Independent Submission V. Dolmatov, Ed. Request for Comments: 8891 JSC "NPK Kryptonite" Updates: 5830 D. Baryshkov Category: Informational Auriga, Inc. ISSN: 20701721 September 2020
GOST R 34.122015: Block Cipher "Magma"
Abstract

In addition to a new cipher with a block length of n=128 bits (referred to as "Kuznyechik" and described in RFC 7801), Russian Federal standard GOST R 34.122015 includes an updated version of the block cipher with a block length of n=64 bits and key length of k=256 bits, which is also referred to as "Magma". The algorithm is an updated version of an older block cipher with a block length of n=64 bits described in GOST 2814789 (RFC 5830). This document is intended to be a source of information about the updated version of the 64bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of the GOST 64bit cipher with the revised version of the cipher for encryption and decryption.
Status of This Memo

This document is not an Internet Standards Track specification; it is published for informational purposes.
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Table of Contents

1. Introduction 2. General Information 3. Definitions and Notation 3.1. Definitions 3.2. Notation 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 [GOSTR34122015] 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 computeraided 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 the 64bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of a GOST 64bit cipher with the revised version of the cipher for encryption and decryption.
2. General Information

The Russian Federal standard [GOSTR34122015] 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 jointstock company "Information Technologies and Communication Systems" (InfoTeCS JSC). GOST R 34.122015 was approved and introduced by Decree #749 of the Federal Agency on Technical Regulating and Metrology on June 19, 2015.
Terms and concepts in the specification comply with the following international standards:
* ISO/IEC 10116 [ISOIEC10116] * series of standards ISO/IEC 18033 [ISOIEC180331][ISOIEC180333]
3. Definitions and Notation

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

encryption algorithm: process that transforms plaintext into ciphertext (Clause 2.19 of [ISOIEC180331]) decryption algorithm: process that transforms ciphertext into plaintext (Clause 2.14 of [ISOIEC180331]) basic block cipher: block cipher that, for a given key, provides a single invertible mapping of the set of fixedlength plaintext blocks into ciphertext blocks of the same length block: string of bits of a defined length (Clause 2.6 of [ISOIEC180331]) 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 [ISOIEC180331])

Note: In GOST R 34.122015, 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 [ISOIEC180331]) round key: sequence of symbols that 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 [ISOIEC180331])

Note:

In GOST R 34.122015, the key must be a binary sequence.
plaintext: unencrypted information (Clause 3.11 of [ISOIEC10116]) key schedule: calculation of round keys from the key, decryption: reversal of a corresponding encipherment (Clause 2.13 of [ISOIEC180331]) 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 [ISOIEC180331]) cipher: alternative term for encipherment system (Clause 2.20 of [ISOIEC180331]) ciphertext: data that has been transformed to hide its information content (Clause 3.3 of [ISOIEC10116])

3.2. Notation

The following notation is 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 nonnegative 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) AB 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) exclusiveor of two binary strings of the same length
[+] addition in the ring Z_(2^32) Vec_s: Z_(2^s) > V_s bijective mapping that 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^(s1)*z_(s1)), where z_i in {0, 1}, i = 0, ..., n1, the equality Vec_s(z) = z_(s1)...z_1z_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^(s1) 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_(9i), 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 document has no IANA actions.
7. Security Considerations

This entire document is about security considerations.
Unlike [RFC5830] (GOST 2814789), but like [RFC7801], this specification does not define exact block modes that should be used together with the updated Magma cipher. One is free to select block modes depending on the protocol and necessity.
8. References
8.1. Normative References

[GOSTR34122015]



Federal Agency on Technical Regulating and Metrology, "Information technology. Cryptographic data security. Block ciphers.", GOST R 34.122015, 2015.


[RFC5830] Dolmatov, V., Ed., "GOST 2814789: Encryption, Decryption, and Message Authentication Code (MAC) Algorithms", RFC 5830, DOI 10.17487/RFC5830, March 2010, <https://www.rfceditor.org/info/rfc5830>. [RFC7801] Dolmatov, V., Ed., "GOST R 34.122015: Block Cipher "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016, <https://www.rfceditor.org/info/rfc7801>.
8.2. Informative References

[GOST2814789]



Government Committee of the USSR for Standards, "Cryptographic Protection for Data Processing System, GOST 2814789, Gosudarstvennyi Standard of USSR", 1989.


[ISOIEC10116]
ISO/IEC, "Information technology  Security techniques  Modes of operation for an nbit block cipher", ISO/ IEC 10116, 2017.
[ISOIEC180331]
ISO/IEC, "Information technology  Security techniques  Encryption algorithms  Part 1: General", ISO/ IEC 180331:2015, 2015.
[ISOIEC180333]
ISO/IEC, "Information technology  Security techniques  Encryption algorithms  Part 3: Block ciphers", ISO/ IEC 180333:2010, 2010. [RFC7836] Smyshlyaev, S., Ed., 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 34.102012 and GOST R 34.112012", RFC 7836, DOI 10.17487/RFC7836, March 2016, <https://www.rfceditor.org/info/rfc7836>.
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,
the 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 Appendix 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 Appendix 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 the [GOSTR34122015] standard. The order of terms in both parts of Section 3 comes from the original text. Combining [RFC7801] with this document will create a complete translation of [GOSTR34122015] into English.
Algorithmically, Magma is a variation of the block cipher defined in [RFC5830] ([GOST2814789]) with the following clarifications and minor modifications:
1. SBOX set is fixed at idtc26gost28147paramZ (see Appendix C of [RFC7836]);
 key is parsed as a single bigendian integer (compared to the littleendian approach used in [GOST2814789]), which results in different subkey values being used;
 data bytes are also parsed as a single bigendian integer (instead of being parsed as littleendian integer).
Authors' Addresses

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