Independent Submission V. Dolmatov, Ed. Request for Comments: 7801 Research Computer Center MSU Category: Informational March 2016 ISSN: 2070-1721
GOST R 34.12-2015: Block Cipher "Kuznyechik"
Abstract
This document is intended to be a source of information about the Russian Federal standard GOST R 34.12-2015 describing the block cipher with a block length of n=128 bits and a key length of k=256 bits, which is also referred to as "Kuznyechik". This algorithm is one of the set of Russian cryptographic standard algorithms (called GOST algorithms).
Status of This Memo
This document is not an Internet Standards Track specification; it is published for informational purposes.
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The Russian Federal standard [GOST3412-2015] 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 specified in this standard 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.
The standard applies to development, operation, and modernization of the information systems of various purposes.
The block cipher "Kuznyechik" [GOST3412-2015] 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 June 19, 2015.
Terms and concepts in the standard comply with the following international standards:
o ISO/IEC 10116 [ISO-IEC10116] and
o series of standards ISO/IEC 18033 [ISO-IEC18033-1] [ISO-IEC18033-3].
encryption algorithm: process that transforms plaintext into ciphertext (Section 2.19 of [ISO-IEC18033-1]),
decryption algorithm: process that transforms ciphertext into plaintext (Section 2.14 of [ISO-IEC18033-1]),
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 (Section 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 (Section 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.
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RFC 7801 GOST R 34.12-2015 March 2016
encryption: reversible transformation of data by a cryptographic algorithm to produce ciphertext, i.e., to hide the information content of the data (Section 2.18 of [ISO-IEC18033-1]),
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 and decipherment) (Section 2.21 of [ISO-IEC18033-1]),
Note: In GOST R 34.12-2015, the key must be a binary sequence.
plaintext: unencrypted information (Section 3.11 of [ISO-IEC10116]),
key schedule: calculation of round keys from the key,
decryption: reversal of a corresponding encipherment (Section 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 (Section 2.32 of [ISO-IEC18033-1]),
cipher: alternative term for encipherment system (Section 2.20 of [ISO-IEC18033-1]), and
ciphertext: data that has been transformed to hide its information content (Section 3.3 of [ISO-IEC10116]).
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),
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RFC 7801 GOST R 34.12-2015 March 2016
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,
Z_(2^n) ring of residues modulo 2^n,
Q finite field GF(2)[x]/p(x), where p(x)=x^8+x^7+x^6+x+1 belongs to GF(2)[x]; elements of field Q are represented by integers in such way that element z_0+z_1*theta+...+z_7*theta^7 belonging to Q corresponds to integer z_0+2*z_1+...+2^7*z_7, where z_i=0 or z_i=1, i=0,1,...,7 and theta denotes a residue class modulo p(x) containing x,
(xor) exclusive-or of the two binary strings of the same length,
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),
delta: V_8 -> Q bijective mapping that maps a binary string from V_8 into an element from field Q as follows: string z_7||...||z_1||z_0, where z_i in {0, 1}, i = 0, ..., 7, corresponds to the element z_0+(z_1*theta)+...+(z_7*theta^7) belonging to Z,
nabla: Q -> V8 the mapping inverse to the mapping delta, i.e., delta = nabla^(-1),
PS composition of mappings, where the mapping S applies first, and
P^s composition of mappings P^(s-1) and P, where P^1=P.
The bijective nonlinear mapping is a substitution: Pi = (Vec_8)Pi'(Int_8): V_8 -> V_8, where Pi': Z_(2^8) -> Z_(2^8). The values of the substitution Pi' are specified below as an array Pi' = (Pi'(0), Pi'(1), ... , Pi'(255)):
Pi^(-1) is the inverse of Pi; the values of the substitution Pi^(-1)' are specified below as an array Pi^(-1)' = (Pi^(-1)'(0), Pi^(-1)'(1), ... , Pi^(-1)'(255)):
for all a_i belonging to V_8, i = 0, 1, ..., 15, where the addition and multiplication operations are in the field Q, and constants are elements of the field as defined above.
The following transformations are applicable for encryption and decryption algorithms:
X[x]:V_128->V_128 X[k](a)=k(xor)a, where k, a belong to V_128,
S:V_128-> V_128 S(a)=(a_15||...||a_0)=pi(a_15)||...||pi(a_0), where a_15||...||a_0 belongs to V_128, a_i belongs to V_8, i=0,1,...,15,
S^(-1):V_128-> V_128 the inverse transformation of S, which may be calculated, for example, as follows: S^(-1)(a_15||...||a_0)=pi^(-1) (a_15)||...||pi^(-1)(a_0), where a_15||...||a_0 belongs to V_128, a_i belongs to V_8, i=0,1,...,15,
R:V_128-> V_128 R(a_15||...||a_0)=l(a_15,...,a_0)||a_15||...||a_1, where a_15||...||a_0 belongs to V_128, a_i belongs to V_8, i=0,1,...,15,
L:V_128-> V_128 L(a)=R^(16)(a), where a belongs to V_128,
R^(-1):V_128-> V_128 the inverse transformation of R, which may be calculated, for example, as follows: R^(-1)(a_15||...||a_0)=a_14|| a_13||...||a_0||l(a_14,a_13,...,a_0,a_15), where a_15||...||a_0 belongs to V_128, a_i belongs to V_8, i=0,1,...,15,
L^(-1):V_128-> V_128 L^(-1)(a)=(R^(-1))(16)(a), where a belongs to V_128, and
F[k]:V_128[*]V_128 -> V_128[*]V_128 F[k](a_1,a_0)=(LSX[k](a_1)(xor)a_0,a_1), where k, a_0, a_1 belong to V_128.
[GOST3412-2015] "Information technology. Cryptographic data security. Block ciphers", GOST R 34.12-2015, Federal Agency on Technical Regulating and Metrology, 2015.