JSC "NPK Kryptonite"

Spartakovskaya sq., 14, bld 2, JSC "NPK Kryptonite" Moscow 105082 Russian Federation vdolmatov@gmail.com

Auriga, Inc.

Torfyanaya Doroga, 7F office 1410 Saint-Petersburg 197374 Russian Federation dbaryshkov@gmail.com

Magma Block Cipher 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 34.12-2015 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 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 the GOST 64-bit cipher with the revised version of the cipher for encryption and decryption.

Introduction The Russian Federal standard 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 the 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of a GOST 64-bit cipher with the revised version of the cipher for encryption and decryption.

General Information The Russian Federal standard 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 June 19, 2015. Terms and concepts in the specification comply with the following international standards:

• ISO/IEC 10116
• series of standards ISO/IEC 18033

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

Definitions

encryption algorithm:

process that transforms plaintext into ciphertext (Clause 2.19 of )

decryption algorithm:

process that transforms ciphertext into plaintext (Clause 2.14 of )

basic block cipher:

block cipher that, 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 )

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 ) 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 )

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 ) Note: In GOST R 34.12-2015, the key must be a binary sequence.

plaintext:

unencrypted information (Clause 3.11 of )

key schedule:

calculation of round keys from the key,

decryption:

reversal of a corresponding encipherment (Clause 2.13 of )

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 )

cipher:

alternative term for encipherment system (Clause 2.20 of )

ciphertext:

data that has been transformed to hide its information content (Clause 3.3 of )

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)

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 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^(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

Parameter Values

Nonlinear Bijection The bijective nonlinear mapping is a set of substitutions: V_4, ]]> where Z_(2^4), i = 0, 1, ..., 7. ]]> The values of the substitution Pi' are specified below as arrays.

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.

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:

Basic Encryption Algorithm

Encryption Depending on the values of round keys K_1,...,K_32, the encryption algorithm is a substitution E_&wj;(K_1,...,K_32) defined as follows: where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.

Decryption Depending on the values of round keys K_1,...,K_32, the decryption algorithm is a substitution D_&wj;(K_1,...,K_32) defined as follows: where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.

IANA Considerations This document has no IANA actions.

Security Considerations This entire document is about security considerations. Unlike (GOST 28147-89), but like , 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.

References Normative References Federal Agency on Technical Regulating and Metrology Informative References Government Committee of the USSR for Standards ISO/IEC ISO/IEC ISO/IEC

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

Transformation t

Transformation g

Key Schedule With key set to the following round keys are generated:

Test Encryption In this test example, encryption is performed on the round keys specified in . Let the plaintext be then Then the ciphertext is

Test Decryption In this test example, decryption is performed on the round keys specified in . Let the ciphertext be then Then the plaintext is

Background This specification is a translation of relevant parts of the standard. The order of terms in both parts of comes from the original text. Combining with this document will create a complete translation of into English. Algorithmically, Magma is a variation of the block cipher defined in () with the following clarifications and minor modifications:

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