Galois Counter Mode with Secure Short Tags (GCM-SST)

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Table of Contents

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 [Sec5G], 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 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][RFC9605]. Short tags are also useful to protect packets transporting a signed payload such as a firmware update. For a comprehensive discussion on the use cases of short tags, see [Comments80038B].¶

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 128-bit block ciphers. The main differences from GCM [GCM] are the use of an additional subkey Q, the derivation of fresh subkeys H and Q for each nonce, and the replacement of the GHASH function with the POLYVAL function from AES-GCM-SIV [RFC8452], see Section 3. This enables short tags with forgery probability close to ideal and significantly decreases the probability of multiple successful forgeries, see Section 6. The performance of GCM-SST is 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 registers several instances of Advanced Encryption Standard (AES) [AES] and Rijndael with 256-bit keys and blocks (Rijndael-256-256) [Rijndael]. See Section 4 and Section 5. NIST is anticipated to standardize Rijndael-256-256 [15], although there may be revisions to the key schedule.¶

GCM-SST was originally developed by ETSI SAGE, under the name Mac5G, following a request from 3GPP, with several years of discussion contributing to its design [SAGE23][SAGE24]. 3GPP has decided to standardize GCM-SST for use with AES-256 [AES], SNOW 5G [SNOW], and ZUC-256 [ZUC] in 3GPP TS 35.240–25.248 [WID256].¶

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]¶

• 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 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].¶

4. AES in GCM-SST Mode

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] = ENC(K, N || BE32(i))¶

where ENC is the AES Cipher function [AES].¶

5. Rijndael-256-256 in GCM-SST Mode

This section defines Rijndael with 256-bit keys and blocks (Rijndael-256-256) [Rijndael] in Galois Counter Mode with Se-cure Short Tags (Rijndael-256-256-GCM-SST). When GCM-SST is instantiated with Rijndael-256-256, the keystream generator is Rijndael-256-256 in counter mode¶

Z[2i] = ENC(K, N || BE32(i))[0] Z[2i+1] = ENC(K, N || BE32(i))[1]¶

where ENC is the Rijndael-256-256 Cipher function [Rijndael].¶

6. 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 < 2³³ 128-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.¶

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 ≈ r² / 2⁹⁷. As an attacker can test r nonces for collisions with complexity r, the security of AES-GCM-SST with random nonces is only ≈ 2⁹⁷ / 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.¶

7. 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.¶

8. References

Appendix A. AES-GCM-SST Test Vectors

       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 }

       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 = { }

       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 = { }

       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 }

       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 }

       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 }

       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 }

       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 }

       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 = { }

       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 = { }

       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 }

       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 }

       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 }

       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 -03 to -04:¶

• Editorial changes.¶

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¶

• 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, Thomas Bellebaum, Scott Fluhrer, Eric Lagergren, Yehuda Lindell, and Eric Thormarker 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