RFC 7801 INFORMATIONAL CRYPTOGRAPHY · BLOCK CIPHER
GOST R 34.12-2015: Block Cipher "Kuznyechik"
The Russian GOST block cipher with 128-bit blocks and 256-bit keys, written up for the Internet community.
RFC EDITOR
Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016, <https://www.rfc-editor.org/info/rfc7801>.
BIBTEX
@misc{rfc7801,
series = {Request for Comments},
number = 7801,
howpublished = {RFC 7801},
publisher = {RFC Editor},
doi = {10.17487/RFC7801},
url = {https://www.rfc-editor.org/info/rfc7801},
author = {V. Dolmatov},
title = {{GOST R 34.12-2015: Block Cipher "Kuznyechik"}},
pagetotal = 14,
year = 2016,
month = mar,
} RFC text
Contents
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.
This is a contribution to the RFC Series, independently of any other
RFC stream. The RFC Editor has chosen to publish this document at
its discretion and makes no statement about its value for
implementation or deployment. Documents approved for publication by
the RFC Editor are not a candidate for any level of Internet
Standard; see Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc7801.
Copyright Notice
Copyright (c) 2016 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document.
Table of Contents
1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. General Information . . . . . . . . . . . . . . . . . . . . . 3
3. Definitions and Notations . . . . . . . . . . . . . . . . . . 3
3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 3
3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 4
4. Parameter Values . . . . . . . . . . . . . . . . . . . . . . 6
4.1. Nonlinear Bijection . . . . . . . . . . . . . . . . . . . 6
4.2. Linear Transformation . . . . . . . . . . . . . . . . . . 7
4.3. Transformations . . . . . . . . . . . . . . . . . . . . . 8
4.4. Key Schedule . . . . . . . . . . . . . . . . . . . . . . 9
4.5. Basic Encryption Algorithm . . . . . . . . . . . . . . . 9
4.5.1. Encryption . . . . . . . . . . . . . . . . . . . . . 9
4.5.2. Decryption . . . . . . . . . . . . . . . . . . . . . 9
5. Examples (Informative) . . . . . . . . . . . . . . . . . . . 10
5.1. Transformation S . . . . . . . . . . . . . . . . . . . . 10
5.2. Transformation R . . . . . . . . . . . . . . . . . . . . 10
5.3. Transformation L . . . . . . . . . . . . . . . . . . . . 10
5.4. Key Schedule . . . . . . . . . . . . . . . . . . . . . . 11
5.5. Test Encryption . . . . . . . . . . . . . . . . . . . . . 12
5.6. Test Decryption . . . . . . . . . . . . . . . . . . . . . 13
6. Security Considerations . . . . . . . . . . . . . . . . . . . 13
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 14
7.1. Normative References . . . . . . . . . . . . . . . . . . 14
7.2. Informative References . . . . . . . . . . . . . . . . . 14
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 14
1. Scope
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.
2. General Information
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].
3. Definitions and Notations
The following terms and their corresponding definitions are used in
the standard.
3.1. Definitions
Definitions
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.
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]).
3.2. Notations
The following notations are used in the standard:
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,
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.
4. Parameter Values
4.1. Nonlinear Bijection
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' =
( 252, 238, 221, 17, 207, 110, 49, 22, 251, 196, 250,
218, 35, 197, 4, 77, 233, 119, 240, 219, 147, 46,
153, 186, 23, 54, 241, 187, 20, 205, 95, 193, 249,
24, 101, 90, 226, 92, 239, 33, 129, 28, 60, 66,
139, 1, 142, 79, 5, 132, 2, 174, 227, 106, 143,
160, 6, 11, 237, 152, 127, 212, 211, 31, 235, 52,
44, 81, 234, 200, 72, 171, 242, 42, 104, 162, 253,
58, 206, 204, 181, 112, 14, 86, 8, 12, 118, 18,
191, 114, 19, 71, 156, 183, 93, 135, 21, 161, 150,
41, 16, 123, 154, 199, 243, 145, 120, 111, 157, 158,
178, 177, 50, 117, 25, 61, 255, 53, 138, 126, 109,
84, 198, 128, 195, 189, 13, 87, 223, 245, 36, 169,
62, 168, 67, 201, 215, 121, 214, 246, 124, 34, 185,
3, 224, 15, 236, 222, 122, 148, 176, 188, 220, 232,
40, 80, 78, 51, 10, 74, 167, 151, 96, 115, 30,
0, 98, 68, 26, 184, 56, 130, 100, 159, 38, 65,
173, 69, 70, 146, 39, 94, 85, 47, 140, 163, 165,
125, 105, 213, 149, 59, 7, 88, 179, 64, 134, 172,
29, 247, 48, 55, 107, 228, 136, 217, 231, 137, 225,
27, 131, 73, 76, 63, 248, 254, 141, 83, 170, 144,
202, 216, 133, 97, 32, 113, 103, 164, 45, 43, 9,
91, 203, 155, 37, 208, 190, 229, 108, 82, 89, 166,
116, 210, 230, 244, 180, 192, 209, 102, 175, 194, 57,
75, 99, 182).
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)):
Pi^(-1)' =
( 165, 45, 50, 143, 14, 48, 56, 192, 84, 230, 158,
57, 85, 126, 82, 145, 100, 3, 87, 90, 28, 96,
7, 24, 33, 114, 168, 209, 41, 198, 164, 63, 224,
39, 141, 12, 130, 234, 174, 180, 154, 99, 73, 229,
66, 228, 21, 183, 200, 6, 112, 157, 65, 117, 25,
201, 170, 252, 77, 191, 42, 115, 132, 213, 195, 175,
43, 134, 167, 177, 178, 91, 70, 211, 159, 253, 212,
15, 156, 47, 155, 67, 239, 217, 121, 182, 83, 127,
193, 240, 35, 231, 37, 94, 181, 30, 162, 223, 166,
254, 172, 34, 249, 226, 74, 188, 53, 202, 238, 120,
5, 107, 81, 225, 89, 163, 242, 113, 86, 17, 106,
137, 148, 101, 140, 187, 119, 60, 123, 40, 171, 210,
49, 222, 196, 95, 204, 207, 118, 44, 184, 216, 46,
54, 219, 105, 179, 20, 149, 190, 98, 161, 59, 22,
102, 233, 92, 108, 109, 173, 55, 97, 75, 185, 227,
186, 241, 160, 133, 131, 218, 71, 197, 176, 51, 250,
150, 111, 110, 194, 246, 80, 255, 93, 169, 142, 23,
27, 151, 125, 236, 88, 247, 31, 251, 124, 9, 13,
122, 103, 69, 135, 220, 232, 79, 29, 78, 4, 235,
248, 243, 62, 61, 189, 138, 136, 221, 205, 11, 19,
152, 2, 147, 128, 144, 208, 36, 52, 203, 237, 244,
206, 153, 16, 68, 64, 146, 58, 1, 38, 18, 26,
72, 104, 245, 129, 139, 199, 214, 32, 10, 8, 0,
76, 215, 116 ).
4.2. Linear Transformation
The linear transformation is denoted by l: (V_8)^16 -> V_8, and
defined as:
l(a_15,...,a_0) = nabla(148*delta(a_15) + 32*delta(a_15) +
133*delta(a_13) + 16*delta(a_12) + 194*delta(a_11) +
192*delta(a_10) + 1*delta(a_9) + 251*delta(a_8) + 1*delta(a_7) +
192*delta(a_6) + 194*delta(a_5) + 16*delta(a_4) + 133*delta(a_3) +
32*delta(a_2) + 148*delta(a_1) +1*delta(a_0)),
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.
4.3. Transformations
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.
4.4. Key Schedule
Key schedule uses round constants C_i belonging to V_128, i=1, 2,
..., 32, defined as
C_i=L(Vec_128(i)), i=1,2,...,32.
Round keys K_i, i=1, 2, ..., 10 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_128;
K_2=k_127||...||k_0;
(K_(2i+1),K_(2i+2))=F[C_(8(i-1)+8)]...
F[C_(8(i-1)+1)](K_(2i-1),K_(2i)), i=1,2,3,4.
4.5. Basic Encryption Algorithm
4.5.1. Encryption
Depending on the values of round keys K_1,...,K_10, the encryption
algorithm is a substitution E_(K_1,...,K_10) defined as follows:
E_(K_1,...,K_10)(a)=X[K_10]LSX[K_9]...LSX[K_2]LSX[K_1](a),
where a belongs to V_128.
4.5.2. Decryption
Depending on the values of round keys K_1,...,K_10, the decryption
algorithm is a substitution D_(K_1,...,K_10) defined as follows:
D_(K_1,...,K_10)(a)=X[K_1]L^(-1)S^(-1)X[K_2]...
L^(-1)S^(-1)X[K_9] L^(-1)S^(-1)X[K_10](a),
where a belongs to V_128.
5. Examples (Informative)
This section is for information only and is not a normative part of
the standard.
5.1. Transformation S
S(ffeeddccbbaa99881122334455667700) =
b66cd8887d38e8d77765aeea0c9a7efc,
S(b66cd8887d38e8d77765aeea0c9a7efc) =
559d8dd7bd06cbfe7e7b262523280d39,
S(559d8dd7bd06cbfe7e7b262523280d39) =
0c3322fed531e4630d80ef5c5a81c50b,
S(0c3322fed531e4630d80ef5c5a81c50b) =
23ae65633f842d29c5df529c13f5acda.
5.2. Transformation R
R(00000000000000000000000000000100) =
94000000000000000000000000000001,
R(94000000000000000000000000000001) =
a5940000000000000000000000000000,
R(a5940000000000000000000000000000) =
64a59400000000000000000000000000,
R(64a59400000000000000000000000000) =
0d64a594000000000000000000000000.
5.3. Transformation L
L(64a59400000000000000000000000000) =
d456584dd0e3e84cc3166e4b7fa2890d,
L(d456584dd0e3e84cc3166e4b7fa2890d) =
79d26221b87b584cd42fbc4ffea5de9a,
L(79d26221b87b584cd42fbc4ffea5de9a) =
0e93691a0cfc60408b7b68f66b513c13,
L(0e93691a0cfc60408b7b68f66b513c13) =
e6a8094fee0aa204fd97bcb0b44b8580.
5.4. Key Schedule
In this test example, the key is equal to:
K = 8899aabbccddeeff0011223344556677fedcba9876543210012345678
9abcdef.
K_1 = 8899aabbccddeeff0011223344556677,
K_2 = fedcba98765432100123456789abcdef.
C_1 = 6ea276726c487ab85d27bd10dd849401,
X[C_1](K_1) = e63bdcc9a09594475d369f2399d1f276,
SX[C_1](K_1) = 0998ca37a7947aabb78f4a5ae81b748a,
LSX[C_1](K_1) = 3d0940999db75d6a9257071d5e6144a6,
F[C_1](K_1, K_2) = = (c3d5fa01ebe36f7a9374427ad7ca8949,
8899aabbccddeeff0011223344556677).
C_2 = dc87ece4d890f4b3ba4eb92079cbeb02,
F [C_2]F [C_1](K_1, K_2) = (37777748e56453377d5e262d90903f87,
c3d5fa01ebe36f7a9374427ad7ca8949).
C_3 = b2259a96b4d88e0be7690430a44f7f03,
F[C_3]...F[C_1](K_1, K_2) = (f9eae5f29b2815e31f11ac5d9c29fb01,
37777748e56453377d5e262d90903f87).
C_4 = 7bcd1b0b73e32ba5b79cb140f2551504,
F[C_4]...F[C_1](K_1, K_2) = (e980089683d00d4be37dd3434699b98f,
f9eae5f29b2815e31f11ac5d9c29fb01).
C_5 = 156f6d791fab511deabb0c502fd18105,
F[C_5]...F[C_1](K_1, K_2) = (b7bd70acea4460714f4ebe13835cf004,
e980089683d00d4be37dd3434699b98f).
C_6 = a74af7efab73df160dd208608b9efe06,
F[C_6]...F[C_1](K_1, K_2) = (1a46ea1cf6ccd236467287df93fdf974,
b7bd70acea4460714f4ebe13835cf004).
C_7 = c9e8819dc73ba5ae50f5b570561a6a07,
F[C_7]...F [C_1](K_1, K_2) = (3d4553d8e9cfec6815ebadc40a9ffd04,
1a46ea1cf6ccd236467287df93fdf974).
C_8 = f6593616e6055689adfba18027aa2a08,
(K_3, K_4) = F [C_8]...F [C_1](K_1, K_2) =
(db31485315694343228d6aef8cc78c44,
3d4553d8e9cfec6815ebadc40a9ffd04).
The round keys K_i, i = 1, 2, ..., 10, take the following values:
K_1 = 8899aabbccddeeff0011223344556677,
K_2 = fedcba98765432100123456789abcdef,
K_3 = db31485315694343228d6aef8cc78c44,
K_4 = 3d4553d8e9cfec6815ebadc40a9ffd04,
K_5 = 57646468c44a5e28d3e59246f429f1ac,
K_6 = bd079435165c6432b532e82834da581b,
K_7 = 51e640757e8745de705727265a0098b1,
K_8 = 5a7925017b9fdd3ed72a91a22286f984,
K_9 = bb44e25378c73123a5f32f73cdb6e517,
K_10 = 72e9dd7416bcf45b755dbaa88e4a4043.
5.5. Test Encryption
In this test example, encryption is performed on the round keys
specified in Section 5.4. Let the plaintext be
a = 1122334455667700ffeeddccbbaa9988,
then
X[K_1](a) = 99bb99ff99bb99ffffffffffffffffff,
SX[K_1](a) = e87de8b6e87de8b6b6b6b6b6b6b6b6b6,
LSX[K_1](a) = e297b686e355b0a1cf4a2f9249140830,
LSX[K_2]LSX[K_1](a) = 285e497a0862d596b36f4258a1c69072,
LSX[K_3]...LSX[K_1](a) = 0187a3a429b567841ad50d29207cc34e,
LSX[K_4]...LSX[K_1](a) = ec9bdba057d4f4d77c5d70619dcad206,
LSX[K_5]...LSX[K_1](a) = 1357fd11de9257290c2a1473eb6bcde1,
LSX[K_6]...LSX[K_1](a) = 28ae31e7d4c2354261027ef0b32897df,
LSX[K_7]...LSX[K_1](a) = 07e223d56002c013d3f5e6f714b86d2d,
LSX[K_8]...LSX[K_1](a) = cd8ef6cd97e0e092a8e4cca61b38bf65,
LSX[K_9]...LSX[K_1](a) = 0d8e40e4a800d06b2f1b37ea379ead8e.
Then the ciphertext is
b = X[K_10]LSX[K_9]...LSX[K_1](a) = 7f679d90bebc24305a468d42b9d4edcd.
5.6. Test Decryption
In this test example, decryption is performed on the round keys
specified in Section 5.4. Let the ciphertext be
b = 7f679d90bebc24305a468d42b9d4edcd,
then
X[K_10](b) = 0d8e40e4a800d06b2f1b37ea379ead8e,
L^(-1)X[K_10](b) = 8a6b930a52211b45c5baa43ff8b91319,
S^(-1)L^(-1)X[K_10](b) = 76ca149eef27d1b10d17e3d5d68e5a72,
S^(-1)L^(-1)X[K_9]S^(-1)L^(-1)X[K_10](b) =
5d9b06d41b9d1d2d04df7755363e94a9,
S^(-1)L^(-1)X[K_8]...S^(-1)L^(-1)X[K_10](b) =
79487192aa45709c115559d6e9280f6e,
S^(-1)L^(-1)X[K_7]...S^(-1)L^(-1)X[K_10](b) =
ae506924c8ce331bb918fc5bdfb195fa,
S^(-1)L^(-1)X[K_6]...S^(-1)L^(-1)X[K_10](b) =
bbffbfc8939eaaffafb8e22769e323aa,
S^(-1)L^(-1)X[K_5]...S^(-1)L^(-1)X[K_10](b) =
3cc2f07cc07a8bec0f3ea0ed2ae33e4a,
S^(-1)L^(-1)X[K_4]...S^(-1)L^(-1)X[K_10](b) =
f36f01291d0b96d591e228b72d011c36,
S^(-1)L^(-1)X[K_3]...S^(-1)L^(-1)X[K_10](b) =
1c4b0c1e950182b1ce696af5c0bfc5df,
S^(-1)L^(-1)X[K_2]...S^(-1)L^(-1)X[K_10](b) =
99bb99ff99bb99ffffffffffffffffff.
Then the plaintext is
a = X[K_1]S^(-1)L^(-1)X[K_2]...S^(-1)L^(-1)X[K_10](b) =
1122334455667700ffeeddccbbaa9988.
6. Security Considerations
This entire document is about security considerations.
7. References
7.1. Normative References
[GOST3412-2015]
"Information technology. Cryptographic data security.
Block ciphers", GOST R 34.12-2015, Federal Agency on
Technical Regulating and Metrology, 2015.
7.2. Informative References
[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, 2015.
[ISO-IEC18033-3]
ISO/IEC, "Information technology -- Security techniques --
Encryption algorithms -- Part 3: Block ciphers", ISO/
IEC 18033-3, 2010.
Author's Address
Vasily Dolmatov (editor)
Research Computer Center MSU
Leninskiye Gory, 1, Building 4, MGU NIVC
Moscow 119991
Russian Federation
Email: dol@srcc.msu.ru
AI ELI5
On this page
PROBLEMThe Russian standard GOST R 34.12-2015 defines a block cipher, and the Internet community needed an accessible description of it.
MECHANISMKuznyechik runs 128-bit blocks through ten round keys derived from a 256-bit key. Nine rounds apply XOR, a byte substitution and a linear transformation, and the last step is a final XOR.
WHY IT MATTERSThe RFC restates the standard's definitions, parameters, key schedule, and encryption and decryption, with test examples. It is informational only.
§1Scope and Background
RFC 7801 is a source of information about the Russian Federal standard GOST R 34.12-2015. It describes a block cipher with a block length of n=128 bits and a key length of k=256 bits, called Kuznyechik. It is one of the set of Russian cryptographic standard algorithms, the GOST algorithms.
The standard covers basic block ciphers for confidentiality, authenticity and integrity of information in transmission, processing and storage. The algorithms are designed for hardware and software, and put no restrictions on the confidentiality level of the protected information.
The RFC says the cipher was developed by the Center for Information Protection and Special Communications of the Federal Security Service of the Russian Federation with participation of InfoTeCS JSC. The standard was approved by Decree #749 of the Federal Agency on Technical Regulating and Metrology on June 19, 2015.
This is a write-up of an official Russian rulebook for a scrambling method. It scrambles data in blocks, using a secret key.
§2Building Blocks of the Cipher
The cipher is built from a few transformations on 128-bit strings. X[k] XORs the block with a 128-bit key k. S replaces each of the 16 bytes using a fixed substitution called Pi, a nonlinear bijection on bytes whose 256 values are listed in the RFC. S^(-1) uses the inverse substitution.
R shifts the 16 bytes by one position and puts a new byte in front. That byte is computed by a linear function l over all 16 bytes, using addition and multiplication in the finite field defined by p(x)=x^8+x^7+x^6+x+1. L is R applied 16 times. F[k] is a step built from these pieces that the key schedule uses.
The cipher mixes a block in three ways: adding a key, swapping every byte using a lookup table, and smearing the bytes together. Each of these can be undone, so the message can be unscrambled.
§3The Key Schedule
The key schedule turns the 256-bit key K into ten 128-bit round keys K_1 to K_10. K_1 is the left (high) half of the key and K_2 is the right half.
The remaining keys come from four repetitions of eight F steps. Each step uses a round constant C_i = L(Vec_128(i)), for i from 1 to 32. Each group of eight steps produces the next pair of round keys.
One long secret key is stretched into ten shorter keys, one for each stage of scrambling.
§4Encryption and Decryption
Encryption of a 128-bit block a applies LSX[K_1] through LSX[K_9] in turn. Each of those does an XOR with the round key, then S, then L. The result goes through a final X[K_10].
Decryption undoes this using the same round keys in reverse order. It applies X[K_10] first, then for each of K_9 down to K_2 it applies L^(-1), S^(-1) and an XOR, and ends with X[K_1].
The RFC describes only the basic block cipher. It does not describe modes of operation, although it cites ISO/IEC 10116 for the terms used.
To scramble, you repeat add key, swap bytes, smear, nine times, then add a last key. To unscramble, you do the same steps backwards with the keys in the opposite order.
Basic encryption algorithm
E(a) = X[K_10]LSX[K_9]...LSX[K_2]LSX[K_1](a)
D(a) = X[K_1]L^(-1)S^(-1)X[K_2]...
L^(-1)S^(-1)X[K_9]L^(-1)S^(-1)X[K_10](a)§5Worked Examples
Section 5 is informative and not a normative part of the standard. It gives intermediate values for the transformations S, R and L, a full key schedule from a sample key, a test encryption and a test decryption.
For the test key 8899aabbccddeeff0011223344556677fedcba98765432100123456789abcdef, the plaintext 1122334455667700ffeeddccbbaa9988 encrypts to 7f679d90bebc24305a468d42b9d4edcd. Decrypting that ciphertext returns the original plaintext.
The RFC includes a worked example with real numbers. If your own code gets the same answer, you probably built it right.
§6Security Considerations
The Security Considerations section is one sentence: "This entire document is about security considerations." It contains no further analysis, and the Scope section says only that the algorithms comply with modern cryptographic requirements.
The whole document is about keeping secrets safe, so it has nothing extra to add in its safety section.
§7References
[GOST3412-2015]"Information technology. Cryptographic data security. Block ciphers", GOST R 34.12-2015, Federal Agency on Technical Regulating and Metrology, 2015.
[ISO-IEC10116]ISO/IEC, "Information technology -- Security techniques -- Modes of operation for an n-bit block cipher", ISO/IEC 10116, 2006.
[ISO-IEC18033-3]ISO/IEC, "Information technology -- Security techniques -- Encryption algorithms -- Part 3: Block ciphers", ISO/IEC 18033-3, 2010.