Internet Engineering Task Force V. Dolmatov, Ed.
Internet-Draft JSC "NPK Kryptonite"
Updates: 5830 (if approved) D. Baryshkov
Intended status: Informational Auriga, Inc
Expires: September 23, 2020 March 22, 2020

GOST R 34.12-2015: Block Cipher "Magma"
draft-dolmatov-magma-06

Abstract

In addition to a new cipher with block length of n=128 bits (referred to as "Kyznyechik" and described in RFC 7801) Russian Federal standard GOST R 34.12-2015 includes an updated version of the block cipher with block length of n=64 bits and key length k=256 bits, which is also referred to as "Magma". The algorithm is an updated version of an older block cipher with block length of n=64 bits described in GOST 28147-89 (RFC 5830). This document is intended to be a source of information about the updated version of the 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of GOST 64-bit cipher with the revised version of the cipher for encryption and decryption.

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Table of Contents

1. Introduction

The Russian Federal standard [GOSTR3412-2015] specifies basic block ciphers used as cryptographic techniques for information processing and information protection including the provision of confidentiality, authenticity, and integrity of information during information transmission, processing and storage in computer-aided systems.

The cryptographic algorithms defined in this specification are designed both for hardware and software implementation. They comply with modern cryptographic requirements, and put no restrictions on the confidentiality level of the protected information.

This document is intended to be a source of information about the updated version of 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of GOST 64-bit cipher with the revised version of the cipher for encryption and decryption.

2. General Information

The Russian Federal standard [GOSTR3412-2015] was developed by the Center for Information Protection and Special Communications of the Federal Security Service of the Russian Federation with participation of the Open Joint-Stock company "Information Technologies and Communication Systems" (InfoTeCS JSC). GOST R 34.12-2015 was approved and introduced by Decree #749 of the Federal Agency on Technical Regulating and Metrology on 19.06.2015.

Terms and concepts in the specification comply with the following international standards:

3. Definitions and Notations

The following terms and their corresponding definitions are used in the specification.

3.1. Definitions

Definitions

3.2. Notations

The following notations are used in the specification:

V*
the set of all binary vector-strings of a finite length (hereinafter referred to as the strings) including the empty string,
V_s
the set of all binary strings of length s, where s is a non-negative integer; substrings and string components are enumerated from right to left starting from zero,
U[*]W
direct (Cartesian) product of two sets U and W,
|A|
the number of components (the length) of a string A belonging to V* (if A is an empty string, then |A| = 0),
A||B
concatenation of strings A and B both belonging to V*, i.e., a string from V_(|A|+|B|), where the left substring from V_|A| is equal to A and the right substring from V_|B| is equal to B,
A<<<_11
cyclic rotation of string A belonging to V_32 by 11 components in the direction of components having greater indices,
Z_(2^n)
ring of residues modulo 2^n,
(xor)
exclusive-or of the two binary strings of the same length,
[+]
addition in the ring Z_(2^32)
Vec_s: Z_(2^s) -> V_s
bijective mapping which maps an element from ring Z_(2^s) into its binary representation, i.e., for an element z of the ring Z_(2^s), represented by the residue z_0 + (2*z_1) + ... + (2^(s-1)*z_(s-1)), where z_i in {0, 1}, i = 0, ..., n-1, the equality Vec_s(z) = z_(s-1)||...||z_1||z_0 holds,
Int_s: V_s -> Z_(2^s)
the mapping inverse to the mapping Vec_s, i.e., Int_s = Vec_s^(-1),
PS
composition of mappings, where the mapping S applies first,
P^s
composition of mappings P^(s-1) and P, where P^1=P,

4. Parameter Values

4.1. Nonlinear Bijection

The bijective nonlinear mapping is a set of substitutions:

Pi_i = Vec_4 Pi'_i Int_4: V_4 -> V_4,

where

Pi'_i: Z_(2^4) -> Z_(2^4), i = 0, 1, ..., 7.

The values of the substitution Pi' are specified below as arrays

Pi'_i = (Pi'_i(0), Pi'_i(1), ... , Pi'_i(15)), i = 0, 1, ..., 7:

Pi'_0 = (12, 4, 6, 2, 10, 5, 11, 9, 14, 8, 13, 7, 0, 3, 15, 1);
Pi'_1 = (6, 8, 2, 3, 9, 10, 5, 12, 1, 14, 4, 7, 11, 13, 0, 15);
Pi'_2 = (11, 3, 5, 8, 2, 15, 10, 13, 14, 1, 7, 4, 12, 9, 6, 0);
Pi'_3 = (12, 8, 2, 1, 13, 4, 15, 6, 7, 0, 10, 5, 3, 14, 9, 11);
Pi'_4 = (7, 15, 5, 10, 8, 1, 6, 13, 0, 9, 3, 14, 11, 4, 2, 12);
Pi'_5 = (5, 13, 15, 6, 9, 2, 12, 10, 11, 7, 8, 1, 4, 3, 14, 0);
Pi'_6 = (8, 14, 2, 5, 6, 9, 1, 12, 15, 4, 11, 0, 13, 10, 3, 7);
Pi'_7 = (1, 7, 14, 13, 0, 5, 8, 3, 4, 15, 10, 6, 9, 12, 11, 2);

4.2. Transformations

The following transformations are applicable for encryption and decryption algorithms:

t: V_32 -> V_32
t(a) = t(a_7||...||a_0) = Pi_7(a_7)||...||Pi_0(a_0), where a=a_7||...||a_0 belongs to V_32, a_i belongs to V_4, i=0, 1, ..., 7;
g[k]: V_32 -> V_32
g[k](a) = (t(Vec_32(Int_32(a) [+] Int_32(k)))) <<<_11, where k, a belong to V_32;
G[k]: V_32[*]V_32 -> V_32[*]V_32
G[k](a_1, a_0) = (a_0, g[k](a_0) (xor) a_1), where k, a_0, a_1 belong to V_32;
G^*[k]: V_32[*]V_32 -> V_64
G^*[k](a_1, a_0) = (g[k](a_0) (xor) a_1) || a_0, where k, a_0, a_1 belong to V_32.

4.3. Key Schedule

Round keys K_i belonging to V_32, i=1, 2, ..., 32 are derived from key K=k_255||...||k_0 belonging to V_256, k_i belongs to V_1, i=0, 1, ..., 255, as follows:

K_1=k_255||...||k_224;
K_2=k_223||...||k_192;
K_3=k_191||...||k_160;
K_4=k_159||...||k_128;
K_5=k_127||...||k_96;
K_6=k_95||...||k_64;
K_7=k_63||...||k_32;
K_8=k_31||...||k_0;
K_(i+8)=K_i, i = 1, 2, ..., 8;
K_(i+16)=K_i, i = 1, 2, ..., 8;
K_(i+24)=K_(9-i), i = 1, 2, ..., 8.

5. Basic Encryption Algorithm

5.1. Encryption

Depending on the values of round keys K_1,...,K_32, the encryption algorithm is a substitution E_(K_1,...,K_32) defined as follows:

E_(K_1,...,K_32)(a)=G^*[K_32]G[K_31]...G[K_2]G[K_1](a_1, a_0),

where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.

5.2. Decryption

Depending on the values of round keys K_1,...,K_32, the decryption algorithm is a substitution D_(K_1,...,K_32) defined as follows:

D_(K_1,...,K_32)(a)=G^*[K_1]G[K_2]...G[K_31]G[K_32](a_1, a_0),

where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.

6. IANA Considerations

This memo includes no request to IANA.

7. Security Considerations

This entire document is about security considerations.

Unlike [RFC5830] (GOST 28147-89), but like [RFC7801] this specification does not define exact block modes which should be used together with updated Magma cipher. One is free to select block modes depending on the protocol and necessity.

8. References

8.1. Normative References

[GOSTR3412-2015] Federal Agency on Technical Regulating and Metrology, "Information technology. Cryptographic data security. Block ciphers. GOST R 34.12-2015", 2015.
[RFC5830] Dolmatov, V., "GOST 28147-89: Encryption, Decryption, and Message Authentication Code (MAC) Algorithms", RFC 5830, DOI 10.17487/RFC5830, March 2010.
[RFC7801] Dolmatov, V., "GOST R 34.12-2015: Block Cipher "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016.

8.2. Informative References

[GOST28147-89] Government Committee of the USSR for Standards, ""Cryptographic Protection for Data Processing System", GOST 28147-89, Gosudarstvennyi Standard of USSR", 1989.
[ISO-IEC10116] ISO-IEC, "Information technology - Security techniques - Modes of operation for an n-bit block cipher, ISO-IEC 10116", 2006.
[ISO-IEC18033-1] ISO-IEC, "Information technology - Security techniques - Encryption algorithms - Part 1: General, ISO-IEC 18033-1", 2013.
[ISO-IEC18033-3] ISO-IEC, "Information technology - Security techniques - Encryption algorithms - Part 3: Block ciphers, ISO-IEC 18033-3", 2010.
[RFC7836] Smyshlyaev, S., Alekseev, E., Oshkin, I., Popov, V., Leontiev, S., Podobaev, V. and D. Belyavsky, "Guidelines on the Cryptographic Algorithms to Accompany the Usage of Standards GOST R 34.10-2012 and GOST R 34.11-2012", RFC 7836, DOI 10.17487/RFC7836, March 2016.

Appendix A. Test Examples

This section is for information only and is not a normative part of the specification.

A.1. Transformation t

t(fdb97531) = 2a196f34,
t(2a196f34) = ebd9f03a,
t(ebd9f03a) = b039bb3d,
t(b039bb3d) = 68695433.

A.2. Transformation g

g[87654321](fedcba98) = fdcbc20c,
g[fdcbc20c](87654321) = 7e791a4b,
g[7e791a4b](fdcbc20c) = c76549ec,
g[c76549ec](7e791a4b) = 9791c849.

A.3. Key schedule

With key set to

K = ffeeddccbbaa99887766554433221100f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff,

following round keys are generated:

K_1 = ffeeddcc,
K_2 = bbaa9988,
K_3 = 77665544,
K_4 = 33221100,
K_5 = f0f1f2f3,
K_6 = f4f5f6f7,
K_7 = f8f9fafb,
K_8 = fcfdfeff,

K_9 = ffeeddcc,
K_10 = bbaa9988,
K_11 = 77665544,
K_12 = 33221100,
K_13 = f0f1f2f3,
K_14 = f4f5f6f7,
K_15 = f8f9fafb,
K_16 = fcfdfeff,

K_17 = ffeeddcc,
K_18 = bbaa9988,
K_19 = 77665544,
K_20 = 33221100,
K_21 = f0f1f2f3,
K_22 = f4f5f6f7,
K_23 = f8f9fafb,
K_24 = fcfdfeff,

K_25 = fcfdfeff,
K_26 = f8f9fafb,
K_27 = f4f5f6f7,
K_28 = f0f1f2f3,
K_29 = 33221100,
K_30 = 77665544,
K_31 = bbaa9988,
K_32 = ffeeddcc.

A.4. Test Encryption

In this test example, encryption is performed on the round keys specified in clause A.3. Let the plaintext be

a = fedcba9876543210,

then

(a_1, a_0) = (fedcba98, 76543210),
G[K_1](a_1, a_0) = (76543210, 28da3b14),
G[K_2]G[K_1](a_1, a_0) = (28da3b14, b14337a5),
G[K_3]...G[K_1](a_1, a_0) = (b14337a5, 633a7c68),
G[K_4]...G[K_1](a_1, a_0) = (633a7c68, ea89c02c),
G[K_5]...G[K_1](a_1, a_0) = (ea89c02c, 11fe726d),
G[K_6]...G[K_1](a_1, a_0) = (11fe726d, ad0310a4),
G[K_7]...G[K_1](a_1, a_0) = (ad0310a4, 37d97f25),
G[K_8]...G[K_1](a_1, a_0) = (37d97f25, 46324615),
G[K_9]...G[K_1](a_1, a_0) = (46324615, ce995f2a),
G[K_10]...G[K_1](a_1, a_0) = (ce995f2a, 93c1f449),
G[K_11]...G[K_1](a_1, a_0) = (93c1f449, 4811c7ad),
G[K_12]...G[K_1](a_1, a_0) = (4811c7ad, c4b3edca),
G[K_13]...G[K_1](a_1, a_0) = (c4b3edca, 44ca5ce1),
G[K_14]...G[K_1](a_1, a_0) = (44ca5ce1, fef51b68),
G[K_15]...G[K_1](a_1, a_0) = (fef51b68, 2098cd86)
G[K_16]...G[K_1](a_1, a_0) = (2098cd86, 4f15b0bb),
G[K_17]...G[K_1](a_1, a_0) = (4f15b0bb, e32805bc),
G[K_18]...G[K_1](a_1, a_0) = (e32805bc, e7116722),
G[K_19]...G[K_1](a_1, a_0) = (e7116722, 89cadf21),
G[K_20]...G[K_1](a_1, a_0) = (89cadf21, bac8444d),
G[K_21]...G[K_1](a_1, a_0) = (bac8444d, 11263a21),
G[K_22]...G[K_1](a_1, a_0) = (11263a21, 625434c3),
G[K_23]...G[K_1](a_1, a_0) = (625434c3, 8025c0a5),
G[K_24]...G[K_1](a_1, a_0) = (8025c0a5, b0d66514),
G[K_25]...G[K_1](a_1, a_0) = (b0d66514, 47b1d5f4),
G[K_26]...G[K_1](a_1, a_0) = (47b1d5f4, c78e6d50),
G[K_27]...G[K_1](a_1, a_0) = (c78e6d50, 80251e99),
G[K_28]...G[K_1](a_1, a_0) = (80251e99, 2b96eca6),
G[K_29]...G[K_1](a_1, a_0) = (2b96eca6, 05ef4401),
G[K_30]...G[K_1](a_1, a_0) = (05ef4401, 239a4577),
G[K_31]...G[K_1](a_1, a_0) = (239a4577, c2d8ca3d).

Then the ciphertext is

b = G^*[K_32]G[K_31]...G[K_1](a_1, a_0) = 4ee901e5c2d8ca3d.

A.5. Test Decryption

In this test example, decryption is performed on the round keys specified in clause A.3. Let the ciphertext be

b = 4ee901e5c2d8ca3d,

then

(b_1, b_0) = (4ee901e5, c2d8ca3d),
G[K_32](b_1, b_0) = (c2d8ca3d, 239a4577),
G[K_31]G[K_32](b_1, b_0) = (239a4577, 05ef4401),
G[K_30]...G[K_32](b_1, b_0) = (05ef4401, 2b96eca6),
G[K_29]...G[K_32](b_1, b_0) = (2b96eca6, 80251e99),
G[K_28]...G[K_32](b_1, b_0) = (80251e99, c78e6d50),
G[K_27]...G[K_32](b_1, b_0) = (c78e6d50, 47b1d5f4),
G[K_26]...G[K_32](b_1, b_0) = (47b1d5f4, b0d66514),
G[K_25]...G[K_32](b_1, b_0) = (b0d66514, 8025c0a5),
G[K_24]...G[K_32](b_1, b_0) = (8025c0a5, 625434c3),
G[K_23]...G[K_32](b_1, b_0) = (625434c3, 11263a21),
G[K_22]...G[K_32](b_1, b_0) = (11263a21, bac8444d),
G[K_21]...G[K_32](b_1, b_0) = (bac8444d, 89cadf21),
G[K_20]...G[K_32](b_1, b_0) = (89cadf21, e7116722),
G[K_19]...G[K_32](b_1, b_0) = (e7116722, e32805bc),
G[K_18]...G[K_32](b_1, b_0) = (e32805bc, 4f15b0bb),
G[K_17]...G[K_32](b_1, b_0) = (4f15b0bb, 2098cd86),
G[K_16]...G[K_32](b_1, b_0) = (2098cd86, fef51b68),
G[K_15]...G[K_32](b_1, b_0) = (fef51b68, 44ca5ce1),
G[K_14]...G[K_32](b_1, b_0) = (44ca5ce1, c4b3edca),
G[K_13]...G[K_32](b_1, b_0) = (c4b3edca, 4811c7ad),
G[K_12]...G[K_32](b_1, b_0) = (4811c7ad, 93c1f449),
G[K_11]...G[K_32](b_1, b_0) = (93c1f449, ce995f2a),
G[K_10]...G[K_32](b_1, b_0) = (ce995f2a, 46324615),
G[K_9]...G[K_32](b_1, b_0) = (46324615, 37d97f25),
G[K_8]...G[K_32](b_1, b_0) = (37d97f25, ad0310a4),
G[K_7]...G[K_32](b_1, b_0) = (ad0310a4, 11fe726d),
G[K_6]...G[K_32](b_1, b_0) = (11fe726d, ea89c02c),
G[K_5]...G[K_32](b_1, b_0) = (ea89c02c, 633a7c68),
G[K_4]...G[K_32](b_1, b_0) = (633a7c68, b14337a5),
G[K_3]...G[K_32](b_1, b_0) = (b14337a5, 28da3b14),
G[K_2]...G[K_32](b_1, b_0) = (28da3b14, 76543210).

Then the plaintext is

a = G^*[K_1]G[K_2]...G[K_32](b_1, b_0) = fedcba9876543210.

Appendix B. Background

This specification is a translation of relevant parts of [GOSTR3412-2015] standard. The order of terms in both parts of Section 3 comes from original text. If one combines [RFC7801] with this document, he will have complete translation of [GOSTR3412-2015] into English.

Algoritmically Magma is a variation of block cipher defined in [RFC5830] ([GOST28147-89]) with the following clarifications and minor modifications:

  1. S-BOX set is fixed at id-tc26-gost-28147-param-Z (See Appendix C of [RFC7836]);
  2. key is parsed as a single big-endian integer (compared to little-endian approach used in [GOST28147-89]), which results in different subkey values being used;
  3. data bytes are also parsed as single big-endian integer (instead of being parsed as little-endian integer).

Authors' Addresses

Vasily Dolmatov (editor) JSC "NPK Kryptonite" Spartakovskaya sq., 14, bld 2, JSC "NPK Kryptonite" Moscow, 105082 Russian Federation EMail: vdolmatov@gmail.com
Dmitry Baryshkov Auriga, Inc Torfyanaya Doroga, 7F, office 1410 Saint-Petersburg, 197374 Russian Federation EMail: dbaryshkov@gmail.com