GOST R 34.12-2015: Block Cipher "Magma"
draft-dolmatov-magma-04

Abstract

In addition to a new cipher with block length of n=128 bits (referred 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 as "Magma". The algorithm is an updated version of 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 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
• 2. General Information
• 3. Definitions and Notations
• 3.1. Definitions
• 3.2. Notations
• 4. Parameter Values
• 4.1. Nonlinear Bijection
• 4.2. Transformations
• 4.3. Key schedule
• 5. Basic encryption algorithm
• 5.1. Encryption
• 5.2. Decryption
• 6. IANA Considerations
• 7. Security Considerations
• 8. References
• 8.1. Normative References
• 8.2. Informative References
• Appendix A. Test Examples
• A.1. Transformation t
• A.2. Transformation g
• A.3. Key schedule
• A.4. Test Encryption
• A.5. Test Decryption
• Appendix B. Background
• Authors' Addresses

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.

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:

• ISO/IEC 10116 [ISO-IEC10116],
• series of standards ISO/IEC 18033 [ISO-IEC18033-1], [ISO-IEC18033-3].

3. Definitions and Notations

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

3.1. Definitions

Definitions

• encryption algorithm: process which transforms plaintext into ciphertext (Clause 2.19 of [ISO-IEC18033-1]),
• decryption algorithm: process which transforms ciphertext into plaintext (Clause 2.14 of [ISO-IEC18033-1]),
• basic block cipher: block cipher which for a given key provides a single invertible mapping of the set of fixed-length plaintext blocks into ciphertext blocks of the same length,
• block: string of bits of a defined length (Clause 2.6 of [ISO-IEC18033-1]),
• block cipher: symmetric encipherment system with the property that the encryption algorithm operates on a block of plaintext, i.e. a string of bits of a defined length, to yield a block of ciphertext (Clause 2.7 of [ISO-IEC18033-1]),
  • Note: In GOST R 34.12-2015, it is established that the terms "block cipher" and "block encryption algorithm" are synonyms.
• encryption: reversible transformation of data by a cryptographic algorithm to produce ciphertext, i.e., to hide the information content of the data (Clause 2.18 of [ISO-IEC18033-1]),
• round key: sequence of symbols which is calculated from the key and controls a transformation for one round of a block cipher,
• key: sequence of symbols that controls the operation of a cryptographic transformation (e.g., encipherment, decipherment) (Clause 2.21 of [ISO-IEC18033-1]),
  • Note: In GOST R 34.12-2015, the key must be a binary sequence.
• plaintext: unencrypted information (Clause 3.11 of [ISO-IEC10116]),
• key schedule: calculation of round keys from the key,
• decryption: reversal of a corresponding encipherment (Clause 2.13 of [ISO-IEC18033-1]),
• symmetric cryptographic technique: cryptographic technique that uses the same secret key for both the originator's and the recipient's transformation (Clause 2.32 of [ISO-IEC18033-1]),
• cipher: alternative term for encipherment system (Clause 2.20 of [ISO-IEC18033-1]),
• ciphertext: data which has been transformed to hide its information content (Clause 3.3 of [ISO-IEC10116]).

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) and 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

8.2. Informative References

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