RFC 9058 | Multilinear Galois Mode (MGM) | June 2021 |
Smyshlyaev, et al. | Informational | [Page] |
Multilinear Galois Mode (MGM) is an Authenticated Encryption with Associated Data (AEAD) block cipher mode based on the Encrypt-then-MAC (EtM) principle. MGM is defined for use with 64-bit and 128-bit block ciphers.¶
MGM has been standardized in Russia. It is used as an AEAD mode for the GOST block cipher algorithms in many protocols, e.g., TLS 1.3 and IPsec. This document provides a reference for MGM to enable review of the mechanisms in use and to make MGM available for use with any block cipher.¶
This document is not an Internet Standards Track specification; it is published for informational purposes.¶
This is a contribution to the RFC Series, independently of any other RFC stream. The RFC Editor has chosen to publish this document at its discretion and makes no statement about its value for implementation or deployment. Documents approved for publication by the RFC Editor are not candidates for any level of Internet Standard; see Section 2 of RFC 7841.¶
Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at https://www.rfc-editor.org/info/rfc9058.¶
Copyright (c) 2021 IETF Trust and the persons identified as the document authors. All rights reserved.¶
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document.¶
Multilinear Galois Mode (MGM) is an Authenticated Encryption with Associated Data (AEAD) block cipher mode based on EtM principle. MGM is defined for use with 64-bit and 128-bit block ciphers. The MGM design principles can easily be applied to other block sizes.¶
MGM has been standardized in Russia [AUTH-ENC-BLOCK-CIPHER]. It is used as an AEAD mode for the GOST block cipher algorithms in many protocols, e.g., TLS 1.3 and IPsec. This document provides a reference for MGM to enable review of the mechanisms in use and to make MGM available for use with any block cipher.¶
This document does not have IETF consensus and does not imply IETF support for MGM.¶
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.¶
This document uses the following terms and definitions for the sets and operations on the elements of these sets:¶
V_s -> V_i¶
The transformation that maps the string X = (x_{s-1}, ... , x_0) in V_s into the string MSB_i(X) = (x_{s-1}, ... , x_{s-i}) in V_i, i <= s (most significant bits).¶
V_s -> Z_{2^s}¶
The transformation that maps the string X = (x_{s-1}, ... , x_0) in V_s, s > 0, into the integer Int_s(X) = 2^{s-1} * x_{s-1} + ... + 2 * x_1 + x_0 (the interpretation of the bit string as an integer).¶
Z_{2^s} -> V_s¶
The transformation inverse to the mapping Int_s (the interpretation of an integer as a bit string).¶
V_n -> V_n¶
The block cipher permutation under the key K in V_k.¶
V_s -> V_{n/2}¶
The transformation that maps a string X in V_s, 0 <= s <= 2^{n/2} - 1, into the string len(X) = Vec_{n/2}(|X|) in V_{n/2}, where n is the block size of the used block cipher.¶
V_n -> V_n¶
The transformation that maps an n-byte string A = L || R into the n-byte string incr_l(A) = Vec_{n/2}(Int_{n/2}(L) [+] 1) || R, where L and R are n/2-byte strings.¶
V_n -> V_n¶
The transformation that maps an n-byte string A = L || R into the n-byte string incr_r(A) = L || Vec_{n/2}(Int_{n/2}(R) [+] 1), where L and R are n/2-byte strings.¶
An additional parameter that defines the functioning of MGM is the bit length S of the authentication tag, 32 <= S <= n. The value of S MUST be fixed for a particular protocol. The choice of the value S involves a trade-off between message expansion and the forgery probability.¶
The MGM encryption and tag generation procedure takes the following parameters as inputs:¶
The MGM encryption and tag generation procedure outputs the following parameters:¶
The MGM encryption and tag generation procedure consists of the following steps:¶
+----------------------------------------------------------------+ | MGM-Encrypt(K, ICN, A, P) | |----------------------------------------------------------------| | 1. Encryption step: | | - if |P| = 0 then | | - C*_q = P*_q | | - C = P | | - else | | - Y_1 = E_K(0^1 || ICN), | | - For i = 2, 3, ... , q do | | Y_i = incr_r(Y_{i-1}), | | - For i = 1, 2, ... , q - 1 do | | C_i = P_i (xor) E_K(Y_i), | | - C*_q = P*_q (xor) MSB_u(E_K(Y_q)), | | - C = C_1 || ... || C*_q. | | | | 2. Padding step: | | - A_h = A*_h || 0^{n-t}, | | - C_q = C*_q || 0^{n-u}. | | | | 3. Authentication tag T generation step: | | - Z_1 = E_K(1^1 || ICN), | | - sum = 0^n, | | - For i = 1, 2, ..., h do | | H_i = E_K(Z_i), | | sum = sum (xor) ( H_i (x) A_i ), | | Z_{i+1} = incr_l(Z_i), | | - For j = 1, 2, ..., q do | | H_{h+j} = E_K(Z_{h+j}), | | sum = sum (xor) ( H_{h+j} (x) C_j ), | | Z_{h+j+1} = incr_l(Z_{h+j}), | | - H_{h+q+1} = E_K(Z_{h+q+1}), | | - T = MSB_S(E_K(sum (xor) ( H_{h+q+1} (x) | | ( len(A) || len(C) ) ))). | | | | 4. Return (ICN, A, C, T). | +----------------------------------------------------------------+¶
The ICN value for each message that is encrypted under the given key K must be chosen in a unique manner.¶
Users who do not wish to encrypt plaintext can provide a string P of zero length. Users who do not wish to authenticate associated data can provide a string A of zero length. The length of the associated data A and of the plaintext P MUST be such that 0 < |A| + |P| < 2^{n/2}.¶
The MGM decryption and tag verification procedure takes the following parameters as inputs:¶
The MGM decryption and tag verification procedure outputs FAIL or the following parameters:¶
The MGM decryption and tag verification procedure consists of the following steps:¶
+----------------------------------------------------------------+ | MGM-Decrypt(K, ICN, A, C, T) | |----------------------------------------------------------------| | 1. Padding step: | | - A_h = A*_h || 0^{n-t}, | | - C_q = C*_q || 0^{n-u}. | | | | 2. Authentication tag T verification step: | | - Z_1 = E_K(1^1 || ICN), | | - sum = 0^n, | | - For i = 1, 2, ..., h do | | H_i = E_K(Z_i), | | sum = sum (xor) ( H_i (x) A_i ), | | Z_{i+1} = incr_l(Z_i), | | - For j = 1, 2, ..., q do | | H_{h+j} = E_K(Z_{h+j}), | | sum = sum (xor) ( H_{h+j} (x) C_j ), | | Z_{h+j+1} = incr_l(Z_{h+j}), | | - H_{h+q+1} = E_K(Z_{h+q+1}), | | - T' = MSB_S(E_K(sum (xor) ( H_{h+q+1} (x) | | ( len(A) || len(C) ) ))), | | - If T' != T then return FAIL. | | | | 3. Decryption step: | | - if |C| = 0 then | | - P = C | | - else | | - Y_1 = E_K(0^1 || ICN), | | - For i = 2, 3, ... , q do | | Y_i = incr_r(Y_{i-1}), | | - For i = 1, 2, ... , q - 1 do | | P_i = C_i (xor) E_K(Y_i), | | - P*_q = C*_q (xor) MSB_u(E_K(Y_q)), | | - P = P_1 || ... || P*_q. | | | | 4. Return (A, P). | +----------------------------------------------------------------+¶
The length of the associated data A and of the ciphertext C MUST be such that 0 < |A| + |C| < 2^{n/2}.¶
MGM was originally proposed in [PDMODE].¶
From the operational point of view, MGM is designed to be parallelizable, inverse free, and online and is also designed to provide availability of precomputations.¶
Parallelizability of MGM is achieved due to its counter-type structure and the usage of the multilinear function for authentication. Indeed, both encryption blocks E_K(Y_i) and authentication blocks H_i are produced in the counter mode manner, and the multilinear function determined by H_i is parallelizable in itself. Additionally, the counter-type structure of the mode provides the inverse-free property.¶
The online property means the possibility of processing messages even if it is not completely received (so its length is unknown). To provide this property, MGM uses blocks E_K(Y_i) and H_i, which are produced based on two independent source blocks Y_i and Z_i.¶
Availability of precomputations for MGM means the possibility of calculating H_i and E_K(Y_i) even before data is retrieved. It holds again due to the usage of counters for calculating them.¶
The security properties of MGM are based on the following:¶
It is crucial to the security of MGM to use unique ICN values. Using the same ICN values for two different messages encrypted with the same key eliminates the security properties of this mode.¶
It is crucial for the security of MGM not to process empty plaintext and empty associated data at the same time. Otherwise, a tag becomes independent from a nonce value, leading to vulnerability to forgery attacks.¶
Security analysis for MGM with E_K being a random permutation was performed in [SEC-MGM]. More precisely, the bounds for confidentiality advantage (CA) and integrity advantage (IA) (for details, see [AEAD-LIMITS]) were obtained. According to these results, for an adversary making at most q encryption queries with the total length of plaintexts and associated data of at most s blocks, and allowed to output a forgery with the summary length of ciphertext and associated data of at most l blocks:¶
CA <= ( 3( s + 4q )^2 )/ 2^n,¶
IA <= ( 3( s + 4q + l + 3 )^2 )/ 2^n + 2/2^S,¶
where n is the block size and S is the authentication tag size.¶
These bounds can be used as guidelines on how to calculate confidentiality and integrity limits (for details, also see [AEAD-LIMITS]).¶
This document has no IANA actions.¶
Test vectors for the Kuznyechik block cipher (n = 128, k = 256) are defined in [GOST3412-2015] (the English version can be found in [RFC7801]).¶
Encryption key K: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF ICN: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Associated authenticated data A: 00000: 02 02 02 02 02 02 02 02 01 01 01 01 01 01 01 01 00010: 04 04 04 04 04 04 04 04 03 03 03 03 03 03 03 03 00020: EA 05 05 05 05 05 05 05 05 Plaintext P: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 00040: AA BB CC¶
Encryption step:¶
0^1 || ICN: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Y_1: 00000: 7F 67 9D 90 BE BC 24 30 5A 46 8D 42 B9 D4 ED CD E_K(Y_1): 00000: B8 57 48 C5 12 F3 19 90 AA 56 7E F1 53 35 DB 74 Y_2: 00000: 7F 67 9D 90 BE BC 24 30 5A 46 8D 42 B9 D4 ED CE E_K(Y_2): 00000: 80 64 F0 12 6F AC 9B 2C 5B 6E AC 21 61 2F 94 33 Y_3: 00000: 7F 67 9D 90 BE BC 24 30 5A 46 8D 42 B9 D4 ED CF E_K(Y_3): 00000: 58 58 82 1D 40 C0 CD 0D 0A C1 E6 C2 47 09 8F 1C Y_4: 00000: 7F 67 9D 90 BE BC 24 30 5A 46 8D 42 B9 D4 ED D0 E_K(Y_4): 00000: E4 3F 50 81 B5 8F 0B 49 01 2F 8E E8 6A CD 6D FA Y_5: 00000: 7F 67 9D 90 BE BC 24 30 5A 46 8D 42 B9 D4 ED D1 E_K(Y_5): 00000: 86 CE 9E 2A 0A 12 25 E3 33 56 91 B2 0D 5A 33 48 C: 00000: A9 75 7B 81 47 95 6E 90 55 B8 A3 3D E8 9F 42 FC 00010: 80 75 D2 21 2B F9 FD 5B D3 F7 06 9A AD C1 6B 39 00020: 49 7A B1 59 15 A6 BA 85 93 6B 5D 0E A9 F6 85 1C 00030: C6 0C 14 D4 D3 F8 83 D0 AB 94 42 06 95 C7 6D EB 00040: 2C 75 52¶
Padding step:¶
A_1 || ... || A_h: 00000: 02 02 02 02 02 02 02 02 01 01 01 01 01 01 01 01 00010: 04 04 04 04 04 04 04 04 03 03 03 03 03 03 03 03 00020: EA 05 05 05 05 05 05 05 05 00 00 00 00 00 00 00 C_1 || ... || C_q: 00000: A9 75 7B 81 47 95 6E 90 55 B8 A3 3D E8 9F 42 FC 00010: 80 75 D2 21 2B F9 FD 5B D3 F7 06 9A AD C1 6B 39 00020: 49 7A B1 59 15 A6 BA 85 93 6B 5D 0E A9 F6 85 1C 00030: C6 0C 14 D4 D3 F8 83 D0 AB 94 42 06 95 C7 6D EB 00040: 2C 75 52 00 00 00 00 00 00 00 00 00 00 00 00 00¶
Authentication tag T generation step:¶
1^1 || ICN: 00000: 91 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Z_1: 00000: 7F C2 45 A8 58 6E 66 02 A7 BB DB 27 86 BD C6 6F H_1: 00000: 8D B1 87 D6 53 83 0E A4 BC 44 64 76 95 2C 30 0B current sum: 00000: 4C F4 27 F4 AD B7 5C F4 C0 DA 39 D5 AB 48 CF 38 Z_2: 00000: 7F C2 45 A8 58 6E 66 03 A7 BB DB 27 86 BD C6 6F H_2: 00000: 7A 24 F7 26 30 E3 76 37 21 C8 F3 CD B1 DA 0E 31 current sum: 00000: 94 95 44 0E F6 24 A1 DD C6 F5 D9 77 28 50 C5 73 Z_3: 00000: 7F C2 45 A8 58 6E 66 04 A7 BB DB 27 86 BD C6 6F H_3: 00000: 44 11 96 21 17 D2 06 35 C5 25 E0 A2 4D B4 B9 0A current sum: 00000: A4 9A 8C D8 A6 F2 74 23 DB 79 E4 4A B3 06 D9 42 Z_4: 00000: 7F C2 45 A8 58 6E 66 05 A7 BB DB 27 86 BD C6 6F H_4: 00000: D8 C9 62 3C 4D BF E8 14 CE 7C 1C 0C EA A9 59 DB current sum: 00000: 09 FE 3F 6A 83 3C 21 B3 90 27 D0 20 6A 84 E1 5A Z_5: 00000: 7F C2 45 A8 58 6E 66 06 A7 BB DB 27 86 BD C6 6F H_5: 00000: A5 E1 F1 95 33 3E 14 82 96 99 31 BF BE 6D FD 43 current sum: 00000: B5 DA 26 BB 00 EB A8 04 35 D7 97 6B C6 B5 46 4D Z_6: 00000: 7F C2 45 A8 58 6E 66 07 A7 BB DB 27 86 BD C6 6F H_6: 00000: B4 CA 80 8C AC CF B3 F9 17 24 E4 8A 2C 7E E9 D2 current sum: 00000: DD 1C 0E EE F7 83 C8 EB 2A 33 F3 58 D7 23 0E E5 Z_7: 00000: 7F C2 45 A8 58 6E 66 08 A7 BB DB 27 86 BD C6 6F H_7: 00000: 72 90 8F C0 74 E4 69 E8 90 1B D1 88 EA 91 C3 31 current sum: 00000: 89 6C E1 08 32 EB EA F9 06 9F 3F 73 76 59 4D 40 Z_8: 00000: 7F C2 45 A8 58 6E 66 09 A7 BB DB 27 86 BD C6 6F H_8: 00000: 23 CA 27 15 B0 2C 68 31 3B FD AC B3 9E 4D 0F B8 current sum: 00000: 99 1A F5 C9 D0 80 F7 63 87 FE 64 9E 7C 93 C6 42 Z_9: 00000: 7F C2 45 A8 58 6E 66 0A A7 BB DB 27 86 BD C6 6F H_9: 00000: BC BC E6 C4 1A A3 55 A4 14 88 62 BF 64 BD 83 0D len(A) || len(C): 00000: 00 00 00 00 00 00 01 48 00 00 00 00 00 00 02 18 sum (xor) ( H_9 (x) ( len(A) || len(C) ) ): 00000: C0 C7 22 DB 5E 0B D6 DB 25 76 73 83 3D 56 71 28 Tag T: 00000: CF 5D 65 6F 40 C3 4F 5C 46 E8 BB 0E 29 FC DB 4C¶
Encryption key K: 00000: 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 FE 00010: DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF 88 ICN: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Associated authenticated data A: 00000: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 Plaintext P: 00000:¶
Encryption step:¶
C: 00000:¶
Padding step:¶
A_1 || ... || A_h: 00000: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 C_1 || ... || C_q: 00000:¶
Authentication tag T generation step:¶
1^1 || ICN: 00000: 91 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Z_1: 00000: 79 32 72 68 96 C4 3E 3F BF D6 50 89 EB F1 E5 B6 H_1: 00000: 99 3A 80 66 CC C0 A4 0F AC 4A 14 F7 A2 F6 6D 9B current sum: 00000: 0A C1 1E 2C 1C D6 07 D8 2F E3 55 54 B4 01 02 81 Z_2: 00000: 79 32 72 68 96 C4 3E 40 BF D6 50 89 EB F1 E5 B6 H_2: 00000: 0C 38 A7 1E E7 93 BF 76 89 81 BF CD 7C DA 78 C8 len(A) || len(C): 00000: 00 00 00 00 00 00 00 80 00 00 00 00 00 00 00 00 sum (xor) ( H_2 (x) ( len(A) || len(C) ) ): 00000: CA 1E F8 92 71 EA 60 C4 53 9E 40 EB 26 C2 80 5D Tag T: 00000: 79 01 E9 EA 20 85 CD 24 7E D2 49 69 5F 9F 8A 85¶
Test vectors for the Magma block cipher (n = 64, k = 256) are defined in [GOST3412-2015] (the English version can be found in [RFC8891]).¶
Encryption key K: 00000: FF EE DD CC BB AA 99 88 77 66 55 44 33 22 11 00 00010: F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA FB FC FD FE FF ICN: 00000: 12 DE F0 6B 3C 13 0A 59 Associated authenticated data A: 00000: 01 01 01 01 01 01 01 01 02 02 02 02 02 02 02 02 00010: 03 03 03 03 03 03 03 03 04 04 04 04 04 04 04 04 00020: 05 05 05 05 05 05 05 05 EA Plaintext P: 00000: FF EE DD CC BB AA 99 88 11 22 33 44 55 66 77 00 00010: 88 99 AA BB CC EE FF 0A 00 11 22 33 44 55 66 77 00020: 99 AA BB CC EE FF 0A 00 11 22 33 44 55 66 77 88 00030: AA BB CC EE FF 0A 00 11 22 33 44 55 66 77 88 99 00040: AA BB CC¶
Encryption step:¶
0^1 || ICN: 00000: 12 DE F0 6B 3C 13 0A 59 Y_1: 00000: 56 23 89 01 62 DE 31 BF E_K(Y_1): 00000: 38 7B DB A0 E4 34 39 B3 Y_2: 00000: 56 23 89 01 62 DE 31 C0 E_K(Y_2): 00000: 94 33 00 06 10 F7 F2 AE Y_3: 00000: 56 23 89 01 62 DE 31 C1 E_K(Y_3): 00000: 97 B7 AA 6D 73 C5 87 57 Y_4: 00000: 56 23 89 01 62 DE 31 C2 E_K(Y_4): 00000: 94 15 52 8B FF C9 E8 0A Y_5: 00000: 56 23 89 01 62 DE 31 C3 E_K(Y_5): 00000: 03 F7 68 BF F1 82 D6 70 Y_6: 00000: 56 23 89 01 62 DE 31 C4 E_K(Y_6): 00000: FD 05 F8 4E 9B 09 D2 FE Y_7: 00000: 56 23 89 01 62 DE 31 C5 E_K(Y_7): 00000: DA 4D 90 8A 95 B1 75 C4 Y_8: 00000: 56 23 89 01 62 DE 31 C6 E_K(Y_8): 00000: 65 99 73 96 DA C2 4B D7 Y_9: 00000: 56 23 89 01 62 DE 31 C7 E_K(Y_9): 00000: A9 00 50 4A 14 8D EE 26 C: 00000: C7 95 06 6C 5F 9E A0 3B 85 11 33 42 45 91 85 AE 00010: 1F 2E 00 D6 BF 2B 78 5D 94 04 70 B8 BB 9C 8E 7D 00020: 9A 5D D3 73 1F 7D DC 70 EC 27 CB 0A CE 6F A5 76 00030: 70 F6 5C 64 6A BB 75 D5 47 AA 37 C3 BC B5 C3 4E 00040: 03 BB 9C¶
Padding step:¶
A_1 || ... || A_h: 00000: 01 01 01 01 01 01 01 01 02 02 02 02 02 02 02 02 00010: 03 03 03 03 03 03 03 03 04 04 04 04 04 04 04 04 00020: 05 05 05 05 05 05 05 05 EA 00 00 00 00 00 00 00 C_1 || ... || C_q: 00000: C7 95 06 6C 5F 9E A0 3B 85 11 33 42 45 91 85 AE 00010: 1F 2E 00 D6 BF 2B 78 5D 94 04 70 B8 BB 9C 8E 7D 00020: 9A 5D D3 73 1F 7D DC 70 EC 27 CB 0A CE 6F A5 76 00030: 70 F6 5C 64 6A BB 75 D5 47 AA 37 C3 BC B5 C3 4E 00040: 03 BB 9C 00 00 00 00 00¶
Authentication tag T generation step:¶
1^1 || ICN: 00000: 92 DE F0 6B 3C 13 0A 59 Z_1: 00000: 2B 07 3F 04 94 F3 72 A0 H_1: 00000: 70 8A 78 19 1C DD 22 AA current sum: 00000: D6 BB 5B EA 81 93 12 62 Z_2: 00000: 2B 07 3F 05 94 F3 72 A0 H_2: 00000: 6F 02 CC 46 4B 2F A0 A3 current sum: 00000: DD 1C 82 4E 91 78 49 A5 Z_3: 00000: 2B 07 3F 06 94 F3 72 A0 H_3: 00000: 9F 81 F2 26 FD 19 6F 05 current sum: 00000: 05 89 22 17 F6 5A DA C7 Z_4: 00000: 2B 07 3F 07 94 F3 72 A0 H_4: 00000: B9 C2 AC 9B E5 B5 DF F9 current sum: 00000: D1 DB 9B 7F C4 9E 7C 97 Z_5: 00000: 2B 07 3F 08 94 F3 72 A0 H_5: 00000: 74 B5 EC 96 55 1B F8 88 current sum: 00000: 56 45 F6 B5 18 5C B7 1A Z_6: 00000: 2B 07 3F 09 94 F3 72 A0 H_6: 00000: 7E B0 21 A4 03 5B 04 C3 current sum: 00000: 3F C2 C2 E6 FB EE D0 4D Z_7: 00000: 2B 07 3F 0A 94 F3 72 A0 H_7: 00000: C2 A9 C3 A8 70 4D 9B B0 current sum: 00000: 15 47 1F B5 CD 8E 6C 02 Z_8: 00000: 2B 07 3F 0B 94 F3 72 A0 H_8: 00000: F5 D5 05 A8 7B 83 83 B5 current sum: 00000: 12 56 78 96 1D 40 E0 93 Z_9: 00000: 2B 07 3F 0C 94 F3 72 A0 H_9: 00000: F7 95 E7 5F DE B8 93 3C current sum: 00000: 6E F4 0A B0 C1 5F 20 48 Z_10: 00000: 2B 07 3F 0D 94 F3 72 A0 H_10: 00000: 65 A1 A3 E6 80 F0 81 45 current sum: 00000: A4 64 A7 08 FF 45 14 22 Z_11: 00000: 2B 07 3F 0E 94 F3 72 A0 H_11: 00000: 1C 74 A5 76 4C B0 D5 95 current sum: 00000: 60 94 4E 05 D0 85 75 14 Z_12: 00000: 2B 07 3F 0F 94 F3 72 A0 H_12: 00000: DC 84 47 A5 14 E7 83 E7 current sum: 00000: EE 98 B9 B5 0F F7 83 E8 Z_13: 00000: 2B 07 3F 10 94 F3 72 A0 H_13: 00000: A7 E3 AF E0 04 EE 16 E3 current sum: 00000: C0 39 0F A2 28 AF 6D CB Z_14: 00000: 2B 07 3F 11 94 F3 72 A0 H_14: 00000: A5 AA BB 0B 79 80 D0 71 current sum: 00000: 73 E0 6E 07 EF 37 CD CC Z_15: 00000: 2B 07 3F 12 94 F3 72 A0 H_15: 00000: 6E 10 4C C9 33 52 5C 5D current sum: 00000: 2F 40 69 0A EB 53 F5 39 Z_16: 00000: 2B 07 3F 13 94 F3 72 A0 H_16: 00000: 83 11 B6 02 4A A9 66 C1 len(A) || len(C): 00000: 00 00 01 48 00 00 02 18 sum (xor) ( H_16 (x) ( len(A) || len(C) ) ): 00000: 73 CE F4 4B AE 6B DB 61 Tag T: 00000: A7 92 80 69 AA 10 FD 10¶
Encryption key K: 00000: 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 FE 00010: DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF 88 ICN: 00000: 00 77 66 55 44 33 22 11 Associated authenticated data A: 00000: Plaintext P: 00000: 22 33 44 55 66 77 00 FF¶
Encryption step:¶
0^1 || ICN: 00000: 00 77 66 55 44 33 22 11 Y_1: 00000: 5B 2A 7E 60 4F 9F BB 95 E_K(Y_1): 00000: 48 A6 A5 17 0D 52 9D B1 C: 00000: 6A 95 E1 42 6B 25 9D 4E¶
Padding step:¶
A_1 || ... || A_h: 00000: C_1 || ... || C_q: 00000: 6A 95 E1 42 6B 25 9D 4E¶
Authentication tag T generation step:¶
1^1 || ICN: 00000: 80 77 66 55 44 33 22 11 Z_1: 00000: 59 73 54 78 7E 52 E6 EB H_1: 00000: EC E3 F9 DA 11 8C 7D 95 current sum: 00000: 25 D0 E4 20 7B 6B F6 3D Z_2: 00000: 59 73 54 79 7E 52 E6 EB H_2: 00000: 31 0C 0D AC C9 D0 4D 93 len(A) || len(C): 00000: 00 00 00 00 00 00 00 40 sum (xor) ( H_2 (x) ( len(A) || len(C) ) ): 00000: 66 D3 8F 12 0F 78 92 49 Tag T: 00000: 33 4E E2 70 45 0B EC 9E¶