Galois Counter Mode with Secure Short Tags (GCM-SST)
draft-mattsson-cfrg-aes-gcm-sst-03
| Document | Type | Active Internet-Draft (individual) | |
|---|---|---|---|
| Authors | Matt Campagna , Alexander Maximov , John Preuß Mattsson | ||
| Last updated | 2024-03-16 | ||
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draft-mattsson-cfrg-aes-gcm-sst-03
Crypto Forum M. Campagna
Internet-Draft Amazon Web Services
Intended status: Informational A. Maximov
Expires: 17 September 2024 J. Preuß Mattsson
Ericsson
16 March 2024
Galois Counter Mode with Secure Short Tags (GCM-SST)
draft-mattsson-cfrg-aes-gcm-sst-03
Abstract
This document defines the Galois Counter Mode with Secure Short Tags
(GCM-SST) Authenticated Encryption with Associated Data (AEAD)
algorithm. GCM-SST can be used with any keystream generator, not
just a block cipher. The main differences compared to GCM [GCM] is
that GCM-SST uses an additional subkey Q, that fresh subkeys H and Q
are derived for each nonce, and that the POLYVAL function from AES-
GCM-SIV is used instead of GHASH. This enables short tags with
forgery probabilities close to ideal. This document also registers
several instances of Advanced Encryption Standard (AES) with Galois
Counter Mode with Secure Short Tags (AES-GCM-SST).
This document is the product of the Crypto Forum Research Group.
About This Document
This note is to be removed before publishing as an RFC.
The latest revision of this draft can be found at
https://emanjon.github.io/draft-mattsson-cfrg-aes-gcm-sst/draft-
mattsson-cfrg-aes-gcm-sst.html. Status information for this document
may be found at https://datatracker.ietf.org/doc/draft-mattsson-cfrg-
aes-gcm-sst/.
Discussion of this document takes place on the Crypto Forum Research
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Source for this draft and an issue tracker can be found at
https://github.com/emanjon/draft-mattsson-cfrg-aes-gcm-sst.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Conventions and Definitions . . . . . . . . . . . . . . . . . 4
3. Galois Counter Mode with Secure Short Tags (GCM-SST) . . . . 5
3.1. Authenticated Encryption Function . . . . . . . . . . . . 6
3.2. Authenticated Decryption Function . . . . . . . . . . . . 7
3.3. Encoding (ct, tag) Tuples . . . . . . . . . . . . . . . . 8
4. AES with Galois Counter Mode with Secure Short Tags . . . . . 9
4.1. AES-GCM-SST AEAD Instances . . . . . . . . . . . . . . . 9
5. Security Considerations . . . . . . . . . . . . . . . . . . . 10
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 11
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
7.1. Normative References . . . . . . . . . . . . . . . . . . 11
7.2. Informative References . . . . . . . . . . . . . . . . . 12
Appendix A. AES-GCM-SST Test Vectors . . . . . . . . . . . . . . 14
A.1. AES-GCM-SST Test #1 (128-bit key) . . . . . . . . . . . . 14
Case #1a . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Case #1b . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Case #1c . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Case #1d . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Case #1e . . . . . . . . . . . . . . . . . . . . . . . . . . 15
A.2. AES-GCM-SST Test #2 (128-bit key) . . . . . . . . . . . . 15
A.3. AES-GCM-SST Test #3 (256-bit key) . . . . . . . . . . . . 15
Case #3a . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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Case #3b . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Case #3c . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Case #3d . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Case #3e . . . . . . . . . . . . . . . . . . . . . . . . . . 16
A.4. AES-GCM-SST Test #4 (256-bit key) . . . . . . . . . . . . 17
Change Log . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 18
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 18
1. Introduction
Advanced Encryption Standard (AES) in Galois Counter Mode (AES-GCM)
[GCM] is a widely used AEAD algorithm [RFC5116] due to its attractive
performance in both software and hardware as well as its provable
security. During the NIST standardization, Ferguson pointed out two
weaknesses in the GCM authentication function [Ferguson]. The
weaknesses are especially concerning when GCM is used with short
tags. The first weakness significantly increases the probability of
successful forgery. The second weakness reveals the subkey H if the
attacker manages to create successful forgeries. With knowledge of
the subkey H, the attacker always succeeds with subsequent forgeries.
The probability of multiple successful forgeries is therefore
significantly increased.
As a comment to NIST, Nyberg et al. [Nyberg] explained how small
changes based on proven theoretical constructions mitigate these
weaknesses. Unfortunately, NIST did not follow the advice from
Nyberg et al. and instead specified additional requirements for use
with short tags in Appendix C of [GCM]. NIST did not give any
motivations for the specific choice of parameters, or for that matter
the security levels they were assumed to give. As shown by Mattsson
et al. [Mattsson], an attacker can almost always gain feedback on
success or failure of forgery attempts, contradicting NIST's
assumptions for short tags. NIST also appears to have used non-
optimal attacks to calculate the parameters. A detailed evaluation
of GCM and other block cipher modes of operation is given by
[Rogaway]. Rogaway is critical of GCM with short tags and recommends
disallowing GCM with tags shorter than 96-bits. NIST is planning to
remove support for GCM with tags shorter than 96-bits [Revise].
While Counter with CBC-MAC (CCM) [RFC5116] with short tags has
forgery probabilities close to ideal, CCM has lower performance than
GCM.
32-bit tags are standard in most radio link layers including 5G,
64-bit tags are very common in transport and application layers of
the Internet of Things, and 32-, 64-, and 80-bit tags are common in
media-encryption applications. Audio packets are small, numerous,
and ephemeral, so on the one hand, they are very sensitive in
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percentage terms to crypto overhead, and on the other hand, forgery
of individual packets is not a big concern. Due to its weaknesses,
GCM is typically not used with short tags. The result is either
decreased performance from larger than needed tags [MoQ], or
decreased performance from using much slower constructions such as
AES-CTR combined with HMAC [RFC3711][I-D.ietf-sframe-enc]. Short
tags are also useful to protect packets transporting a signed payload
such as a firmware update.
This document defines the Galois Counter Mode with Secure Short Tags
(GCM-SST) Authenticated Encryption with Associated Data (AEAD)
algorithm following the recommendations from Nyberg et al. [Nyberg].
GCM-SST is defined with a general interface so that it can be used
with any keystream generator, not just a 128-bit block cipher. The
main differences compared to GCM [GCM] is that GCM-SST uses an
additional subkey Q, that fresh subkeys H and Q are derived for each
nonce, and that the POLYVAL function from AES-GCM-SIV [RFC8452] is
used instead of GHASH, see Section 3. This enables short tags with
forgery probability close to ideal and significantly decreases the
probability of multiple successful forgeries, see Section 5. The
performance of GCM-SST is very similar to GCM [GCM]. The two
additional AES invocations are compensated by the use of POLYVAL, the
”little-endian version” of GHASH, which is faster on little-endian
architectures. GCM-SST maintains the additive encryption
characteristic of GCM, which enables efficient implementations on
modern processor architectures, see [Gueron] and Section 2.4 of
[GCM-Update]. This document also registers several instances of
Advanced Encryption Standard (AES) with Galois Counter Mode with
Secure Short Tags (AES-GCM-SST) where AES [AES] in counter mode is
used as the keystream generator. See Section 4. GCM-SST has been
standardized for use with AES-256 and SNOW 5G [SNOW] in 3GPP 5G
Advance.
2. Conventions and Definitions
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 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
Primitives:
* K is the key as defined in [RFC5116]
* N is the nonce as defined in [RFC5116]
* A is the associated data as defined in [RFC5116]
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* P is the plaintext as defined in [RFC5116]
* = is the assignment operator
* != is the inequality operator
* x || y is concatenation of the octet strings x and y
* XOR is the bitwise exclusive OR operator
* len(x) is the length of x in bits.
* zeropad(x) right pads an octet string x with zeroes to a multiple
of 128 bits
* truncate(x, t) is the truncation operation. The first t bits of x
are kept
* n is the number of 128-bit chunks in zeropad(P)
* m is the number of 128-bit chunks in zeropad(A)
* POLYVAL is defined in [RFC8452]
* BE32(x) is the big-endian encoding of 32-bit integer x
* LE64(x) is the little-endian encoding of 64-bit integer x
* V[y] is the 128-bit chunk with index y in the array V; the first
chunk has index 0.
* V[x:y] are the range of chunks x to y in the array V
3. Galois Counter Mode with Secure Short Tags (GCM-SST)
This section defines the Galois Counter Mode with Secure Short Tags
(GCM-SST) AEAD algorithm following the recommendations from Nyberg et
al. [Nyberg]. GCM-SST is defined with a general interface so that
it can be used with any keystream generator, not just a 128-bit block
cipher.
GCM-SST adheres to an AEAD interface [RFC5116] and the encryption
function takes four variable-length octet string parameters. A
secret key K, a nonce N, the associated data A, and a plaintext P.
The keystream generator is instantiated with K and N. The keystream
MAY depend on P and A. The minimum and maximum lengths of all
parameters depend on the keystream generator. The keystream
generator produces a keystream Z consisting of 128-bit chunks where
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the first three chunks Z[0], Z[1], and Z[2] are used as the three
subkeys H, Q, and M. The following keystream chunks Z[3], Z[4], ...,
Z[n + 2] are used to encrypt the plaintext. Instead of GHASH [GCM],
GCM-SST makes use of the POLYVAL function from AES-GCM-SIV [RFC8452],
which results in more efficient software implementations on little-
endian architectures. GHASH and POLYVAL can be defined in terms of
one another [RFC8452]. The subkeys H and Q are field elements used
in POLYVAL while the subkey M is used for the final masking of the
tag. Both encryption and decryption are only defined on inputs that
are a whole number of octets.
Figures illustrating the GCM-SST encryption and decryption functions
are shown in [SST1][SST2].
3.1. Authenticated Encryption Function
Encrypt(K, N, A, P)
The encryption function encrypts a plaintext and returns the
ciphertext along with an authentication tag that verifies the
authenticity of the plaintext and associated data, if provided.
Prerequisites and security:
* The key MUST be randomly chosen from a uniform distribution.
* For a given key, the nonce MUST NOT be reused under any
circumstances.
* Supported tag_length associated with the key.
* Definitions of supported input-output lengths.
Inputs:
* Key K (variable-length octet string)
* Nonce N (variable-length octet string)
* Associated data A (variable-length octet string)
* Plaintext P (variable-length octet string)
Outputs:
* Ciphertext ct (variable-length octet string)
* Tag tag (octet string with length tag_length)
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Steps:
1. If the lengths of K, N, A, P are not supported return error and
abort
2. Initiate keystream generator with K and N
3. Let H = Z[0], Q = Z[1], M = Z[2]
4. Let ct = P XOR truncate(Z[3:n + 2], len(P))
5. Let S = zeropad(A) || zeropad(ct)
6. Let L = LE64(len(ct)) || LE64(len(A))
7. Let X = POLYVAL(H, S[0], S[1], ...)
8. Let full_tag = POLYVAL(Q, X XOR L) XOR M
9. Let tag = truncate(full_tag, tag_length)
10. Return (ct, tag)
3.2. Authenticated Decryption Function
Decrypt(K, N, A, ct, tag)
The decryption function decrypts a ciphertext, verifies that the
authentication tag is correct, and returns the plaintext on success
or an error if tag verification failed.
Prerequisites and security:
* The calculation of the plaintext P (step 10) MAY be done in
parallel with the tag verification (step 3-9). If tag
verification fails, the plaintext P and the expected_tag MUST NOT
be given as output.
* The comparison of the input tag with the expected_tag MUST be done
in constant time.
* Supported tag_length associated with the key.
* Definitions of supported input-output lengths.
Inputs:
* Key K (variable-length octet string)
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* Nonce N (variable-length octet string)
* Associated data A (variable-length octet string)
* Ciphertext ct (variable-length octet string)
* Tag tag (octet string with length tag_length)
Outputs:
* Plaintext P (variable-length octet string) or an error indicating
that the authentication tag is invalid for the given inputs.
Steps:
1. If the lengths of K, N, A, or ct are not supported, or if
len(tag) != tag_length return error and abort
2. Initiate keystream generator with K and N
3. Let H = Z[0], Q = Z[1], M = Z[2]
4. Let S = zeropad(A) || zeropad(ct)
5. Let L = LE64(len(ct)) || LE64(len(A))
6. Let X = POLYVAL(H, S[0], S[1], ...)
7. Let full_tag = POLYVAL(Q, X XOR L) XOR M
8. Let expected_tag = truncate(full_tag, tag_length)
9. If tag != expected_tag, return error and abort
10. Let P = ct XOR truncate(Z[3:n + 2], len(ct))
11. Return P
3.3. Encoding (ct, tag) Tuples
Applications MAY keep the ciphertext and the authentication tag in
distinct structures or encode both as a single octet string C. In
the latter case, the tag MUST immediately follow the ciphertext ct:
C = ct || tag
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4. AES with Galois Counter Mode with Secure Short Tags
This section defines Advanced Encryption Standard (AES) with Galois
Counter Mode with Secure Short Tags (AES-GCM-SST). When GCM-SSM is
instantiated with AES, the keystream generator is AES in counter mode
Z[i] = AES-ENC(K, N || BE32(i))
where AES-ENC is the AES encrypt function [AES].
4.1. AES-GCM-SST AEAD Instances
We define six AEAD instances, in the format of [RFC5116], that use
AES-GCM-SST. They differ only in key length (K_LEN) and tag length.
The tag lengths 32, 64, and 80 have been chosen to align with secure
media frames [I-D.ietf-sframe-enc]. The key length and tag length
are related to different security properties, and an application
encrypting audio packets with small tags might require 256-bit
confidentiality.
+============+=========================+===============+============+
| Numeric ID | Name | K_LEN | tag_length |
| | | (bytes) | (bits) |
+============+=========================+===============+============+
| TBD1 | AEAD_AES_128_GCM_SST_4 | 16 | 32 |
+------------+-------------------------+---------------+------------+
| TBD2 | AEAD_AES_128_GCM_SST_8 | 16 | 64 |
+------------+-------------------------+---------------+------------+
| TBD3 | AEAD_AES_128_GCM_SST_10 | 16 | 80 |
+------------+-------------------------+---------------+------------+
| TBD4 | AEAD_AES_256_GCM_SST_4 | 32 | 32 |
+------------+-------------------------+---------------+------------+
| TBD5 | AEAD_AES_256_GCM_SST_8 | 32 | 64 |
+------------+-------------------------+---------------+------------+
| TBD6 | AEAD_AES_256_GCM_SST_10 | 32 | 80 |
+------------+-------------------------+---------------+------------+
Table 1: AEAD Algorithms
Common parameters for the six AEAD instances:
* P_MAX (maximum size of the plaintext) is 2^36 - 48 octets.
* A_MAX (maximum size of the associated data) is 2^36 octets.
* N_MIN and N_MAX (minimum and maximum size of the nonce) are both
12 octets
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* C_MAX (maximum size of the ciphertext and tag) is P_MAX +
tag_length (in bytes)
5. Security Considerations
GCM-SST uses an additional subkey Q and that new subkeys H, Q are
derived for each nonce. The use of an additional subkey Q enables
short tags with forgery probabilities close to ideal. Deriving new
subkeys H, Q for each nonce significantly decreases the probability
of multiple successful forgeries. These changes are based on proven
theoretical constructions and follows the recommendations in
[Nyberg]. See [Nyberg] for details and references to security proofs
for the construction.
GCM-SST MUST be used in a nonce-respecting setting: for a given key,
a nonce MUST only be used once. The nonce MAY be public or
predictable. It can be a counter, the output of a permutation, or a
generator with a long period. Every key MUST be randomly chosen from
a uniform distribution. Implementations SHOULD randomize the nonce
by mixing a unique number like a sequence number with a per-key
random salt. This improves security against pre-computation attacks
and multi-key attacks [Bellare].
The GCM-SST tag_length SHOULD NOT be smaller than 4 bytes and cannot
be larger than 16 bytes. For short tags of length t < 128 - log2(n +
m + 1) bits, the worst-case forgery probability is bounded by ≈ 2^-t
[Nyberg]. With the constraints listed in Section 4.1, n + m + 1 <
2^33 128-bit blocks, and tags of length up to 95 bits therefore have
an almost perfect security level. This is significantly better than
GCM where the security level is only t – log2(n + m + 1) bits [GCM].
As one can note, for 128-bit tags and long messages, the forgery
probability is not close to ideal and similar to GCM [GCM]. If tag
verification fails, the plaintext and expected_tag MUST NOT be given
as output. The full_tag in GCM-SST does not depend on the tag
length. An application can make the tag dependent on the tag length
by including tag_length in the nonces.
The confidentiality offered by AES-GCM-SST against passive attackers
is equal to AES-GCM [GCM] and given by the birthday bound. The
maximum size of the plaintext (P_MAX) has been adjusted from GCM
[RFC5116] as there is now three subkeys instead of two.
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For the AES-GCM-SST algorithms in Table 1 the worst-case forgery
probability is bounded by ≈ 2^-t where t is the tag length in bits
[Nyberg]. This is true for all allowed plaintext and associated data
lengths. The maximum size of the associated data (A_MAX) has been
lowered from GCM [RFC5116] to enable forgery probability close to
ideal for 80-bit tags even with maximum size plaintexts and
associated data. Just like [RFC5116] AES-GCM-SST only allows 96-bit
nonces.
If r random nonces are used with the same key, the collision
probability for AES-GCM-SST is ≈ r^2 / 2^97. As an attacker can test
r nonces for collisions with complexity r, the security of AES-GCM-
SST with random nonces is only ≈ 2^97 / r. It is therefore NOT
RECOMMENDED to use AES-GCM-SST with random nonces.
In general, there is a very small possibility in GCM-SST that either
or both of the subkeys H and Q are zero, so called weak keys. If
both keys are zero, the resulting tag will not depend on the message.
There are no obvious ways to detect this condition for an attacker,
and the specification admits this possibility in favor of
complicating the flow with additional checks and regeneration of
values. In AES-GCM-SST, H and Q are generated with the AES-ENC
permutation on different input, so H and Q cannot both be zero.
6. IANA Considerations
IANA is requested to assign the entries in the first two columns of
Table 1 to the "AEAD Algorithms" registry under the "Authenticated
Encryption with Associated Data (AEAD) Parameters" heading with this
document as reference.
7. References
7.1. Normative References
[AES] "ADVANCED ENCRYPTION STANDARD (AES)", NIST Federal
Information Processing Standards Publication 197, November
2001, <https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.197-upd1.pdf>.
[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>.
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[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>.
7.2. Informative References
[Bellare] Bellare, M. and B. Tackmann, "The Multi-User Security of
Authenticated Encryption: AES-GCM in TLS 1.3", November
2017, <https://eprint.iacr.org/2016/564.pdf>.
[Ferguson] Ferguson, N., "Authentication weaknesses in GCM", May
2005, <https://csrc.nist.gov/CSRC/media/Projects/Block-
Cipher-Techniques/documents/BCM/Comments/CWC-GCM/
Ferguson2.pdf>.
[GCM] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Galois/Counter Mode (GCM) and GMAC",
NIST Special Publication 800-38D, November 2007,
<https://nvlpubs.nist.gov/nistpubs/Legacy/SP/
nistspecialpublication800-38d.pdf>.
[GCM-Update]
McGrew, D. and J. Viega, "GCM Update", May 2005,
<https://csrc.nist.gov/csrc/media/projects/block-cipher-
techniques/documents/bcm/comments/cwc-gcm/gcm-update.pdf>.
[Gueron] Gueron, S., "Constructions based on the AES Round and
Polynomial Multiplication that are Efficient on Modern
Processor Architectures", October 2023,
<https://csrc.nist.gov/csrc/media/Presentations/2023/
constructions-based-on-the-aes-round/images-media/sess-5-
gueron-bcm-workshop-2023.pdf>.
[I-D.ietf-sframe-enc]
Omara, E., Uberti, J., Murillo, S. G., Barnes, R., and Y.
Fablet, "Secure Frame (SFrame)", Work in Progress,
Internet-Draft, draft-ietf-sframe-enc-07, 29 February
2024, <https://datatracker.ietf.org/doc/html/draft-ietf-
sframe-enc-07>.
[I-D.irtf-cfrg-aegis-aead]
Denis, F. and S. Lucas, "The AEGIS Family of Authenticated
Encryption Algorithms", Work in Progress, Internet-Draft,
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draft-irtf-cfrg-aegis-aead-10, 20 January 2024,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
aegis-aead-10>.
[Mattsson] Mattsson, J. and M. Westerlund, "Authentication Key
Recovery on Galois/Counter Mode (GCM)", May 2015,
<https://eprint.iacr.org/2015/477.pdf>.
[MoQ] IETF, "Media Over QUIC", September 2022,
<https://datatracker.ietf.org/wg/moq/about/>.
[Nyberg] Nyberg, K., Gilbert, H., and M. Robshaw, "Galois MAC with
forgery probability close to ideal", June 2005,
<https://csrc.nist.gov/CSRC/media/Projects/Block-Cipher-
Techniques/documents/BCM/Comments/general-comments/papers/
Nyberg_Gilbert_and_Robshaw.pdf>.
[Revise] NIST, "Announcement of Proposal to Revise SP 800-38D",
August 2023, <https://csrc.nist.gov/news/2023/proposal-to-
revise-sp-800-38d>.
[RFC3711] Baugher, M., McGrew, D., Naslund, M., Carrara, E., and K.
Norrman, "The Secure Real-time Transport Protocol (SRTP)",
RFC 3711, DOI 10.17487/RFC3711, March 2004,
<https://www.rfc-editor.org/rfc/rfc3711>.
[Rogaway] Rogaway, P., "Evaluation of Some Blockcipher Modes of
Operation", February 2011,
<https://www.cryptrec.go.jp/exreport/cryptrec-ex-
2012-2010r1.pdf>.
[SNOW] Ekdahl, P., Johansson, T., Maximov, A., and J. Yang,
"SNOW-Vi: an extreme performance variant of SNOW-V for
lower grade CPUs", March 2021,
<https://eprint.iacr.org/2021/236>.
[SST1] Campagna, M., Maximov, A., and J. Preuß Mattsson, "Galois
Counter Mode with Secure Short Tags (GCM-SST)", October
2023, <https://csrc.nist.gov/csrc/media/Events/2023/third-
workshop-on-block-cipher-modes-of-operation/documents/
accepted-papers/Galois%20Counter%20Mode%20with%20Secure%20
Short%20Tags.pdf>.
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[SST2] Campagna, M., Maximov, A., and J. Preuß Mattsson, "Galois
Counter Mode with Secure Short Tags (GCM-SST)", October
2023,
<https://csrc.nist.gov/csrc/media/Presentations/2023/
galois-counter-mode-with-secure-short-tags/images-media/
sess-5-mattsson-bcm-workshop-2023.pdf>.
Appendix A. AES-GCM-SST Test Vectors
A.1. AES-GCM-SST Test #1 (128-bit key)
KEY = { 00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f }
NONCE = { 30 31 32 33 34 35 36 37 38 39 3a 3b }
H = { 22 ce 92 da cb 50 77 4b ab 0d 18 29 3d 6e ae 7f }
Q = { 03 13 63 96 74 be fa 86 4d fa fb 80 36 b7 a0 3c }
M = { 9b 1d 49 ea 42 b0 0a ec b0 bc eb 8d d0 ef c2 b9 }
Case #1a
AAD = { }
PLAINTEXT = { }
encode-LEN = { 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 }
full-TAG = { 9b 1d 49 ea 42 b0 0a ec b0 bc eb 8d d0 ef c2 b9 }
TAG = { 9b 1d 49 ea }
CIPHERTEXT = { }
Case #1b
AAD = { 40 41 42 43 44 }
PLAINTEXT = { }
encode-LEN = { 00 00 00 00 00 00 00 00 28 00 00 00 00 00 00 00 }
full-TAG = { 7f f3 cb a4 d5 f3 08 a5 70 4e 2f d5 f2 3a e8 f9 }
TAG = { 7f f3 cb a4 }
CIPHERTEXT = { }
Case #1c
AAD = { }
PLAINTEXT = { 60 61 62 63 64 65 66 67 68 69 6a 6b }
encode-LEN = { 60 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 }
full-TAG = { f8 de 17 85 fd 1a 90 d9 81 8f cb 7b 44 69 8a 8b }
TAG = { f8 de 17 85 }
CIPHERTEXT = { 64 f0 5b ae 1e d2 40 3a 71 25 5e dd }
Case #1d
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AAD = { 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f }
PLAINTEXT = { 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f
70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e }
encode-LEN = { f8 00 00 00 00 00 00 00 80 00 00 00 00 00 00 00 }
full-TAG = { 93 43 56 14 0b 84 48 2c d0 14 c7 40 7e e9 cc b6 }
TAG = { 93 43 56 14 }
CIPHERTEXT = { 64 f0 5b ae 1e d2 40 3a 71 25 5e dd 53 49 5c e1
7d c0 cb c7 85 a7 a9 20 db 42 28 ff 63 32 10 }
Case #1e
AAD = { 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e }
PLAINTEXT = { 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f
70 }
encode-LEN = { 88 00 00 00 00 00 00 00 78 00 00 00 00 00 00 00 }
full-TAG = { f8 50 b7 97 11 43 ab e9 31 5a d7 eb 3b 0a 16 81 }
TAG = { f8 50 b7 97 }
CIPHERTEXT = { 64 f0 5b ae 1e d2 40 3a 71 25 5e dd 53 49 5c e1
7d }
A.2. AES-GCM-SST Test #2 (128-bit key)
KEY = { 29 23 be 84 e1 6c d6 ae 52 90 49 f1 f1 bb e9 eb }
NONCE = { 9a 50 ee 40 78 36 fd 12 49 32 f6 9e }
AAD = { 1f 03 5a 7d 09 38 25 1f 5d d4 cb fc 96 f5 45 3b
13 0d }
PLAINTEXT = { ad 4f 14 f2 44 40 66 d0 6b c4 30 b7 32 3b a1 22
f6 22 91 9d }
H = { 2d 6d 7f 1c 52 a7 a0 6b f2 bc bd 23 75 47 03 88 }
Q = { 3b fd 00 96 25 84 2a 86 65 71 a4 66 e5 62 05 92 }
M = { 9e 6c 98 3e e0 6c 1a ab c8 99 b7 8d 57 32 0a f5 }
encode-LEN = { a0 00 00 00 00 00 00 00 90 00 00 00 00 00 00 00 }
full-TAG = { 45 03 bf b0 96 82 39 b3 67 e9 70 c3 83 c5 10 6f }
TAG = { 45 03 bf b0 96 82 39 b3 }
CIPHERTEXT = { b8 65 d5 16 07 83 11 73 21 f5 6c b0 75 45 16 b3
da 9d b8 09 }
A.3. AES-GCM-SST Test #3 (256-bit key)
KEY = { 00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f }
NONCE = { 30 31 32 33 34 35 36 37 38 39 3a 3b }
H = { 3b d9 9f 8d 38 f0 2e a1 80 96 a4 b0 b1 d9 3b 1b }
Q = { af 7f 54 00 16 aa b8 bc 91 56 d9 d1 83 59 cc e5 }
M = { b3 35 31 c0 e9 6f 4a 03 2a 33 8e ec 12 99 3e 68 }
Case #3a
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AAD = { }
PLAINTEXT = { }
encode-LEN = { 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 }
full-TAG = { b3 35 31 c0 e9 6f 4a 03 2a 33 8e ec 12 99 3e 68 }
TAG = { b3 35 31 c0 e9 6f 4a 03 }
CIPHERTEXT = { }
Case #3b
AAD = { 40 41 42 43 44 }
PLAINTEXT = { }
encode-LEN = { 00 00 00 00 00 00 00 00 28 00 00 00 00 00 00 00 }
full-TAG = { 63 ac ca 4d 20 9f b3 90 28 ff c3 17 04 01 67 61 }
TAG = { 63 ac ca 4d 20 9f b3 90 }
CIPHERTEXT = { }
Case #3c
AAD = { }
PLAINTEXT = { 60 61 62 63 64 65 66 67 68 69 6a 6b }
encode-LEN = { 60 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 }
full-TAG = { e1 de bf fd 5f 3a 85 e3 48 bd 6f cc 6e 62 10 90 }
TAG = { e1 de bf fd 5f 3a 85 e3 }
CIPHERTEXT = { fc 46 2d 34 a7 5b 22 62 4f d7 3b 27 }
Case #3d
AAD = { 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f }
PLAINTEXT = { 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f
70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e }
encode-LEN = { f8 00 00 00 00 00 00 00 80 00 00 00 00 00 00 00 }
full-TAG = { c3 5e d7 83 9f 21 f7 bb a5 a8 a2 8e 1f 49 ed 04 }
TAG = { c3 5e d7 83 9f 21 f7 bb }
CIPHERTEXT = { fc 46 2d 34 a7 5b 22 62 4f d7 3b 27 84 de 10 51
33 11 7e 17 58 b5 ed d0 d6 5d 68 32 06 bb ad }
Case #3e
AAD = { 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e }
PLAINTEXT = { 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f
70 }
encode-LEN = { 88 00 00 00 00 00 00 00 78 00 00 00 00 00 00 00 }
full-TAG = { 49 7c 14 77 67 a5 3d 57 64 ce fd 03 26 fe e7 b5 }
TAG = { 49 7c 14 77 67 a5 3d 57 }
CIPHERTEXT = { fc 46 2d 34 a7 5b 22 62 4f d7 3b 27 84 de 10 51
33 }
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A.4. AES-GCM-SST Test #4 (256-bit key)
KEY = { 29 23 be 84 e1 6c d6 ae 52 90 49 f1 f1 bb e9 eb
b3 a6 db 3c 87 0c 3e 99 24 5e 0d 1c 06 b7 b3 12 }
NONCE = { 9a 50 ee 40 78 36 fd 12 49 32 f6 9e }
AAD = { 1f 03 5a 7d 09 38 25 1f 5d d4 cb fc 96 f5 45 3b
13 0d }
PLAINTEXT = { ad 4f 14 f2 44 40 66 d0 6b c4 30 b7 32 3b a1 22
f6 22 91 9d }
H = { 13 53 4b f7 8a 91 38 fd f5 41 65 7f c2 39 55 23 }
Q = { 32 69 75 a3 3a ff ae ac af a8 fb d1 bd 62 66 95 }
M = { 59 48 44 80 b6 cd 59 06 69 27 5e 7d 81 4a d1 74 }
encode-LEN = { a0 00 00 00 00 00 00 00 90 00 00 00 00 00 00 00 }
full-TAG = { c4 a1 ca 9a 38 c6 73 af bf 9c 73 49 bf 3c d5 4d }
TAG = { c4 a1 ca 9a 38 c6 73 af bf 9c }
CIPHERTEXT = { b5 c2 a4 07 f3 3e 99 88 de c1 2f 10 64 7b 3d 4f
eb 8f f7 cc }
Change Log
This section is to be removed before publishing as an RFC.
Changes from -02 to -03:
* Added performance information and considerations.
* Editorial changes.
Changes from -01 to -02:
* The length encoding chunk is now called L
* Use of the notation POLYVAL(H, X_1, X_2, ...) from RFC 8452
* Removed duplicated text in security considerations.
Changes from -00 to -01:
* Link to NIST decision to remove support for GCM with tags shorter
than 96-bits based on Mattsson et al.
* Mention that 3GPP 5G Advance will use GCM-SST with AES-256 and
SNOW 5G.
* Corrected reference to step numbers during decryption
* Changed T to full_tag to align with tag and expected_tag
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* Link to images from the NIST encryption workshop illustrating the
GCM-SST encryption and decryption functions.
* Updated definitions
* Editorial changes.
Acknowledgments
The authors thank Richard Barnes, Scott Fluhrer, and Eric Lagergren
for their valuable comments and feedback. Some of the formatting and
text were inspired by and borrowed from [I-D.irtf-cfrg-aegis-aead].
Authors' Addresses
Matthew Campagna
Amazon Web Services
Canada
Email: campagna@amazon.com
Alexander Maximov
Ericsson AB
Sweden
Email: alexander.maximov@ericsson.com
John Preuß Mattsson
Ericsson AB
Sweden
Email: john.mattsson@ericsson.com
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