits, not the ra-ROR bound. Let K count epoch keys in this scope, q_j their encryption counts, s_j their processed block counts, and v_j their forgery-attempt counts. A union bound gives the random-nonce term, and summing the single-key block-size bounds, here AES-GCM's (), gives a conservative contribution in the independent key hybrid: The applicable AEAD analysis supplies any further terms. Key collisions and KDF distinguishing costs are charged separately as in . For equal q_j, allocating epsilon_nonce to nonce collisions gives: A published multi-user bound can improve on this conservative accounting when applied with its full workload parameters and hypotheses. Derived-nonce MRAE accounting is given in .

Limit Classes Five phenomena bound how much may be encrypted. Usage-limit classes

Limit class	Applies to	Depends on	Failure mode
Random-nonce collision	random nonce modes	nonce size, or a lower specification cap	confidentiality and integrity
Forgery bound	all AEADs	MAC strength, segment size	integrity
Block-size birthday	block-cipher AEADs	total blocks	confidentiality
Derived-nonce MRAE workload	derived-nonce MRAE	total blocks, and blocks per (key, nonce) pair	confidentiality and integrity
Epoch-key collision	128-bit-key AEADs	key size	confidentiality

Maximum Object Size A write-once object is bounded by each epoch key's AEAD write budget, the aggregate security budget (), and the 2^63 segment index ceiling. The same limits bound an append-only object, at the write counts given at the end of this section. Under a flat key (one epoch key for the whole object), the AEAD budget sets the size. Which class binds follows from the AEAD: Flat-key write-once size limit by binding class

Binding class	Flat-key write-once limit
Block-size birthday	the AEAD's own block-count bound, for AES-GCM 2^((8*Nb + 1 - 32)/2) / n_blk segments
Derived-nonce MRAE workload	the AEAD's coupled multi-user bound ()
No block-cipher structure	2^63 segments, the index ceiling
No published block-size analysis	2^63 segments, the index ceiling

The last two classes carry the same limit for different reasons. An AEAD with no block-cipher structure, such as one built on a stream cipher, has no block-size term. An AEAD whose analysis publishes none may still have one, so a suite that places an AEAD in this class says which case applies. These figures assume derived nonce mode, which a non-MRAE AEAD may use only under a nonce-uniqueness discipline, the write-once or append-only profiles (). In random nonce mode such an AEAD binds earlier, at the random-nonce-collision budget of 2^((8*Nn + 1 - 32)/2), about 2^32 per epoch key at Nn = 12 (), or at a lower cap that the AEAD's own specification sets for random nonces, such as AES-GCM's 2^32 encryptions per key (). An append-only object re-encrypts one retained segment per append (), so a segment appended one at a time is written twice rather than once, at two distinct (i, is_final) pairs. The block-size birthday figure, which counts blocks, therefore halves, and an MRAE AEAD's multi-user bound counts the doubled writes in its total workload (). The 2^63 index ceiling is unchanged. Epoch rotation supplies fresh keys but does not reset the aggregate security budget. The structural ceiling is 2^63 segments, about 2^79 octets at segment_max 65536. Reaching it also requires the applicable multi-user bounds to meet the aggregate target (). An AEAD subject to the epoch-key collision class additionally needs a sufficiently large epoch_length. At epoch_length 0 that floor caps the total across every object in the aggregate scope near 2^(4*Nk - 16) segments, about 2^48 at Nk = 16 (). Reaching 2^63 segments in one object then needs epoch_length at least 15, which spends the scope's whole budget of about 2^48 epoch keys on that object. A rotating profile MUST keep each epoch key's 2^epoch_length initial writes within its per-key budget. For a derived-nonce MRAE AEAD, which has no per-key figure, the per-object rule of takes the place of that budget absent an allocation. An append-only profile adds one re-mark per superseded segment, so each epoch key spans up to 2^(epoch_length + 1) pairs, and an encryptor MUST size the per-key budget to cover those encryptions (). Rewrite capacity is a separate condition ().

Rewrite Capacity A rewrite consumes the same budget as an initial write. How that budget is shared depends on the nonce mode. For a random-nonce AEAD, epoch_length divides one per-epoch-key pool among the 2^epoch_length segments that share the key. If encryptions are spread evenly, the count each segment can take falls as epoch_length rises: The count includes each segment's initial write, so it leaves one fewer rewrite. At Nn = 12 that is about 2^(32 - epoch_length): about 2^32 encryptions per segment at epoch_length 0, about 2^26 at 6, and about 2^22 at 10. For AES-GCM the numerator is instead its cap of 2^32 (), which counts initial writes and rewrites together, so at epoch_length 32 an AES-GCM epoch has room for its initial writes and no rewrites. For a derived-nonce MRAE AEAD, a rewrite reuses the segment's derived nonce. Its isolated hot-segment cap depends on length, but its allowed rewrite count also depends on the aggregate workload. For AES-GCM-SIV, the multi-user bound couples total processed blocks to the maximum blocks at one (epoch key, nonce) pair (). Giving every segment the isolated hot-segment cap exceeds the same advantage target. Distinct-nonce counts and forgery attempts also enter that bound. An MRAE AEAD built another way uses its own analysis. The random-nonce figures above are per-key nonce-collision figures; scales them to an aggregate target. An AEAD whose nonce size makes a flat key safe uses one, subject to its full confidentiality and integrity bounds. Applications MUST track segment encryptions per key, and for a derived-nonce MRAE AEAD the accounted blocks of , and freeze the object before a per-key, per-object, or aggregate budget is exceeded. The CEK is fixed per object and cannot be rotated in place, so continued writing requires a new object under a fresh CEK, whose budgets are new but still count in the aggregate ().

Choosing epoch_length epoch_length means different things by mode. For the random-nonce AEADs, a smaller epoch_length puts fewer segments under each key, so each segment keeps a larger share of the random-nonce collision pool, at the cost of more epoch keys to derive and hold. For a derived-nonce MRAE AEAD, a smaller epoch_length reduces the distinct derived nonces under an epoch key, but the allowed rewrite count still depends on the aggregate workload (). An AEAD with a 256-bit nonce (Nn = 32) makes collision negligible and has a high forgery floor, so a flat key (epoch_length 63) is the natural choice. The cipher suite's default epoch_length, used when no epoch_length is chosen, is 0 for the suites with an epoch_length range and 63 for the suites whose nonce size makes a flat key safe. A referencing protocol may choose directly, or by citing a profile or named instantiation that fixes a value. A referencing protocol that chooses an epoch_length tuned to its expected segment count, rather than taking the default, trades some rotation for fewer epoch keys while staying within budget. Because a segment may be shorter than segment_max, size epoch_length by the number of segments rather than the object's octet length. The epoch keys are independent under the PRF security of the KDF (), so the epoch_length parameter controls budget distribution, not key strength. An AEAD with a 128-bit key (Nk = 16) adds one further constraint. The epoch-key collision term () over the n_ep distinct epoch keys is about: A profile whose AEAD has Nk = 16 SHOULD keep total distinct epoch keys in the aggregate scope below about 2^(4*Nk - 16), which is about 2^48 at Nk = 16 and holds that term within the 2^-32 target. At epoch_length 0 this caps the total across every object in that scope at about 2^48 segments, about 2^64 octets at segment_max 65536.

Derivations

Confidentiality (Nonce Collision) For random nonce mode with Nn-octet nonces and q segment encryptions under one key, the collision probability follows the birthday bound: When epoch_length = r is specified, q counts encryptions per epoch key (initial writes plus rewrites within that epoch), not across the whole content. The probability of any collision across keys is the sum bound in , so per-key budgets share an aggregate allocation. A collision costs integrity as well. For a non-MRAE AEAD whose authenticator is a polynomial universal hash it recovers an authentication key (): under AES-GCM the GHASH key (), which authenticates every nonce under that epoch key, and under ChaCha20-Poly1305 the one-time Poly1305 key for that nonce. For derived nonce mode, nonces are deterministic and distinct across segment indices, so this collision term does not apply. The limits on reusing a derived nonce are in .

Confidentiality (Block-Size Birthday Bound) Nonce collisions alone do not exhaust the confidentiality bound. A block-cipher AEAD has a distinguishing bound that grows with the total number of cipher blocks processed under a key, which each AEAD takes from its own analysis. For AES-GCM, following the AEAD usage-limits analysis (), if s is the total number of AAD-plus-plaintext blocks, each Nb octets, and q is the number of encryption queries under a key, the confidentiality advantage is at most: Each encryption processes at most n_blk blocks, so s <= n_blk * q and CA is at most about q^2 * n_blk^2 / 2^(8*Nb + 1). Solved against the 2^-32 target, the per-key budget is about: about 2^36 at Nb = 16 and n_blk = 4096. In random nonce mode the nonce-collision bound dominates for typical deployments, and the block-size term overtakes it only once n_blk^2 exceeds the threshold below, which is 2^32 at Nb = 16 and Nn = 12: 2^(8*(Nb - Nn)) ]]> In derived nonce mode the nonce-collision term vanishes and the block-size term is the binding confidentiality constraint. An AEAD with no block-cipher structure, such as one built on a stream cipher, has no comparable block-size bound, leaving nonce collision and forgery as the only relevant terms. Nonce collision is negligible at a large Nn, and the per-query forgery bound governs integrity. SEAL implementations MUST enforce usage budgets computed from the AEAD-specific confidentiality and integrity bounds, not from nonce-collision probability alone, and within any cap the AEAD's own specification sets. The budgets derive from the consuming protocol's allocation of the aggregate target (), or, absent an allocation, are the per-key figures of this section, with the per-object rule of as the data-volume budget for a derived-nonce MRAE AEAD.

Integrity (Forgery) Each AEAD decryption query gives the adversary a chance to forge a valid ciphertext. The forgery advantage per query depends on the AEAD's own analysis and on segment_max: where v is the number of forgery attempts and F(segment_max) is the per-query forgery advantage the AEAD's analysis gives at a segment of segment_max octets. F grows with segment_max, so a larger segment lowers the attempt budget for a fixed target. The tag length bounds F from below, at about 2^(-8*Nt), so no AEAD offers more than about 8*Nt bits of forgery resistance per query. An AEAD's authenticator may achieve less than its tag length suggests, so F is not determined by Nt and a suite takes F from the analysis of its own AEAD. gives F for several AEADs.

Derived-Nonce Bounds A derived-nonce MRAE AEAD needs its own multi-user analysis. Counts of distinct nonces and repeated encryptions at each nonce are coupled to the total workload and are not independent budgets. For AES-GCM-SIV this section takes one term of the bound, the data-volume term of Theorem 6, with c the theorem's hash parameter: L is the total block length of encryption and verification queries. B bounds encryption blocks at any one (user, nonce) pair, a user being one epoch key here. Block accounting includes associated data and padding as in that analysis. The theorem's bound is all-in-one, so this term governs integrity as well as confidentiality. The full bound adds a constant term and further terms in L, in the ideal-cipher work, and in the cross-user nonce repetition, and its hypotheses must hold. Those terms share the aggregate allocation of . This section's figures take an adversary that reads ciphertexts and makes no verification queries, so L counts encryption blocks. Assigning epsilon_data to this term requires: For an illustration of the scaling, let ell be the accounted blocks per encryption, with the whole workload in scope n_rw encryptions at one (key, nonce) pair and no other encryption, or H equally busy pairs, each encrypted n_rw times: The allocated term gives: POLYVAL has c = 1.5 ( Remark 1), so C = 102, and an epsilon_data of 2^-32 then gives one active pair about 2^34.7 encryptions of a 16 KiB segment and about 2^32.7 of a 64 KiB one. Initial writes and the finality re-marks of appends and truncations also contribute to the full workload. Absent an allocation of the aggregate target (), the object is the scope for this term. The encryptor tracks L_obj, the accounted blocks of every segment encryption under the object's epoch keys, and B_obj, the largest total of accounted blocks over all encryptions at any one (epoch key, nonce) pair. It freezes the object before the term exceeds 2^96, the term at 2^-32: Verifying a ciphertext that no encryption produced at the same (epoch key, nonce, associated data) is a forgery attempt (), and its blocks enter L as well. Each attempt adds about the following for every block it processes, with B the largest encryption load at any one pair, whichever pair the attempt targets: Where a deployment admits such attempts, L_obj also counts the blocks of those the consuming protocol allows, which the encryptor does not observe.

Security Considerations For a position-respecting adversary, raAE's ra-ROR security target () rests on a multi-user real-or-random (mu-ROR$) AEAD, a multi-user pseudorandom (mu-PRF) KDF, a fresh per-message salt, and, where configured, nonces that do not collide under a nonce hedge, the hedge KDF's PRF security under HedgedRandom, and the snapshot authenticator's forgery resistance (, ). Integrity is bounded by the AEAD tag, about 8*Nt bits per query (). A larger AEAD key raises confidentiality margins, not the tag-length forgery floor.

Resource Exhaustion An adversary can supply large segment counts, long ciphertexts or associated data, or repeated invalid objects to exhaust memory, storage, or verification time. Snapshot verification can require work over the entire segment set before rejecting an object. These are denial-of-service threats of the kind Section 4.6 of describes. Cryptographic authentication does not prevent them, since a verifier does the work before it rejects. Consuming protocols MUST define and enforce limits on segment and epoch counts, object and segment lengths, associated-data lengths, allocations, storage, and verification work. Implementations MUST check these limits before allocating from untrusted counts or lengths or undertaking the corresponding verification work. Offset and size arithmetic MUST be checked for overflow and for bounds within the supplied object before accessing data. A consuming protocol also needs limits on repeated presentations of objects, valid or not, since individually bounded objects can exhaust aggregate resources. It sets these limits according to its available resources; the cryptographic usage budgets alone do not supply them.

Detection Summary The rows detected by SnapVerify assume a snapshot authenticator is configured. Without one, those modes go undetected, except the write-once truncation case that the finality requirement of detects (the truncation row). Failure modes and the checks that detect them

Failure mode	Detected by
Wrong CEK, salt, or parameter set	The commitment, before any segment decryption (), when reader and writer share the payload_info construction.
Modified ciphertext core or AEAD tag	AEAD.Decrypt for the affected segment.
Segment moved to a different index	AEAD.Decrypt: index and finality are bound by segment_aad (random nonce mode) or the nonce (derived nonce mode).
Segment copied from another object at the same index	AEAD.Decrypt, when the source used a different CEK or salt; a reused salt under the same CEK breaks this separation ().
Segment copied from another version at the same index	SnapVerify, not per-segment AEAD alone, unless the whole object including its snapshot is rolled back to that earlier valid version, whether presented as is or after a writer updates it from a verified snapshot that is not current ().
Dropped trailing segment(s) (truncation)	Write-once: the finality requirement of (top present segment carries is_final = 0). Length-changing: SnapVerify, since a re-marked terminal () can be replayed; the mutable profile always configures an authenticator. Truncation to the count of an intermediate snapshot, presented with that snapshot: SnapVerify with the value declared complete, and the finality requirement. Rollback (). Truncation to zero: the zero-segment prohibition (), or SnapVerify.
Missing interior, duplicated, reordered, or inserted segment	SnapVerify (index set, count, authenticator inputs, recomputed keyed snapshot).
Stale keyed snapshot	SnapVerify, unless the stale value is part of a whole-object rollback.
Whole-object rollback	Not detected by raAE alone; the consuming protocol needs authenticated external freshness state.
Equality leakage in derived nonce mode	Not an authentication failure; rewriting equal plaintext at the same index can reveal equality (, ).

Nonce Misuse Nonce reuse under a non-MRAE AEAD leaks plaintext: an adversary who observes two ciphertexts under the same key and nonce recovers the XOR of the plaintexts (for CTR-based AEADs) and can forge new ciphertexts. When such an AEAD's authenticator is a polynomial universal hash, nonce reuse also recovers the authentication key, enabling forgery of arbitrary messages. Random nonce mode depends on the CSPRNG. If the CSPRNG returns duplicated state, segments collide unless a hedge prevents it (, ). Derived nonce mode removes that dependence, since nonces are deterministic, but the determinism is itself a hazard: re-encrypting a segment with different content under its repeated derived nonce is a two-time pad, catastrophic for a non-MRAE AEAD. A non-MRAE AEAD therefore uses derived nonces only under the write-once or append-only discipline of , which draws a fresh salt per object and never encrypts an (i, is_final) pair twice under that salt, including after a crash. Retransmission of saved ciphertext does not invoke encryption. An MRAE AEAD instead degrades only to equality leakage, not plaintext recovery. The plaintext-bound construction () partially defends against CSPRNG duplication: different plaintexts or segment AAD at the same index produce different nonces because the derivation input differs, but an equal plaintext under equal segment AAD still collides. Implementations that need segment contents defended against random number generator (RNG) state duplication MUST use derived nonce mode with an MRAE AEAD, which limits what duplication reveals about segment contents to equality. HedgedRandom with a tag2 that stays unique covers duplication of the CSPRNG state alone (), but an implementation rarely knows whether a restore also rolled back tag2, so the hedge does not meet this requirement.

Parameter Set Mismatch The full parameter set that affects encryption, decryption, AAD construction, nonce construction, and key derivation is bound into payload_info (see ) and therefore into the commitment. A reader using a different parameter set than the writer triggers a commitment mismatch before any AEAD operation is attempted. A reader supplying a different G than the encryptor likewise triggers a commitment mismatch (). Consuming protocols MUST still reject unrecognized or unsupported parameter values before decryption, since the commitment check detects mismatch but does not by itself indicate which parameter value the recipient is unable to support. One profile-level constant is bound transitively rather than via payload_info: aad_label is bound through protocol_id (each profile fixes its own aad_label). Profiles MUST NOT share a protocol_id across distinct aad_label values. Reusing a protocol_id with a changed aad_label produces objects whose commitment matches the wrong reader but whose per-segment AEAD verification fails with no clear error attribution.

Framing and Label Errors Two classes of implementation error break cross-role isolation. A non-injective framing function maps distinct KDF input tuples to the same primitive input, correlating outputs that should be independent. Implementations MUST verify injectivity per . Reusing a label across roles (for example, "commit" for both commitment and payload key) has the same effect. Labels MUST be distinct within a protocol version, and a new version that changes any derivation MUST change the protocol_id.

Parameter Misuse The nonce mode and AEAD choice are coupled, and the table gives the rule for each pairing: Nonce mode by AEAD class and profile

AEAD class / profile	random nonce	derived nonce
non-MRAE, mutable	valid	unsafe
non-MRAE, write-once or append-only	valid	valid
MRAE, any profile	wasteful	valid

Rewrite is where the coupling matters: a derived nonce is reused where a random nonce is redrawn, and the consequences of that reuse by AEAD class are in and .

Snapshot Integrity Limitations A reader that does not run snapshot verification () gets per-segment AEAD authenticity only (): the ciphertext core is authenticated under its index and finality bit, but substitution of a previous valid same-index segment, and dropping or rolling back other segments, go undetected. Such readers MUST still verify the commitment per . Applications that support random-access single-segment reads MUST either run snapshot verification on every read or explicitly document that they accept per-segment authenticity without snapshot freshness. Snapshot verification authenticates the segment set, its positions, and the count. Without the ciphertext digest it does not confirm that a tag is a valid AEAD tag for the ciphertext beside it. With the ciphertext digest set, the strict authenticators bind the ciphertext bytes, tag, nonce field, and segment AAD, but do not establish that the tag opens the ciphertext under the AEAD (), which decrypting the segment does (). Snapshot integrity does not provide freshness against whole-object rollback. A storage adversary that rolls back the entire encrypted object, including the snapshot, to a previously valid version is not detected by raAE alone, because the rolled-back snapshot is itself a valid snapshot for that prior state. This is replay, not forgery. Applications that require whole-object rollback resistance MUST bind an authenticated version field, timestamp, monotonic counter, or authenticated storage layer into the snapshot context. An update that meets the writer rule of from a current verified snapshot cannot launder a rolled-back snapshot into a valid ongoing history. Same-index rollback within a snapshot is detected when snapshot verification runs: replacing one segment with a previously valid same-index segment under the current keyed snapshot changes the recomputed value, so verification fails except with the forgery probability of . Truncation, including removal of the final segment marked is_final = 1, is detected by snapshot verification, since the removed segment is absent from the recomputed value and the count n_seg no longer matches. Truncation to the count of an earlier complete version, presented with that version's snapshot, is the exception states.

Salt Reuse Reusing a salt with the same CEK, protocol_id, and other payload_info fields across two files produces the same payload_key, the same snap_key, and, in derived nonce mode, the same nonce_base. It defeats schedule-based object separation in every nonce mode, but it does not by itself make an individual swap pass a fixed snapshot. With equal protocol_id and payload_info, a donor segment can pass the recipient's per-segment AEAD check at the same index when finality and A_i also match. That check binds the segment key, nonce, and effective AAD (); it does not separately bind the object's commitment or G. In random nonce mode the donor's stored nonce travels with the segment. Without a snapshot authenticator, a reader relying only on per-segment AEAD checks accepts this substitution. An individual substitution that changes the authenticated leaf fails snapshot verification, except by forgery, if the recipient's current snapshot stays in place (). Substitution together with donor snapshot state can pass when the resulting segment set, count, and bound context match that donor state. This includes replay of the donor's entire object in a recipient context that admits it. A keyed snapshot over indexed tags and the count alone binds, through snap_key, protocol_id and payload_info but not G. One that also includes the commitment, as SEAL's strict authenticators do, rejects a donor snapshot under a different recipient commitment (). G changes the commitment but not payload_key, snap_key, or nonce_base (). Where all bound contexts match, no snapshot authenticator supplies a separate object identity to distinguish cross-object replay. A consuming protocol's authenticated object identity or freshness can reject that replay (). In derived nonce mode the nonces also repeat across the two files, so an MRAE AEAD degrades to deterministic encryption and leaks plaintext equality between same-index segments. A non-MRAE AEAD then permits plaintext recovery: its discipline () keeps derived nonces unique only within one object, and a reused salt repeats nonce_base, hence every derived nonce, across two. In random nonce mode (and with the plaintext-bound hedge) fresh nonces keep confidentiality intact, although the per-key nonce-collision budget of then counts encryptions across both files under each shared segment key. The object-separation failure above remains. Applications MUST therefore ensure salt uniqueness per CEK when creating a new message. The freshness requirement in exists for this reason.

Rewrite Hazards The tracking and freezing requirement of applies to rewrites. In random nonce mode with Nn = 12 the per-key nonce-collision figure is roughly 2^32 encryptions per epoch key, and exceeding it risks nonce collisions, which a non-MRAE AEAD turns into plaintext recovery (). A mutable profile with derived nonces and an MRAE AEAD reuses a segment's deterministic nonce across non-terminal rewrites, and a writer that encrypts when it retries after a crash reuses it once more. Confidentiality then rests not on nonce uniqueness but on the workload-dependent rewrite bound (): the AEAD degrades to equality leakage between identical rewrites rather than to plaintext recovery, as long as the per-object or allocated aggregate budget of is respected. The append-only profile has no such margin. It admits a non-MRAE AEAD, so its safety rests on never re-encrypting a segment with different content (), and a writer that breaks that rule gets a two-time pad rather than a bounded leak. Per-segment associated data A_i is rewritable, so a reader cannot treat it as context fixed at creation (). An application that needs creation-fixed context places it in G, which the commitment binds (), not in A_i. raAE also does not guarantee atomic rewrites. A segment rewrite touches the nonce metadata, ciphertext core, AEAD tag, the keyed snapshot, and any stored summary such as the masked accumulator or the epoch heads. A crash between any two of these leaves the content inconsistent. Applications MUST use write-ahead logging, copy-on-write, or an equivalent mechanism to make rewrites recoverable.

Constant-Time Implementation Several raAE operations handle secret data and MUST be implemented in constant time to prevent timing side-channels. The KDF calls in the payload schedule and epoch key derivation take the CEK or payload_key as input keying material. Implementations MUST ensure that the KDF's keyed operations execute in constant time with respect to their key inputs. For an HMAC-based KDF this is satisfied by implementations that do not branch on key octets. Both the commitment comparison () and the snapshot comparison in SnapVerify MUST use a constant-time octet comparison. A variable-time comparison lets an adversary who can retry tampered inputs learn the expected value one octet at a time, reducing the forgery cost of either check to a linear number of trials. AEAD.Encrypt and AEAD.Decrypt operations inherit the constant-time requirements of the underlying AEAD. Implementations SHOULD use AEAD libraries that document constant-time guarantees.

Properties Not Provided raAE protects segment content and binds segments together. Everything a complete storage or messaging system needs beyond that is the consuming protocol's responsibility.

Freshness and whole-object rollback:

Snapshot integrity binds the segment set of one recorded object state, not its recency. A party holding the ciphertext can present an earlier honest state in full, and both per-segment and snapshot verification still pass. Telling the current state from a stale one requires external freshness ().

Forward secrecy:

The CEK must remain available as long as any reader needs access, so raAE provides none.

Sender identity:

Ciphertexts are not bound to any sender. A signing or MAC layer is needed for sender authentication.

Unlinkability:

Key identifiers and structural features of the encrypted format are visible, so unlinkability requires application-layer measures.

Whole-message replacement:

Snapshot verification covers segments within a message but cannot detect replacement of the message itself. An adversary who swaps one encrypted message for another goes undetected unless the application binds message identity externally.

Serialization, storage, and key management:

raAE emits and consumes component values but defines no wire container, storage transactions, or key lifecycle. A consuming protocol supplies these.

Cross-Application Domain Separation Two applications that both reuse the same SEAL profile label with the same input keying material, the same payload_info, and the same G derive identical commitments, keys, nonces, and AADs. The protocol_id provides cross-application domain separation only when it is distinct per application. Applications whose keying material may be shared across systems SHOULD use an application-specific protocol_id (for example, "myapp-backup-v1") rather than a SEAL profile label. An application adopting a SEAL profile unchanged MAY use that profile's label.

IANA Considerations This document has no IANA actions. It defines an abstract primitive and a parameterized construction and requests no code points or registries of its own. The cipher-suite code points and the registries of named instantiations and snapshot authenticators are specified in the companion (). The normative reference to , which defines the one-step KDF class this document's combiner admits, is a reference to a work in progress, so publication of this document waits on it.

References Normative References This document defines algorithms for Authenticated Encryption with Associated Data (AEAD), and defines a uniform interface and a registry for such algorithms. The interface and registry can be used as an application-independent set of cryptoalgorithm suites. This approach provides advantages in efficiency and security, and promotes the reuse of crypto implementations. [STANDARDS-TRACK] This document specifies a simple Hashed Message Authentication Code (HMAC)-based key derivation function (HKDF), which can be used as a building block in various protocols and applications. The key derivation function (KDF) is intended to support a wide range of applications and requirements, and is conservative in its use of cryptographic hash functions. This document is not an Internet Standards Track specification; it is published for informational purposes. This document provides recommendations for the implementation of public-key cryptography based on the RSA algorithm, covering cryptographic primitives, encryption schemes, signature schemes with appendix, and ASN.1 syntax for representing keys and for identifying the schemes. This document represents a republication of PKCS #1 v2.2 from RSA Laboratories' Public-Key Cryptography Standards (PKCS) series. By publishing this RFC, change control is transferred to the IETF. This document also obsoletes RFC 3447. This memo specifies two authenticated encryption algorithms that are nonce misuse resistant -- that is, they do not fail catastrophically if a nonce is repeated. This document is the product of the Crypto Forum Research Group. This document describes a scheme for hybrid public key encryption (HPKE). This scheme provides a variant of public key encryption of arbitrary-sized plaintexts for a recipient public key. It also includes three authenticated variants, including one that authenticates possession of a pre-shared key and two optional ones that authenticate possession of a key encapsulation mechanism (KEM) private key. HPKE works for any combination of an asymmetric KEM, key derivation function (KDF), and authenticated encryption with additional data (AEAD) encryption function. Some authenticated variants may not be supported by all KEMs. We provide instantiations of the scheme using widely used and efficient primitives, such as Elliptic Curve Diffie-Hellman (ECDH) key agreement, HMAC-based key derivation function (HKDF), and SHA2. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. Cisco Selkie Cryptography Updating key exchange and public-key encryption protocols to resist attack by quantum computers is a high priority given the possibility of "harvest now, decrypt later" attacks. Hybrid Public Key Encryption (HPKE) is a widely-used public key encryption scheme based on combining a Key Encapsulation Mechanism (KEM), a Key Derivation Function (KDF), and an Authenticated Encryption with Associated Data (AEAD) scheme. In this document, we define KEM algorithms for HPKE based on both post-quantum KEMs and hybrid constructions of post- quantum KEMs with traditional KEMs, as well as a KDF based on SHA-3 that is suitable for use with these KEMs. When used with these algorithms, HPKE is resilient with respect to attacks by a quantum computer. In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Informative References All RFCs are required to have a Security Considerations section. Historically, such sections have been relatively weak. This document provides guidelines to RFC authors on how to write a good Security Considerations section. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. This document specifies version 1.3 of the Transport Layer Security (TLS) protocol. TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery. This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961. This document also specifies new requirements for TLS 1.2 implementations. A certain maximum amount of data can be safely encrypted when encryption is performed under a single key. This amount is called the "key lifetime". This specification describes a variety of methods for increasing the lifetime of symmetric keys. It provides two types of re-keying mechanisms based on hash functions and block ciphers that can be used with modes of operations such as CTR, GCM, CBC, CFB, and OMAC. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. Randomness is a crucial ingredient for Transport Layer Security (TLS) and related security protocols. Weak or predictable "cryptographically secure" pseudorandom number generators (CSPRNGs) can be abused or exploited for malicious purposes. An initial entropy source that seeds a CSPRNG might be weak or broken as well, which can also lead to critical and systemic security problems. This document describes a way for security protocol implementations to augment their CSPRNGs using long-term private keys. This improves randomness from broken or otherwise subverted CSPRNGs. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. This document specifies the message formats used in OpenPGP. OpenPGP provides encryption with public key or symmetric cryptographic algorithms, digital signatures, compression, and key management. This document is maintained in order to publish all necessary information needed to develop interoperable applications based on the OpenPGP format. It is not a step-by-step cookbook for writing an application. It describes only the format and methods needed to read, check, generate, and write conforming packets crossing any network. It does not deal with storage and implementation questions. It does, however, discuss implementation issues necessary to avoid security flaws. This document obsoletes RFCs 4880 ("OpenPGP Message Format"), 5581 ("The Camellia Cipher in OpenPGP"), and 6637 ("Elliptic Curve Cryptography (ECC) in OpenPGP"). Authenticated Encryption with Associated Data (AEAD) algorithms provide both confidentiality and integrity of data. The widespread use of AEAD algorithms in various applications has led to an increased demand for AEAD algorithms with additional properties, driving research in the field. This document provides definitions for the most common of those properties and aims to improve consistency in the terminology used in documentation. This document is a product of the Crypto Forum Research Group. IBM Research Europe - Zurich Mozilla Cloudflare An Authenticated Encryption with Associated Data (AEAD) algorithm provides confidentiality and integrity. Excessive use of the same key can give an attacker advantages in breaking these properties. This document provides simple guidance for users of common AEAD functions about how to limit the use of keys in order to bound the advantage given to an attacker. It considers limits in both single- and multi-key settings. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF.

Optional Plaintext-Bound Nonce Construction This appendix is informative. It describes an optional encryptor-side construction that mixes plaintext content into the per-segment nonce derivation to defend against RNG state duplication. The construction is encryptor-only: the decryptor reads the resulting nonce from the wire (in the same slot used by random mode) and never invokes any of the machinery below. Implementations MAY use this construction in place of a fresh CSPRNG call when generating nonces under nonce_mode "random". The wire format is indistinguishable from random mode and decryption is unaffected. One such construction: This construction fixes two labels: Plaintext-bound construction labels

Derivation role	Label variable	Value
Plaintext digest binding	pt_hash_label	"pt-nonce"
Final nonce derivation	pt_nonce_label	"nonce"

Both labels are distinct from all other SEAL labels. Neither derivation uses nonce_base_label (): the "nonce_base" label belongs to derived nonce mode and does not appear in this construction. In the final derivation nonce_ctx enters the info list as one element after the payload_info elements: its encode output is framed behind a length prefix like any other element, not spliced flat into the list. LH is the over-large-field digest of . Its collision resistance is justified in . nonce_ctx carries segment_aad (), so the derivation binds the finality bit and A_i as well as the plaintext and index. A derivation over the plaintext and index alone does not bind the complete effective AEAD context. Under duplicated RNG state, an unchanged-plaintext terminal re-mark or a change to A_i would repeat the earlier nonce under different associated data. For a non-MRAE AEAD with a polynomial-hash authenticator, that recovers the authentication key (). When the encryptor's CSPRNG produces duplicated state (for example, from a virtual machine snapshot or a fork without reseed), two encryptions that differ in plaintext or segment AAD at the same index yield different derivation inputs, subject to LH and KDF collisions. Nonce collisions remain subject to the Nn-octet output bound. Under the same payload schedule, identical plaintexts, index, segment AAD, and random input yield identical nonces and ciphertexts, revealing only plaintext equality. An identical rewrite then also repeats its tag, which voids the random-mode exemption that gives removed tags under the writer rule (). For rewrites under this construction, the encryptor recomputes pt_hash(i) and nonce_ctx from the new plaintext and segment AAD, derives a fresh nonce(i) with a new Random(Nn), seals the new plaintext under the new nonce, and updates the keyed snapshot as in .

Optional Hedged Randomness When a long-term symmetric key sk of at least Nh octets is available to the encryptor, implementations SHOULD mix it into random generation using the hedging pattern of . If only an asymmetric private key is available, it MUST first be processed through a KDF to produce a uniform symmetric key. This construction fixes one label, hedge_label = "hedge", distinct from all other SEAL labels. Here tag2 is the per-call nonce of Section 4: a value unique to each call under one hedge_key, such as a counter that never repeats or a timer guaranteed to differ per call. With it no two calls present the KDF the same input, even when their CSPRNG draws repeat. Calls under one hedge_key MUST NOT repeat tag2, including calls by another process or device that holds sk and calls after a restart ( Section 4). A counter therefore needs persistent state or an instance-unique prefix, the role tag1 plays in . HedgedRandom output depends on both the CSPRNG and sk, so a weak CSPRNG alone cannot predict it. Hedging does not help when duplicated state also rolls back tag2's source, as restoring a virtual machine snapshot can roll back a counter: the CSPRNG output and tag2 then repeat together, against the rule above, and HedgedRandom repeats its output. describes an optional encryptor-side construction that partially defends against state duplication. It is orthogonal to hedging and the two MAY be combined.

Proof Status and Security Claim Provenance This appendix is informative. gives each security claim's source, argument, and assumptions. Each is inherited from , argued in this document, referenced from external work, or deferred to the proof paper in preparation (). The one claim proved in full here is the KDF combiner's injectivity. The combiner's input encoding is injective by its length-prefixed framing, not by any KDF property (, ). Collision resistance is assumed only of LH for over-large fields, of the commitment derivation (), and, with the ciphertext digest set, of LH and, against a key holder, of the KDF under a known snap_key, to bind each segment's ciphertext ().

Provenance of the Security Claims Provenance of the security claims

Property	Source	Argument	Rests on
ra-ROR	notion and base proof; SEAL's arbitrary-position ra-ROR syntax is a SEAL-specific obligation; re-encrypting a position is outside the base proof, formal treatment in	,	mu-PRF KDF (two keying levels), mu-ROR$ AEAD, a nonce-collision term only under a nonce hedge, a PRF hedge KDF under HedgedRandom keyed by an sk sampled independently of all CEKs, fresh per-message salt, an information-theoretic commitment guess for a forged StartDec header (q_sd / 2^(8*commitment_length)), and the configured snapshot authenticator's resistance to forgery (Adv_snap)
ra-CMT (commitment, position-matched, fixed A_i)	notion, restricted here to fixed A_i		collision resistance of the commitment derivation map over (protocol_id, "commit", CEK, payload_info, G, commitment_length); differing A_i requires a separate AEAD AAD-commitment term not established here
ra-CMT-p (position commitment, fixed A_i)	notion and base proof; for fixed A_i it reduces to the underlying AEAD's commitment bound, which SEAL's suites do not provide against a CEK holder, and the weaker per-index binding of applies; formal write-up in		scoped ra-CMT collision bound plus the underlying AEAD's commitment bound for the forged position, not restored against a CEK holder, where SEAL's strict snapshot authenticators with the ciphertext digest set give the weaker per-index binding of in both nonce modes and every suite under an externally authenticated snapshot; differing A_i remains outside the ra-CMT-p claim
KDF combiner injectivity and domain separation	this document (injectivity structural and proof-complete; domain separation by assumption)	,	injectivity of the length-prefixed encoding (KDF need not be injective); collision resistance of LH for over-large fields only; domain separation further rests on HMAC used as a PRF through its message input in the two-step form, where the secret enters Extract's ikm under the public protocol_id salt, and on the XOF used as a PRF through a secret element of its framed input in the one-step form
Snapshot integrity	this document (notion, ); configured authenticator (bound, with no writer oracle; a game with one is deferred to )		unforgeability of the keyed snapshot by a party without snap_key; per-object separation via salt-bound snap_key
AEAD usage, rewrite, and max-object bounds	external work (operational, not proven here)	, ,	, Section 9 with , Section 8.3 for the AES-GCM random-nonce cap, 2^63 segment-index ceiling
Derived-nonce unique-nonce transform	precedent, not proof (TLS 1.3 , STREAM )	,	write-once or append-only uniqueness discipline reducing to nonce-respecting AEAD security
Derived-nonce equality leakage (MRAE)	this document; full proof in		MRAE AEAD (); the coupled data-volume term of the AEAD's multi-user bound ()

Advantage Notation and Adversary Parameters For a ra-ROR adversary () whose messages and StartDec queries all use one parameter set (), using at most u distinct CEKs and q_m messages, each encrypted with an independent fresh 32-octet per-content salt (), across n_ep total epochs and making q_sd StartDec queries, and q_e encryption and q_d decryption segment queries with sigma = q_e + q_d, the advantage is bounded by: The parameter set fixes the nonce mode (), on which the AEAD term depends. The bound holds for a position-respecting adversary, one that never queries EncSeg twice at one position of one session, as in . In derived nonce mode the write-once and append-only disciplines guarantee that (, ). Re-encrypting a position is outside the bound in either nonce mode, pending . Under a derived nonce the reduction fails for an in-place rewrite, which repeats the nonce with new content, and the claim itself fails for an identical re-encryption, which reproduces the first write's ciphertext where the random ra-ROR game would return a fresh one.

Adv_salt_coll

The probability that two messages encrypted under one CEK draw the same salt. Because the salt is a 32-octet value drawn uniformly at random, this term is at most q_m^2 / 2^256. A salt collision is not a PRF-distinguishing event: the KDF deterministically produces identical payload_key, snap_key, and nonce_base outputs whenever (CEK, payload_info) repeats, so the event must be charged separately. This term holds only under the fresh per-message uniform salt requirement of . A profile that reuses salts or draws them non-uniformly forfeits it and must argue payload-schedule separation by other means ().

Adv_muPRF(KDF, B_KDF)

The multi-user PRF advantage of the KDF, in a game that draws each user's key uniformly from that user's key space: 32 octets for a CEK, Nk for a payload_key, and Nh for a snap_key. The bound charges it twice (). Level A is keyed by the CEK and produces the commitment, payload_key, snap_key, and nonce_base. It has u users and at most 4 * (q_m + q_sd) queries, four per StartEnc or StartDec call. Level B is keyed by payload_key (producing epoch_key per and, in the plaintext-bound construction, per-segment nonces per ) and by snap_key (producing the snapshot authenticator's keyed derivations). It has up to 2 * q_m users, a payload_key and a snap_key per message, with at most 2 * q_e + q_d payload_key queries plus the snapshot authenticator's snap_key queries.

q_sd / 2^(8*commitment_length)

The header-forgery term. StartDec verifies the stored commitment (), and the random ra-ROR game accepts no header at StartDec, while the real game refuses as a trivial win any header a StartEnc produced (). The term bounds the probability that one of the q_sd StartDec queries accepts a (salt, G, commitment) that no StartEnc under that CEK produced, the event charges for its own header tag. At commitment_length = 32 it is q_sd / 2^256.

Adv_muROR$(AEAD, B_AEAD)

The multi-user real-or-random advantage of the AEAD over sigma total segment queries. When every nonce is nonce(i) = Random(Nn) taken directly from the CSPRNG, it is the advantage in the variant of whose encryption oracle draws each nonce uniformly at random instead of taking it from the adversary, which is how those nonces are drawn. Otherwise, under a nonce hedge or in derived nonce mode, B_AEAD plays the nonce-respecting game of and supplies the nonces itself, and Adv_muROR$ denotes that game's advantage. There is one mu-ROR user per epoch key, n_ep in total (n_ep = q_m when each message uses a single flat epoch key). This advantage absorbs a key-collision birthday term of about n_ep^2/2^(8*Nk) over the n_ep keys. For the 256-bit-key suites (Nk = 32) that term is about n_ep^2/2^256 and is negligible. For the 128-bit-key suite (Nk = 16) it is about n_ep^2/2^128 and is the binding epoch-key collision floor. bounds n_ep for that suite.

Adv_nonce_coll

The probability of a nonce collision under any segment key. When every nonce is taken directly from the CSPRNG, Adv_muROR$(AEAD, B_AEAD) includes it, so the bound does not charge it separately: a nonce-respecting AEAD bound becomes a bound on Adv_muROR$ by adding this probability (). Under a nonce hedge it is the term the bound adds, because B_AEAD's queries are nonce-respecting only while no nonce repeats under one segment key. In random nonce mode (with or without the plaintext-bound hedge) it is bounded per . Under HedgedRandom () that bound holds once Adv_hedge is charged. In derived nonce mode, within the scope above, it is zero ().

Adv_hedge

Present only under HedgedRandom (): the PRF advantage of the KDF keyed by sk on its one hedge_label query, plus that of the KDF keyed by hedge_key over the HedgedRandom calls, one per salt and per drawn nonce, none of which an Adv_muPRF level covers. Because tag2 gives every call a distinct input, replacing that KDF with a random function makes every HedgedRandom output, salt or nonce, uniform and independent, as a direct CSPRNG draw is (). It assumes an sk sampled independently of all CEKs.

Adv_snap

The snapshot-forgery advantage of the configured snapshot authenticator in the combined game (), which adds SnapVerify to the game that the Level B and AEAD hops leave (), where its snap_key-keyed KDF is a random function and each segment AEAD output is a random string. It is zero in the game and under None (). It covers the forgery and any further terms the authenticator's own construction requires. An intermediate snapshot () is one more SnapVerify target in that game, at its own count. Both replacements are charged elsewhere: the KDF's to the snap_key subset of Level B in Adv_muPRF(KDF, B_KDF), and the AEAD's to Adv_muROR$(AEAD, B_AEAD). A key-holder content-binding property, where an authenticator provides one, is a separate notion from this without-key advantage and is not counted here.

ra-ROR Reduction The reduction follows the hybrid over the two-level key schedule (). Under HedgedRandom, with sk sampled independently of all CEKs, it first replaces the KDF keyed by sk, on its one hedge_label query, with a random function, which makes hedge_key uniform, and then replaces the KDF keyed by hedge_key with a random function. The two hops together cost Adv_hedge, after which every HedgedRandom output is distributed as a direct CSPRNG draw. Condition on no salt collision (Adv_salt_coll). A flat epoch key is the single-epoch case of the same argument.

Level A PRF hop

Replace the KDF keyed by each CEK with an independent random function. A multi-user PRF adversary with one user per CEK, u users, runs A and answers every CEK-keyed derivation from its oracle. The hop costs that adversary's advantage. With no salt collision, distinct messages and roles reach the random function at distinct inputs, so the commitment, payload_key, snap_key, and nonce_base are now uniform and independent for every message.

Header hop

Make StartDec reject every (salt, G, commitment) that no StartEnc under that CEK produced. After the Level A hop such a tuple passes the commitment check only by matching a uniform value that A has not seen, so the q_sd StartDec queries together accept one with probability at most q_sd / 2^(8*commitment_length), the cost of this hop. Every decryption session from here on belongs to a message that StartEnc produced.

Level B PRF hop

Replace the KDF keyed by each payload_key and by each snap_key with an independent random function, through a second multi-user PRF adversary with one user per payload_key and one per snap_key, up to 2 * q_m users. The two levels cannot share one game: a multi-user PRF game draws each user's key uniformly and independently from that user's key space, and payload_key and snap_key have that distribution only after the Level A hop. The epoch keys are then uniform and independent, one per distinct epoch index under each payload_key. B_KDF runs one of the two hop adversaries, chosen uniformly at random, so the two hops together cost 2 * Adv_muPRF(KDF, B_KDF). B_KDF has the users and queries of the level it runs (), so at most max(u, 2 * q_m) users.

AEAD hop

B_AEAD runs A with each epoch key as one user of its multi-user AEAD game, n_ep users over sigma segment queries, and answers every segment encryption and decryption from that game. The Level B hop made the epoch keys uniform and independent, as that game draws its keys. In the game's random world each segment ciphertext is a uniformly random string and each segment decryption fails. When every nonce is taken directly from the CSPRNG, the game draws each nonce as the construction does, so a nonce collision is one of the events Adv_muROR$ already measures. Under a nonce hedge B_AEAD supplies the nonces to the nonce-respecting game instead, which is valid except when a nonce repeats under one segment key, an event charged to the conditional Adv_nonce_coll term. In derived nonce mode B_AEAD supplies the derived nonces, which the injective transform keeps distinct at the distinct positions a position-respecting adversary encrypts, so Adv_nonce_coll is zero (). The hop costs Adv_muROR$(AEAD, B_AEAD), plus the conditional Adv_nonce_coll term under a nonce hedge.

Snapshot remainder

The snapshot authenticator's forgery, a SnapVerify acceptance that snapshot integrity () rules out, in the game the AEAD hop leaves. Its probability is Adv_snap (, ).

B_KDF and B_AEAD each run in time approximately that of A.

Commitment For fixed per-segment A_i at the shared position, ra-CMT security reduces to collision resistance of the commitment derivation map over the tuple (protocol_id, "commit", CEK, payload_info, G, commitment_length), with G empty by default (). Openings that differ only in A_i are outside this reduction: the map has no A_i input. The full ra-CMT game needs an additional AEAD AAD-commitment term, for which no SEAL instantiation bound is established here. For commitment_length = L octets, the relevant quantities are: Thus 16 octets gives about 2^64 collision-search work, 32 octets about 2^128, 48 octets about 2^192, and 64 octets about 2^256, each capped by the collision resistance of the underlying hash. The fixed-pair collision probabilities at 32, 48, and 64 octets are 2^(-256), 2^(-384), and 2^(-512), respectively. For fixed A_i, the ra-CMT-p advantage is bounded by two terms: the commitment collision bound above and the underlying AEAD's commitment bound for the forged position. Against a CEK holder, SEAL's strict authenticators with the ciphertext digest set give, under an externally authenticated snapshot, only the per-index binding of , not ra-CMT-p ().

Nonce Modes The unique-nonce transform of , which XORs the segment index and finality bit into nonce_base, follows TLS 1.3 () static-IV-XOR-identifier and STREAM () counter-plus-final-bit precedent. The transform is injective in the pair (i, is_final). The leading Nn - 8 octets of nonce_base are unchanged; XOR by its fixed low 8-octet value is a bijection on 8-octet strings; and (i, is_final) maps to the integer (i << 1) | is_final, which is a bijection from the index range i < 2^63 onto the 64-bit values. Distinct pairs therefore yield distinct nonces, and a derived nonce repeats only when an object encrypts twice at one pair. Under both disciplines of every encryption invocation uses a distinct (i, is_final) pair (, ), so each reduces to nonce-respecting AEAD security under distinct nonces. That reduction is precedent, not a new proof. In derived nonce mode Adv_nonce_coll is therefore zero within the scope of the bound (), conditional on no salt collision. A rewrite reuses a segment's derived nonce, so the construction relies on the underlying MRAE AEAD: re-encrypting the same plaintext and associated data under the same key and nonce reproduces the same ciphertext, which leaks only equality of those inputs, while distinct inputs stay real-or-random secure (). The formal treatment, in preparation (), replaces the nonce-respecting AEAD assumption of with deterministic-MRAE security.

Design Rationale This appendix is informative.

Key Schedule Design Rationale The per-content salt makes the payload schedule unique even when a CEK is reused across messages, which matters for applications that derive CEKs from group keys. The encryptor chooses the salt locally at write time. A per-message counter would instead require synchronized state. The CEK is 32 octets regardless of the AEAD key size Nk, so a 128-bit-key AEAD still derives its keys from a 256-bit CEK. Epoch keys bound the number of AEAD invocations under any one segment encryption key. The underlying AEAD's per-key bounds (the birthday bound for 96-bit-nonce schemes, the block-size bound for AES, and the forgery bound for every scheme) limit security long before the nonce space is exhausted. Large content reaches them under one key even when written once, and rewrites only reach them sooner. Rekeying all the content would defeat random access, so epoch keys cap the per-key count without a full re-encryption. Labels separate derivation roles: commitment and payload_key share the same inputs but different labels, making them independent under the PRF assumption. Once CEK and salt are chosen the hierarchy is fixed, with no mutable state to synchronize across writers.

Nonce Mode Design Rationale Random mode is simplest but trusts the CSPRNG completely. Derived mode removes that trust. In a mutable profile it requires an MRAE AEAD, because an in-place rewrite reuses the segment nonce (). In the write-once profile the write-once rule keeps every derived nonce unique, and in the append-only profile the append-only rules and the current-count rule of do. Under either, derived mode therefore admits any AEAD. A third rule was available and rejected: permitting a length change in either direction would let a truncation free indices the object had already spent, for a later append to encrypt new content at (). The nonce mode is a profile parameter: a profile selects a valid (nonce_mode, snap_id, segment_commitment) tuple, subject to the MRAE requirement above.

Changes Since -03

• The strict snapshot authenticators' segment leaf carries the stored nonce in random nonce mode or the counter (i << 1) | is_final in derived nonce mode, then the segment AAD, and metadata entries hold its leading fields in leaf order. With the ciphertext digest set, per-index binding under an authenticated snapshot holds in both nonce modes for every suite, for any A_i, and under an intermediate snapshot. SnapVerify takes each segment's A_i and the snapshot's declared state.
• ra-CMT and ra-CMT-p are scoped to fixed A_i. An authenticated strict snapshot with the ciphertext digest set gives per-index binding, not ra-CMT-p. The plaintext-bound nonce derivation frames the full segment AAD.
• EncSeg keeps its base signature and outputs only the ciphertext. The snapshot is a function of the (index, input) set and the count. RewriteSeg and SnapVerify take a witness, and before an update the writer checks the witness, and any input it removes, against a verified snapshot unless it produced them itself as the sole writer. The crash-retry rule is reconciled.
• A truncation to a nonempty prefix drops the trailing segments and re-marks the new last segment as final, the reverse of the append re-mark, and the append-only profile forbids truncation itself rather than a reduced count. An append's re-mark carries the segment's existing plaintext, and Rewrite's inputs are bound.
• An authenticator with a strict ordering has intermediate snapshots, its keyed and public snapshots at any count where the object is open, and a linear one has none; what such a value binds and how truncation to that count is detected are stated.
• A strict authenticator defines a public snapshot, an unkeyed function of payload_info and the same inputs, which a verifier without the CEK accepts only under a signed statement naming the object, the count, whether the object was open or complete, and the value. A key holder that claims the signer's origin checks both values.
• The ra-ROR bound is restated with a header-forgery term and the configured authenticator's Adv_snap; the LH collision argument is stated precisely. HedgedRandom carries a per-call tag2.
• Aggregate usage accounting and the coupled MRAE rewrite bounds; the AES-GCM random-nonce cap of 2^32 per epoch key; the salt-reuse swap discussion.
• The salt is public in the threat model; resource-exhaustion considerations are added; references are updated; the discussion venue is raae@ietf.org.
• Terms: keyed snapshot, public snapshot, intermediate snapshot, prefix verification, and ciphertext digest.

Acknowledgments The author thanks Andrés Fábrega, Thomas Ristenpart, Gregory Rubin, Richard Barnes, Brendan McMillion, Thibault Meunier, Kenny Paterson, Christopher Patton, Martin Thomson, Stanislav V. Smyshlyaev, and Christopher A. Wood for their reviews, comments, and discussions.