Multilinear Galois Mode (MGM)

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.¶

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.¶

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."¶

This Internet-Draft will expire on 14 October 2021.¶

Copyright Notice

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. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.¶

Table of Contents

1. Introduction

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 [R1323565.1.026-2019]. 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.¶

3. Basic Terms and Definitions

This document uses the following terms and definitions for the sets and operations on the elements of these sets:¶

V*

the set of all bit strings of a finite length (hereinafter referred to as strings), including the empty string; substrings and string components are enumerated from right to left starting from zero;¶

V_s

the set of all bit strings of length s, where s is a non-negative integer. For s = 0, the V_0 consists of a single empty string;¶

|X|

the bit length of the bit string X (if X is an empty string, then |X| = 0);¶

X || Y

concatenation of strings X and Y both belonging to V*, i.e., a string from V_{|X|+|Y|}, where the left substring from V_{|X|} is equal to X, and the right substring from V_{|Y|} is equal to Y;¶

a^s

the string in V_s that consists of s 'a' bits;¶

(xor)

exclusive-or of the two bit strings of the same length;¶

Z_{2^s}

ring of residues modulo 2^s;¶

MSB_i: 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);¶

Int_s: 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);¶

Vec_s: Z_{2^s} -> V_s

the transformation inverse to the mapping Int_s (the interpretation of an integer as a bit string);¶

E_K: V_n -> V_n

the block cipher permutation under the key K in V_k;¶

k

the bit length of the block cipher key;¶

n

the block size of the block cipher (in bits);¶

len: 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;¶

[+]

the addition operation in Z_{2^{n/2}}, where n is the block size of the used block cipher;¶

(x)

the transformation that maps two strings X = (x_{n-1}, ... , x_0) in V_n and Y = (y_{n-1}, ... , y_0) in V_n into the string Z = X (x) Y = (z_{n-1}, ... , z_0) in V_n; the string Z corresponds to the polynomial Z(w) = z_{n-1} * w^{n-1} + ... + z_1 * w + z_0 which is the result of multiplying the polynomials X(w) = x_{n-1} * w^{n-1} + ... + x_1 * w + x_0 and Y(w) = y_{n-1} * w^{n-1} + ... + y_1 * w + y_0 in the field GF(2^n), where n is the block size of the used block cipher; if n = 64, then the field polynomial is equal to f(w) = w^64 + w^4 + w^3 + w + 1; if n = 128, then the field polynomial is equal to f(w) = w^128 + w^7 + w^2 + w + 1;¶

incr_l: V_n -> V_n

the transformation that maps a string L || R, where L, R in V_{n/2}, into the string incr_l(L || R) = Vec_{n/2}(Int_{n/2}(L) [+] 1) || R;¶

incr_r: V_n -> V_n

the transformation that maps a string L || R, where L, R in V_{n/2}, into the string incr_r(L || R) = L || Vec_{n/2}(Int_{n/2}(R) [+] 1).¶

5. Rationale

The MGM was originally proposed in [PDMODE].¶

From the operational point of view the MGM is designed to be parallelizable, inverse-free, online and to provide availability of precomputations.¶

Parallelizability of the 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 to process message even if it is not completely received (so its length is unknown). To provide this property the MGM uses blocks E_K(Y_i) and H_i which are produced basing on two independent source blocks Y_i and Z_i.¶

Availability of precomputations for the MGM means the possibility to calculate H_i and E_K(Y_i) even before data is retrieved. It holds again due to the usage of counters for calculating them.¶

6. Security Considerations

The security properties of the MGM are based on the following:¶

• Different functions generating the counter values:¶

  The functions incr_r and incr_l are chosen to minimize intersection (if it happens) of counter values Y_i and Z_i.¶

• Encryption of the multilinear function output:¶

  It allows to resist attacks based on padding and linear properties (see [Ferg05] for details).¶

• Multilinear function for authentication:¶

  It allows to resist the small subgroup attacks [Saar12].¶

• Encryption of the nonces (0^1 || ICN) and (1^1 || ICN):¶

  The use of this encryption minimizes the number of plaintext/ciphertext pairs of blocks known to an adversary. It allows to resist attacks that need substantial amount of such material (e.g., linear and differential cryptanalysis, side-channel attacks).¶

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 attack.¶

Security analysis for MGM with E_K being a random permutation was performed in [SecMGM]. More precisely, the bounds for confidentiality advantage (CA) and integrity advantage (IA) (for details see [I-D.irtf-cfrg-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 [I-D.irtf-cfrg-aead-limits]).¶

7. IANA Considerations

This document does not require any IANA actions.¶

Appendix A. Test Vectors

-------------------------Example 1--------------------------

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

1. 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

2. 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


3. 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

-------------------------Example 2--------------------------

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:

1. Encryption step:

C:
00000:

2. 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:


3. 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

-------------------------Example 1--------------------------

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

1. 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

2. 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


3. 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

-------------------------Example 2--------------------------

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

1. 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

2. Padding step:

A_1 || ... || A_h:
00000:

C_1 || ... || C_q:
00000:   6A 95 E1 42 6B 25 9D 4E


3. 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

Appendix B. Contributors

• Evgeny Alekseev¶

  CryptoPro¶

  alekseev@cryptopro.ru¶

• Alexandra Babueva¶

  CryptoPro¶

  babueva@cryptopro.ru¶

• Lilia Akhmetzyanova¶

  CryptoPro¶

  lah@cryptopro.ru¶

• Grigory Marshalko¶

  TC 26¶

  marshalko_gb@tc26.ru¶

• Vladimir Rudskoy¶

  TC 26¶

  rudskoy_vi@tc26.ru¶

• Alexey Nesterenko¶

  National Research University Higher School of Economics¶

  anesterenko@hse.ru¶

• Lidia Nikiforova¶

  CryptoPro¶

  nikiforova@cryptopro.ru¶

Authors' Addresses