Random-Access Authenticated Encryption

1.1. Related Work

CHAIN ([HRRV15]) 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 ([HRRV15]) 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 (Section 4.5.3.2) follows STREAM's counter-plus-final-bit structure and adds those operations.¶

Tink Streaming AEAD ([Tink]) and OpenPGP v2 Symmetrically Encrypted and Integrity Protected Data (SEIPD) packets ([RFC9580]) 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) ([RFC5869]), 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's metadata leaf, which binds the segment's content when the segment commitment is set. It verifies the whole segment set against the snapshot, and optionally a single segment (Section 4.7.1). A consuming protocol that authenticates the one snapshot value obtains integrity over the whole segment set and its count, and, where the segment commitment is set over a strict ordering, per-segment origin authentication that holds against holders of the content-encryption key (CEK).¶

Fábrega et al. ([FLRR25]) 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 Section 5.1 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.¶

2.1. Taxonomy

This document uses the following terms to keep the raAE primitive, the SEAL construction, profiles, and consuming protocols distinct.¶

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 Section 4.¶

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.¶

Snapshot value:

The public value that, when a snapshot authenticator is configured, authenticates one segment set.¶

Snapshot authenticator:

A pluggable SEAL component that produces and verifies the snapshot value. Its abstract interface is Section 4.7.1, and its concrete instantiations are in [I-D.sullivan-seal-concrete].¶

Per-segment authenticity:

AEAD verification for one segment only.¶

Snapshot integrity:

Verification of the complete segment set and snapshot.¶

Segment commitment:

A hash of one segment's ciphertext, stored in that segment's metadata. It binds the segment's content, not its position (Section 4.7.1).¶

External freshness:

Rollback protection supplied outside raAE.¶

2.2. Notation

I2OSP(n, w):

The w-octet big-endian encoding of the non-negative integer n, as defined in [RFC8017].¶

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 Section 4.3. frame is total over all field lengths. The construction requires an injective framing (Section 5.4) but does not mandate this encoding. Another profile MAY use any injective encoding that meets Section 5.4.¶

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 Section 5.8 is expressed in Nb and does not apply to an AEAD with no block-cipher structure.¶

Na:

The snapshot value 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 (Section 4.7).¶

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 (Section 3.2).¶

3.1. 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 [FLRR25], 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 last recorded it, so a reader can detect these changes. The extension (Section 3.3) 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) (Section 5.1). Rewriting leaves both untouched, since replacing a segment is an encryption the read-only adversary could already ask for. Snapshot authentication adds the one notion of its own, snapshot integrity (Section 5.1.4).¶

3.2. Interface

The base raAE interface, from [FLRR25], 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. That immutability is what makes arbitrary-order and fully parallel operation possible. The ciphertext header T_g commits to K, the nonce N, and global associated data G. A headerless scheme emits T_g = empty.¶

3.3. 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, and it leaves ra-ROR and ra-CMT untouched.¶

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 (Section 4.7.1).¶

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 the one the writer last recorded.¶

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

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, and the current snapshot. Outputs replacement ciphertext C'_i and an updated snapshot value, snapshot'.¶

SnapVerify(S, segments, snapshot):

Deterministic. Takes the encryption state S, the segments to verify as (position, ciphertext segment) pairs, and the snapshot. These 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 changes two base signatures. In the extended interface:¶

StartEnc(K, N, G):

Deterministic. As in Section 3.2, and additionally outputs the initial snapshot value, the snapshot over the empty segment set.¶

EncSeg(S, p, A_i, M_i):

Randomized. As in Section 3.2, and additionally outputs the snapshot value over the segment set that results from adding C_i at position p.¶

The snapshot is an authenticator over the set of segments belonging to the current object state. The base primitive has no snapshot value.¶

These additions define the extended raAE interface of this document: the tuple (KeyGen, StartEnc, EncSeg, StartDec, DecSeg, RewriteSeg, SnapVerify) over the snapshot value. The first five algorithms are those of Section 3.2. The snapshot value, RewriteSeg, and SnapVerify are the extension. A scheme can realize the base interface alone, as FLOE ([FLRR25]) does. SEAL (Section 4) realizes the full extended interface.¶

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 Section 5.1.1).¶

A holder appends by encrypting the new segments and re-marking the old final segment with RewriteSeg to clear its terminal bit. It truncates by re-marking the new final segment with RewriteSeg, dropping the trailing segments, and updating the snapshot over the surviving set. Appending to an empty object skips the re-mark, since there is no old final segment, and truncating away every segment yields the empty object, with no new final segment to re-mark.¶

A length change appends segments or drops a suffix. Each step updates the snapshot, and Section 4.9.3 gives the construction for both directions.¶

4.1. 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 Section 3.2 as follows:¶

SEAL's salt, payload_info, and G carry the raAE per-message inputs, and the commitment stands in for the header (Section 4.2).¶

4.2. Component Suite and Parameters

SEAL fixes the segment additional authenticated data (AAD) encoding (Section 4.4.2), the commitment derivation (Section 4.6), and the snapshot value (Section 4.7) identically across all suites. Their octet lengths still vary by suite, because Nh and Nt are suite-dependent.¶

4.3. The KDF Combiner

The KDF combiner uses a length-prefixed encoding for all of its inputs.¶

frame(x):
    if len(x) <= 0xFFFE:  return uint16(len(x)) || x     ;; literal
    else:                 return uint16(0xFFFF) || LH(x) ;; digest

encode(x1, ..., xn) = frame(x1) || ... || frame(xn)

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 ([RFC9180]) uses its extract step, and a one-step KDF ([I-D.ietf-hpke-pq]) its XOF, with x carried under the label "raAE-LP-v1":¶

two-step:  LH(x) = Extract("raAE-LP-v1", x)
one-step:  LH(x) = XOF("raAE-LP-v1" || x, Nh)

Running LH through the full KDF would re-enter frame on the over-large x and recurse. The direct native call avoids that.¶

Section 5.4 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, by the reduction Section 5.3 gives for the commit derivation. 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 Section 5.4.¶

Key material is derived through a KDF with the interface¶

KDF(protocol_id, label, ikm, info, L)

• 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.¶

KDF(protocol_id, label, ikm, info, L):
  extract_input = encode(protocol_id, label,
                         ...ikm)
  prk = Extract(salt=protocol_id,
                ikm=extract_input)
  expand_info = encode(protocol_id, label,
                       ...info, uint16(L))
  return Expand(prk, expand_info, L)

KDF(protocol_id, label, ikm, info, L):
  M = encode(protocol_id, label,
             encode(...ikm), encode(...info),
             uint16(L))
  return XOF(M, L)

4.4. SEAL Encodings and Labels

payload_info = [aead_id, segment_max_be, kdf_id, snap_id,
                segment_commitment, nonce_mode, epoch_length_u8, salt]

segment_aad(i, is_final, A_i):
  if nonce_mode is "random":
    if A_i is empty:
      return encode(aad_label, uint64(i), uint8(is_final))
    return encode(aad_label, uint64(i), uint8(is_final), A_i)
  ;; derived nonce mode
  if A_i is empty:
    return ""
  return encode(aad_label, A_i)

4.5. 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 Section 4.3.¶

payload_info = [aead_id,
                uint32(segment_max),
                kdf_id,
                snap_id,
                segment_commitment,
                nonce_mode,
                uint8(epoch_length),
                salt]

commitment  = KDF(protocol_id, commit_label,
                  [CEK], [...payload_info, G], commitment_length)
payload_key = KDF(protocol_id, payload_key_label,
                  [CEK], payload_info, Nk)
snap_key     = KDF(protocol_id, snap_key_label,
                  [CEK], payload_info, Nh)

;; For derived nonce mode only:
nonce_base  = KDF(protocol_id, nonce_base_label,
                  [CEK], payload_info, Nn)

segment_key(i):
  epoch_index = i >> epoch_length
  return KDF(protocol_id, epoch_key_label,
             [payload_key],
             [uint64(epoch_index)], Nk)

nonce(i) = Random(Nn)

nonce(i) = nonce_base[0:Nn-8]
           || (nonce_base[Nn-8:Nn]
               XOR uint64((i << 1) | is_final))

4.6. Commitment

The commitment is a commitment_length-octet value the payload schedule derives from the CEK, payload_info, and the global associated data G (Section 4.5).¶

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 (Section 5.1.2). The reduction outline and bound are in Section 5.6.¶

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 (Section 4.7).¶

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 (Section 4.9.1.2) the same way a wrong CEK does (Section 6.3).¶

4.7. Snapshot Authenticator

The snapshot authenticator binds the current segment set into the public snapshot value. A SEAL profile selects one with snap_id.¶

is_final(i) = 1 if i = n_seg - 1, else 0

4.8. 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 (Section 4.9.1.1, Section 4.9.1.2, Section 4.9.3) and the rewrite procedure (Section 4.9.2.1) compose them.¶

Each subroutine is the cryptographic core of one operation of the base or extended raAE interface (Section 3.2, Section 3.3), refining Table 1 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). leaf(i) is the segment's leaf (Section 4.7.1), and new_leaf(i) the leaf of a rewritten segment.¶

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 (Section 4.4.2).¶

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 Section 4.5, with nonce(i) following the chosen nonce_mode, and segment_aad(i, is_final, A_i) as defined in Section 4.4.2.¶

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(i, is_final, A_i, P_i):
  key   = segment_key(i)
  nonce = nonce(i)
  aad   = segment_aad(i, is_final, A_i)
  C_i   = AEAD.Encrypt(key, nonce, aad, P_i)
  split C_i into ct_i and tag_i
  return (nonce_metadata_i, ct_i, tag_i)

DecryptSegment(i, is_final, A_i, stored_i):
  nonce_metadata_i, ct_i, tag_i = stored_i
  key   = segment_key(i)
  nonce = nonce_metadata_i or nonce(i)
  aad   = segment_aad(i, is_final, A_i)
  C_i   = ct_i || tag_i
  P_i   = AEAD.Decrypt(key, nonce, aad, C_i)
          (on verification failure, return a decryption error)
  return P_i

4.9. Top-level Algorithms

The top-level algorithms compose the segment subroutines (Section 4.8) over complete messages. They call the snapshot-authenticator operations of Section 4.7 (snapshot() and verify() in every profile, and add(i, input), remove(i, input), and set_length(n) in a mutable or append-only profile) without referring to how any is computed. The profile's selected authenticator realizes those operations (Section 4.7.1).¶

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.¶

derive  commitment, payload_key, snap_key from the payload schedule
        (and nonce_base, in derived mode)
store   commitment

for i in 0 .. n_seg-1:
    is_final = 1 if i = n_seg-1, else 0
    stored_i = EncryptSegment(i, is_final, empty, P_i)
    store stored_i

if snapshot authentication is enabled:
    snapshot = snapshot()
    store snapshot

derive  commitment from CEK, salt, and G
derive  payload_key, snap_key from CEK and salt
if stored commitment != derived commitment:  return error
P_i = DecryptSegment(i, is_final, empty, stored_i)
       (return its error on failure)
if snapshot authentication is enabled and the full set is available:
    if SnapVerify(snapshot) fails:  return error  (do not deliver P_i)
return P_i

read leaf(i)
new_stored_i = RewriteSegment(i, is_final, empty, new_P_i)
remove(i, leaf(i))
add(i, new_leaf(i))
snapshot = snapshot()
store new_stored_i, snapshot

def Append(P_new):
  k = len(P_new)
  t = n_seg - 1

  if n_seg > 0:
    P_t = DecryptSegment(t, 1, empty, stored_t)
    new_stored_t = RewriteSegment(t, 0, empty, P_t)
    remove(t, leaf(t))

  set_length(n_seg + k)

  if n_seg > 0:
    store new_stored_t
    add(t, new_leaf(t))

  for j in n_seg .. n_seg+k-1:
    is_final = 1 if j == n_seg+k-1 else 0
    stored_j = EncryptSegment(j, is_final, empty, P_new[j-n_seg])
    store stored_j
    add(j, leaf(j))

  store snapshot()

def Truncate(m):
  t = m - 1

  if m > 0:
    P_t = DecryptSegment(t, 0, empty, stored_t)
    new_stored_t = RewriteSegment(t, 1, empty, P_t)
    remove(t, leaf(t))

  for j in m .. n_seg-1:
    remove(j, leaf(j))

  set_length(m)

  if m > 0:
    store new_stored_t
    add(t, new_leaf(t))

  discard segments m .. n_seg-1
  store snapshot()

5.1. Security Notions

raAE has two security tiers. The base tier comprises the notions inherited from [FLRR25]: ra-ROR, ra-CMT, and its position-choosing variant ra-CMT-p, summarized here. The extension tier adds one notion, snapshot integrity, defined by this document. A construction MAY provide the base tier only. Advantage definitions and proofs for ra-ROR, ra-CMT, and ra-CMT-p are in [FLRR25].¶

5.2. Relations to Other Notions

AEAD ([RFC5116]):

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

nOAE2 ([Tink]):

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 ([Tink]), 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 ([FLRR25]).¶

Commitment ([RFC9771]):

CMT-1 and CMT-4 ([RFC9771]) are per-AEAD commitment notions. ra-CMT is the corresponding notion for segmented random-access schemes. See Section 5.1.2.¶

Rewrite safety and extension safety are corollaries of the notions above, not additional notions. Replacing a segment in place is an EncSeg at an already-used position together with a snapshot update. In random nonce mode it adds no adversary capability beyond ra-ROR (Section 5.1.1) and snapshot integrity (Section 5.1.4). In derived nonce mode the rewrite repeats the segment nonce, so it MUST use an MRAE AEAD (Section 4.5.3.2), and it adds the equality-leakage relaxation that derived nonce mode already documents (Appendix C.5). Each rewrite also counts against the per-key AEAD usage budget (Section 5.8).¶

Appending and truncating likewise add no algorithm (Section 4.9.3) and no notion. An adversary's ability to add, drop, reorder, or re-mark a terminal segment is exactly the snapshot integrity adversary of Section 5.1.4, and detection follows from the index and finality binding of Section 4.4.2 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 (Section 6.6). The application supplies it.¶

5.3. Adversary Model and Assumptions

The adversary model is that of the ra-ROR game (Section 5.1.1, [FLRR25]). In the construction's terms: the adversary can observe all ciphertexts and content metadata, tamper with individual segments or their ordering, replace the snapshot value, and attempt decryption with chosen keys. The adversary does not know the CEK, any derived key, or the per-content salt. 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 multi-message advantage grows linearly in the number of messages.¶

The commitment notions ra-CMT and ra-CMT-p (Section 5.6) also cover a shared-CEK regime, where the adversary holds the CEK. A CEK holder defeats the per-segment AEAD: it holds the key, so it can decrypt and forge tags at will, and confidentiality and per-segment integrity do not bind it.¶

One binding can still hold against a CEK holder, under three conditions that each close a distinct gap. The snapshot value MUST be authenticated outside the construction, because a CEK holder derives snap_key and can otherwise forge any snapshot value directly. The segment commitment 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. Setting it adds a collision-resistant commitment to the ciphertext that holding the CEK does not defeat. The authenticator's ordering MUST be strict: under a linear ordering a snap_key holder can present a different segment set with the same snapshot value even when every leaf commits to its content, and only a strict ordering makes finding one a collision problem. A snapshot meeting all three binds each segment's content to its position against a CEK holder.¶

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:

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 the segment commitment is set, each segment's content commitment (Section 4.7.1).¶

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¶

Commit(CEK, payload_info, G, L) =
    KDF(protocol_id, "commit", [CEK], [...payload_info, G], L)

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.¶

5.4. raAE Construction Requirements

The bounds below rely on properties of the construction's components, namely the KDF framing and the snapshot authenticator. The requirements those components must satisfy are obligations on the raAE construction, not part of the raAE primitive of Section 3.¶

A profile selects the concrete framing for every derivation surface: the KDF input assembly (Section 4.5), the payload_info construction (Section 4.2), the segment AAD (Section 4.4.2), and the snapshot authenticator's keyed inputs (Section 4.7). The requirements below are the contract that any such framing MUST meet. SEAL is one such framing (Section 4.3, Section 4.4).¶

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 (Section 4.3).¶

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 to ensure that derived values from one protocol cannot be confused with those from another.¶

Output length commitment:

The requested output length L MUST be part of the KDF primitive input. This prevents attacks in which an adversary attempts to use a truncated version of a longer derived output as a valid 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:

The construction MUST bind the current segment set and the segment count into a public snapshot value that an adversary without the authenticator's secret key cannot forge for a modified segment set or count, even after observing snapshot values 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 Section 4.7.¶

SEAL's construction (Section 4) satisfies these requirements. Its KDF (Section 4.3), keyed by the CEK, is modeled as a pseudorandom function. Its encode framing (Section 4.3) is injective 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 (Table 4, each configured snapshot authenticator's own labels, the plaintext-bound construction's labels in Appendix A, and the hedged-randomness label in Appendix B) 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 Section 5.7.¶

SEAL's encode framing meets the injectivity requirement. Its frame/encode construction, the LH digest for over-large fields, and LH's domain separation from the literal encoding are defined and justified in Section 4.3. SEAL's own derived and fixed fields (the payload_info elements, the commitment, the leaf, and the uint-encoded scalars) are all at most 0xFFFE octets, so for them frame is byte-identical to a plain 2-octet length prefix. The two caller-supplied octet strings, G (Section 4.2.4) and A_i, are unbounded, and a field longer than 0xFFFE octets is bound as 0xFFFF || LH of it. Cross-protocol separation comes from protocol_id in the KDF inputs and from aad_label in the segment AAD, not from LH (Section 4.3).¶

SEAL's additional components, the epoch keys and the snapshot maintained across rewrite and length change, are analyzed in Section 5.5 and Section 5.7.¶

5.5. Segment Confidentiality and Integrity

The construction targets ra-ROR security (Section 5.1.1). The ra-ROR advantage bound, its adversary parameters, and the per-term analysis are in Appendix C, with the full proof in preparation ([SEALPROOFS]).¶

Ciphertext cores are indistinguishable from random under the ra-ROR definition, up to the public length leakage, the equality leakage allowed by derived nonce mode, and public metadata exposed by the consuming format (file-level headers, stored nonces in random mode, the salt, and the commitment). 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. Same-index rollback to an older valid segment within the same message is not detected by per-segment AEAD alone. This requires the snapshot verification of Section 4.7.¶

Three quadratic floors bound the multi-message advantage:¶

salt collision       q_m^2 / 2^256          all suites
epoch-key collision  n_ep^2 / 2^128         128-bit-key suite
nonce collision      q^2 / 2^(8*Nn + 1)     random nonce mode
                     q^2 / 2^97  at Nn = 12

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 (Appendix C.2). In random nonce mode, with or without the plaintext-bound hedge, the nonce-collision floor applies. 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 Section 5.8.¶

Segment size enters the analysis only through the forgery and block-size terms, both bounded in Section 5.8. It does not affect the confidentiality or commitment terms. 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.¶

5.6. Commitment Security

raAE's commitment target is ra-CMT (Section 5.1.2), not the per-AEAD CMT-1 ([RFC9771]): 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.¶

ra-CMT relies on the collision resistance of the commitment derivation map over the tuple (protocol_id, "commit", CEK, payload_info, G, commitment_length), with G empty by default. PRF security alone does not suffice, because the commitment adversary may choose the CEK and the context values (Section 4.5). 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 for this assumption and the collision quantities for a general commitment_length are in Appendix C.4.¶

The commitment bounds the ra-CMT variant in which the positions match (Section 5.1.2). 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 [FLRR25]. 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 snapshot authenticator that sets the segment commitment over a strict ordering, with the snapshot authenticated outside the construction, restores ra-CMT-p against adversarially chosen keys: the collision-resistant leaf commitment and the strict ordering together pin each segment's ciphertext to its index even against a CEK holder (Section 4.7.1, Section 5.3). It applies only where a profile selects that authenticator and a consuming protocol authenticates the one snapshot value. The base construction pins position no more strongly than the AEAD commits under an adversarial 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. Contexts that differ only in A_i are therefore not commitment collisions. Their separation relies on AEAD commitment for the segment AAD. A_i is also rewritable across rewrites and is not bound at the snapshot level. An application that needs it bound there MUST bind it externally. The exact accounting of this term in the ra-CMT reduction is deferred to Appendix C.¶

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. These are non-normative. SEAL adds none of them to the base construction.¶

• 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.¶

Both changes act in the base construction. A snapshot authenticator with the segment commitment set over a strict ordering (Section 4.7.1) is a separate, conditional route: it leaves the base construction unchanged and closes the gap only where a profile selects it and a consuming protocol authenticates the one snapshot value.¶

None of the SEAL AEADs is relied upon to provide CMT-1 or CMT-4 ([RFC9771]). In particular AES-256-GCM-SIV is not key-committing, with known attacks such as partitioning oracles. raAE obtains ra-CMT context commitment from the external commitment over (CEK, payload_info, G) regardless of the AEAD, provided the commitment check is not bypassed and payload_info carries the full parameter context (Section 5.1.2).¶

With commitment_length = Nh and Nt = 16, ra-CMT is bounded by the commitment collision resistance, and ra-CMT-p adds the per-segment AEAD commitment term. The ra-CMT collision bound is derived in Appendix C.4, and the ra-CMT-p bound is stated there as a sum. The two key regimes differ. 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 (Section 5.8). Under an adversarially chosen CEK the position term is the AEAD's commitment level, which the SEAL AEADs are not relied upon to provide.¶

The global associated data G (Section 4.6) enters the committed map as an additional input, empty by default, and the collision-resistance argument above applies unchanged with G in the committed context. This matches the ra-CMT treatment of global associated data in [FLRR25].¶

5.7. Snapshot Authenticator Security

The snapshot authenticator adds two operations (RewriteSeg, SnapVerify) over a snapshot value and one new security property, snapshot integrity (Section 5.1.4). Integrating its reduction into a single combined proof with the ra-ROR framework is in preparation and will be published separately ([SEALPROOFS]).¶

The keyed snapshot is not read as sender attribution.¶

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 (Section 4.7.1). Forgery of a fresh snapshot value gives no protection among parties that share the CEK, because any CEK-holder can recompute snap_key, and the value is not a third-party-verifiable commitment to a segment set. Whether a fixed, externally authenticated snapshot value binds segment content against key holders depends on the authenticator (Section 4.7.1). An application that needs sender attribution or third-party verifiability MUST add a signing layer over the snapshot context, and the configured authenticator determines whether its value can carry that layer.¶

The snapshot authenticator adds authentication of the full segment set (over the authenticator's per-segment input) and the count n_seg as a single unit, which detects same-index rollback, segment-set modification, and count changes. Its mandatory index-set check catches a duplicated or dropped index that an authenticator's verify might otherwise accept (Section 4.7.1).¶

A profile MUST keep each of an authenticator's KDF labels inside the injective encode frame (Section 4.3) so distinct roles cannot collide on the primitive input.¶

Whole-object rollback to a previously valid snapshot is out of scope and is treated in Section 6.6. snap_key is not exposed through any public API. It is derived internally per message from the CEK and salt, so snap_key exposure is not a threat surface in the construction itself.¶

5.8. 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 segment-encryption key (an epoch key). For random-nonce AEADs that budget is a single per-epoch-key pool. For a derived-nonce MRAE AEAD there are two separate budgets: a per-epoch-key budget for distinct derived nonces, and a per-derived-nonce budget for repeated encryption of one segment. Such an AEAD therefore does not follow a simple "divide the per-key budget by 2^epoch_length" model.¶

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 (Appendix C.2), and on the suite's segment_max. A suite that fixes those works out every figure below. The mu-PRF security is what makes each epoch key's budget independent of every other's, which the per-epoch-key accounting assumes.¶

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.¶

rewrites per segment  =  2^((8*Nn + 1 - 32)/2) / 2^epoch_length

P(collision) <= q^2 / 2^(8*Nn + 1)

CA <= ((s + q + 1)^2) / 2^(8*Nb + 1)

q  <=  2^((8*Nb + 1 - 32)/2) / n_blk

IA <= v * F(segment_max)

((s + q + 1)^2) / 2^(8*Nb + 1)  <=  2^-32

n_rw  <=  2^((8*Nb + 1 - 32)/2) / n_blk

6.1. Detection Summary

The rows detected by SnapVerify assume a snapshot authenticator is configured. Without one, those modes go undetected.¶

The one exception is a dropped trailing segment under a write-once profile, which the per-segment finality requirement of Section 4.9.1.2 detects with no snapshot authenticator (the truncation row below).¶

6.2. 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. For an AEAD whose authenticator is a polynomial universal hash, nonce reuse also recovers the authentication key, enabling forgery of arbitrary messages.¶

Random nonce mode depends entirely on the CSPRNG. If the CSPRNG returns duplicated state, segments collide. 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 a discipline that keeps every (index, finality bit) pair unique, the write-once or append-only profiles, drawing a fresh salt per object and never reusing a pair under that salt, including after a crash (Section 4.5.3.2). Write-once meets this by never re-encrypting with changed inputs, and by drawing a fresh salt rather than retrying an object it did not complete. Append-only meets it by permitting at most one re-encryption per segment, the finality re-mark, under the three rules of Section 4.9.3.1. An MRAE AEAD instead degrades only to equality leakage, not plaintext recovery.¶

The plaintext-bound construction (Appendix A) partially defends against CSPRNG duplication: different plaintexts at the same index produce different nonces because the plaintext digest differs, but equal plaintexts still collide. Implementations that need a full defense against random number generator (RNG) state duplication MUST use derived nonce mode with an MRAE AEAD.¶

6.3. Parameter Set Mismatch

The full parameter set that affects encryption, decryption, AAD construction, nonce construction, and key derivation is bound into payload_info (see Section 4.2) 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 (Section 4.6). 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). nonce_mode, by contrast, is carried in payload_info, so the commitment binds it directly. 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.¶

6.4. 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 Section 5.4. 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.¶

6.5. Parameter Misuse

The nonce mode and AEAD choice are coupled, and the table gives the rule for each pairing:¶

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 Section 6.2 and Section 4.5.3.2.¶

6.6. Snapshot Integrity Limitations

First, a reader that does not run snapshot verification (Section 4.7) does not verify that a segment belongs to the current authenticated snapshot. Such a reader gets per-segment AEAD authenticity only, without the snapshot integrity guarantee of Section 5.1.4: the ciphertext core is authenticated under the segment index and finality bit, but the reader cannot detect that the segment was substituted from a previous valid version of the same message at the same index, nor that other segments were dropped or rolled back. Such readers MUST still verify the commitment per Section 4.6. 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.¶

Conversely, snapshot verification authenticates the segment set, its positions, and the count. Without the segment commitment it does not confirm that a tag is a valid AEAD tag for the ciphertext beside it. With the segment commitment set it binds the ciphertext bytes and the tag, but not that the tag opens the ciphertext under the AEAD (Section 4.7.1). Decrypting the segment is what establishes that, so snapshot verification layers set, position, and count binding on top of per-segment AEAD without replacing it.¶

Second, 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 of an intact prior snapshot, not a forgery: it stays out of scope unless the consuming protocol authenticates external freshness into the snapshot context. Applications that require whole-object rollback resistance MUST bind an authenticated version field, timestamp, monotonic counter, or authenticated storage layer into that context. Relatedly, Section 4.9.2.1 requires a writer to update only trusted snapshot state, so a rewrite cannot launder a rolled-back snapshot into a valid ongoing history.¶

Third, same-index rollback within a snapshot is detected when snapshot verification runs. If an adversary replaces one segment with a previously valid same-index segment but leaves the current snapshot value in place, the recomputed snapshot value no longer matches the stored one, so verification fails except with negligible forgery probability (see Section 5.7).¶

Truncation, including removal of the final segment marked is_final = 1, is detected by snapshot verification. The removed segment is absent from the recomputed snapshot value and the count n_seg no longer matches the segments present, so verification fails. Truncation is a special case of the first limitation above, for readers that skip snapshot verification.¶

6.7. Salt Reuse

Reusing a salt with the same CEK across two files produces identical payload schedule outputs: the same payload_key, the same snap_key, and, in derived nonce mode, the same nonce_base. The damage depends on the nonce mode.¶

In every nonce mode, an adversary can silently swap same-index segments between the two files: both per-segment AEAD checks and the snapshot authenticator accept the swap. Salt reuse is therefore an integrity break in every configuration.¶

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. Such an AEAD is safe under a derived nonce only within a single object, where the write-once or append-only discipline keeps each derived nonce unique (Section 4.5.3.2). Reusing the salt repeats nonce_base across two objects, hence every derived nonce, and breaks that scoping.¶

In random nonce mode (and with the plaintext-bound hedge) fresh nonces keep confidentiality intact, although the per-key nonce-collision budget of Section 5.8.6.1 then counts encryptions across both files under the single CEK. The integrity break above remains. Applications MUST therefore ensure salt uniqueness per CEK when creating a new message. The freshness requirement in Section 4.9.1.1 exists for this reason.¶

6.8. Rewrite Hazards

Applications MUST track total segment encryptions per key and freeze the object before exceeding the per-epoch-key budget of Section 5.8.4. For a 96-bit-nonce AEAD (Nn = 12) that budget is roughly 2^32 encryptions per epoch key, and exceeding it risks nonce collisions and plaintext recovery (Section 5.8.5).¶

A mutable profile with derived nonces and an MRAE AEAD reuses a segment's deterministic nonce across non-terminal rewrites, and a crash that replays a write reuses it again. Confidentiality there rests on the per-segment rewrite limit (Section 5.8.4), not on nonce uniqueness: the AEAD degrades to equality leakage between identical rewrites rather than to plaintext recovery, as long as that budget 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 (Section 4.9.3.1), 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 (Section 4.4.2). An application that needs creation-fixed context places it in G, which the commitment binds (Section 4.6), not in A_i.¶

raAE also does not guarantee atomic rewrites. A segment rewrite touches the nonce metadata, ciphertext core, AEAD tag, and the snapshot value. 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.¶

6.9. 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 (Section 4.9.1.2) and the snapshot comparison in SnapVerify MUST use a constant-time octet comparison. A variable-time comparison reveals the position of the first differing octet. An adversary who can retry tampered inputs learns the expected value one octet at a time and can then present a matching stored value. This reduces the forgery cost of either check to a linear number of trials (for the snapshot, the bound of Section 5.7).¶

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.¶

6.10. 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. This section is the authoritative boundary of what raAE does not provide.¶

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 (Section 6.6).¶

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.¶

6.11. 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.¶

8.1. Normative References

[I-D.ietf-hpke-pq]

Barnes, R. and D. Connolly, "Post-Quantum and Post-Quantum/Traditional Hybrid Algorithms for HPKE", Work in Progress, Internet-Draft, draft-ietf-hpke-pq-05, 6 July 2026, <https://datatracker.ietf.org/doc/html/draft-ietf-hpke-pq-05>.

[RFC2119]

Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <https://www.rfc-editor.org/rfc/rfc2119>.

[RFC5116]

McGrew, D., "An Interface and Algorithms for Authenticated Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008, <https://www.rfc-editor.org/rfc/rfc5116>.

[RFC5869]

Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/RFC5869, May 2010, <https://www.rfc-editor.org/rfc/rfc5869>.

[RFC8017]

Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch, "PKCS #1: RSA Cryptography Specifications Version 2.2", RFC 8017, DOI 10.17487/RFC8017, November 2016, <https://www.rfc-editor.org/rfc/rfc8017>.

[RFC8174]

Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.

[RFC8452]

Gueron, S., Langley, A., and Y. Lindell, "AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption", RFC 8452, DOI 10.17487/RFC8452, April 2019, <https://www.rfc-editor.org/rfc/rfc8452>.

[RFC9180]

Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180, February 2022, <https://www.rfc-editor.org/rfc/rfc9180>.

[RFC9861]

Viguier, B., Wong, D., Ed., Van Assche, G., Ed., Dang, Q., Ed., and J. Daemen, Ed., "KangarooTwelve and TurboSHAKE", RFC 9861, DOI 10.17487/RFC9861, October 2025, <https://www.rfc-editor.org/rfc/rfc9861>.

8.2. Informative References

[ADG22]

Albertini, A., Duong, T., Gueron, S., Kölbl, S., Luykx, A., and S. Schmieg, "How to Abuse and Fix Authenticated Encryption Without Key Commitment", USENIX Security 2022 pp. 3291-3308, 2022, <https://www.usenix.org/conference/usenixsecurity22/presentation/albertini>.

[BHT18]

Bose, P., Hoang, V. T., and S. Tessaro, "Revisiting AES-GCM-SIV: Multi-user Security, Faster Key Derivation, and Better Bounds", IACR ePrint 2018/136, 2018, <https://eprint.iacr.org/2018/136>.

[DGRW18]

Dodis, Y., Grubbs, P., Ristenpart, T., and J. Woodage, "Fast Message Franking: From Invisible Salamanders to Encryptment", CRYPTO 2018, LNCS vol. 10991, pp. 155-186, DOI 10.1007/978-3-319-96884-1_6, 2018, <https://doi.org/10.1007/978-3-319-96884-1_6>.

[FLRR25]

Fábrega, A., Len, J., Ristenpart, T., and G. Rubin, "Random-Access AEAD for Fast Lightweight Online Encryption", EUROCRYPT 2026, DOI 10.1007/978-3-032-25333-0_10, 2026, <https://eprint.iacr.org/2025/2275>.

[HRRV15]

Hoang, V. T., Reyhanitabar, R., Rogaway, P., and D. Vizár, "Online Authenticated-Encryption and its Nonce-Reuse Misuse-Resistance", IACR ePrint 2015/189, 2015, <https://eprint.iacr.org/2015/189>.

[I-D.irtf-cfrg-aead-limits]

Günther, F., Thomson, M., and C. A. Wood, "Usage Limits on AEAD Algorithms", Work in Progress, Internet-Draft, draft-irtf-cfrg-aead-limits-11, 4 December 2025, <https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-aead-limits-11>.

[I-D.sullivan-seal-concrete]

Sullivan, N., "SEAL Cipher Suites and Instantiations", Work in Progress, Internet-Draft, draft-sullivan-seal-concrete-00, 2026, <https://datatracker.ietf.org/doc/html/draft-sullivan-seal-concrete-00>.

[RFC8446]

Rescorla, E., "The Transport Layer Security (TLS) Protocol Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018, <https://www.rfc-editor.org/rfc/rfc8446>.

[RFC8645]

Smyshlyaev, S., Ed., "Re-keying Mechanisms for Symmetric Keys", RFC 8645, DOI 10.17487/RFC8645, August 2019, <https://www.rfc-editor.org/rfc/rfc8645>.

[RFC8937]

Cremers, C., Garratt, L., Smyshlyaev, S., Sullivan, N., and C. Wood, "Randomness Improvements for Security Protocols", RFC 8937, DOI 10.17487/RFC8937, October 2020, <https://www.rfc-editor.org/rfc/rfc8937>.

[RFC9580]

Wouters, P., Ed., Huigens, D., Winter, J., and Y. Niibe, "OpenPGP", RFC 9580, DOI 10.17487/RFC9580, July 2024, <https://www.rfc-editor.org/rfc/rfc9580>.

[RFC9771]

Bozhko, A., Ed., "Properties of Authenticated Encryption with Associated Data (AEAD) Algorithms", RFC 9771, DOI 10.17487/RFC9771, May 2025, <https://www.rfc-editor.org/rfc/rfc9771>.

[SEALPROOFS]

Sullivan, N., "Security Analysis of the SEAL Construction: raAE, Snapshot Integrity, and Commitment", Work in Progress manuscript in preparation.

[Tink]

Hoang, V. T. and Y. Shen, "Security of Streaming Encryption in Google's Tink Library", IACR ePrint 2020/1019, 2020, <https://eprint.iacr.org/2020/1019>.

C.1. Provenance of the Security Claims

C.2. Advantage Notation and Adversary Parameters

For a ra-ROR adversary (Section 5.3) using at most u distinct CEKs and q_m messages, each encrypted with an independent fresh 32-octet per-content salt (Section 4.9.1.1), across n_ep total epochs and making q_e encryption and q_d decryption segment queries with sigma = q_e + q_d, the advantage is bounded by:¶

Adv_raROR(A) <= Adv_salt_coll
                   + Adv_muPRF(KDF, B_KDF)
                   + Adv_muROR(AEAD, B_AEAD)
                   + Adv_nonce_coll
                   + Adv_snap

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. Conditioned on no salt collision, distinct messages under one CEK have distinct payload_info values and therefore independent KDF outputs under the mu-PRF assumption. This term holds only under the fresh per-message uniform salt requirement of Section 4.9.1.1. A profile that reuses salts or draws them non-uniformly forfeits it and must argue payload-schedule separation by other means (Section 6.7).¶

Adv_muPRF(KDF, B_KDF)

The multi-user PRF advantage of the KDF, covering two keying levels. Level A is keyed by the CEK and produces payload_key, snap_key, and nonce_base. It has u users, queried once per message. Level B is keyed by payload_key (producing epoch_key per Section 4.5.2 and, in the plaintext-bound construction, per-segment nonces per Appendix A) and by snap_key (producing the snapshot authenticator's keyed derivations). It has q_m users. The snap_key subset of Level B feeds the configured snapshot authenticator and is counted under Adv_snap below. It is not counted again here.¶

Adv_muROR(AEAD, B_AEAD)

The multi-user real-or-random advantage of the AEAD over sigma total segment queries. There is one mu-ROR user per distinct segment key, for n_ep epoch keys 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 distinct 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. Section 5.8.5 bounds n_ep for that suite.¶

Adv_nonce_coll

The probability of a nonce collision under any segment key. In derived nonce mode it is zero, conditional on no salt collision (already charged via Adv_salt_coll). In random nonce mode (with or without the plaintext-bound hedge) it is bounded per Section 5.8.6.1. The derived-mode statement relies on the deterministic-MRAE analysis in Appendix C.5.¶

Adv_snap

The snapshot-forgery advantage of the configured snapshot authenticator, present only under an authenticator that produces a snapshot value and zero under None (Section 4.7.2). It covers the mu-PRF cost of the authenticator's snap_key derivations (the snap_key subset of Level B, counted here and not again in Adv_muPRF(KDF, B_KDF)) with the forgery and any further terms the authenticator's own construction requires. 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.¶

C.3. ra-ROR Reduction

The reduction follows the [FLRR25] hybrid over the two-level key schedule (Section 4.5). Condition on no salt collision (Adv_salt_coll). Replace the CEK-keyed KDF outputs and the payload_key-keyed outputs with uniformly random values, charged to Adv_muPRF; these are Level A and the payload_key subset of Level B. The snap_key-keyed outputs are idealized likewise, but their mu-PRF cost is the snap_key subset of Level B, charged to Adv_snap and not to Adv_muPRF (Section 5.7). Bound the resulting segment AEAD outputs (Adv_muROR). A flat epoch key is the single-epoch case of the same argument. The segment AEAD calls are nonce-respecting only under no nonce collision, the event charged to Adv_nonce_coll (Appendix C.2). In derived nonce mode this term is zero conditional on the same no-salt-collision event (Appendix C.5). The snapshot authenticator's forgery is the remaining part of Adv_snap (Section 5.7). The reduction constructs adversaries B_KDF against multi-user PRF security of the KDF and B_AEAD against multi-user real-or-random security of the AEAD, each running in time approximately that of A.¶

C.4. Commitment

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. PRF security alone is not sufficient for this reduction, because the commitment adversary may choose the CEK and the context values (Section 4.5).¶

For commitment_length = L octets, the relevant quantities are:¶

fixed-pair collision probability:  2^(-8*L)
q-query birthday probability:      q^2 / 2^(8*L + 1)
collision-search work factor:      about 2^(4*L)

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.¶

The ra-CMT-p advantage is bounded by the sum of two terms: the commitment collision bound above and the underlying AEAD's commitment bound for the forged position.¶

Position binding is inherited from the underlying AEAD, restored by the segment commitment over a strict ordering where the snapshot is authenticated outside the construction (Section 5.6). The notion derives from [FLRR25], and the per-segment associated-data and position accounting is deferred to [SEALPROOFS] (Appendix C.1).¶

C.5. Nonce Modes

The unique-nonce transform of Section 4.5.3.2, which XORs the segment index and finality bit into nonce_base, follows TLS 1.3 ([RFC8446]) static-IV-XOR-identifier and STREAM ([HRRV15]) 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.¶

Both disciplines of Section 4.5.3.2 keep every derived nonce carrying one plaintext, so each reduces unique-nonce record protection to nonce-respecting AEAD security. That reduction is precedent, not a SEAL-specific proof.¶

Under both disciplines no segment is ever re-encrypted with a different plaintext or associated data (Section 6.2, Section 4.9.3.1), so where a nonce is used twice both uses carry the same inputs, AEAD.Encrypt reproduces the same ciphertext, and a reduction answers the second query from the first one's output. The bound is therefore the same in both cases: the underlying AEAD's bound under distinct nonces.¶

In derived nonce mode the nonce-collision term is zero conditional on no salt collision, because each segment index maps to one derived nonce and a fresh per-message salt makes the segment keys distinct across messages. 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 remain real-or-random secure ([RFC8452]). The formal real-or-random treatment of this equality leakage for derived nonce mode is in preparation ([SEALPROOFS]). That treatment builds on the [FLRR25] ra-ROR analysis and changes its nonce-respecting hypothesis: a rewrite repeats a segment's derived nonce, so the proof replaces the nonce-respecting AEAD assumption with deterministic-MRAE security, under which nonce reuse leaks only input equality.¶

D.1. 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.¶

AEAD per-key bounds:

The per-key bounds of the underlying AEAD (birthday for 96-bit-nonce schemes, block-size for AES, integrity forgery for all schemes) become the limiting factor on security long before the nonce space is fully exhausted.¶

Write-once content:

Large content with many segments can place many AEAD invocations under one key, even when the content is written once.¶

Rewrites:

Rewrites consume additional invocations and can exhaust the same budget faster than write-once use, but they are not the only reason for epoching. Write-once large content benefits from the same partitioning.¶

Random access:

Rekeying the entire content would defeat the random-access property, so epoch keys bound the per-key invocation count without requiring 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.¶

D.2. 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 (Section 6.5). In the write-once profile the write-once rule keeps every derived nonce unique, and in the append-only profile the append-only rule does, so under either, derived mode pairs with 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 (Section 4.9.3.1).¶

The nonce mode is a profile parameter: a profile selects a valid (nonce_mode, snap_id) tuple, subject to the MRAE requirement above.¶