Internet DRAFT - draft-dolmatov-kuznyechik
draft-dolmatov-kuznyechik
Internet Engineering Task Force V. Dolmatov, Ed.
Internet-Draft Research Computer Center MSU
Intended status: Informational January 17, 2016
Expires: July 20, 2016
GOST R 34.12-2015: Block Cipher "Kuznyechik"
draft-dolmatov-kuznyechik-05
Abstract
This document is intended to be a source of information about the
Russian Federal standard GOST R 34.12-2015 describing block cipher
with block length of n=128 bits and key length k=256 bits, which is
also referred as "Kuznyechik". This algorithm is one of the set of
Russian cryptographic standard algorithms (called GOST algorithms).
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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 . . . . . . . . . . . . . . . . . . . . . . 5
4.1. Nonlinear Bijection . . . . . . . . . . . . . . . . . . . 5
4.2. Linear Transformation . . . . . . . . . . . . . . . . . . 7
4.3. Transformations . . . . . . . . . . . . . . . . . . . . . 7
4.4. Key schedule . . . . . . . . . . . . . . . . . . . . . . 8
4.5. Basic encryption algorithm . . . . . . . . . . . . . . . 8
4.5.1. Encryption . . . . . . . . . . . . . . . . . . . . . 8
4.5.2. Decryption . . . . . . . . . . . . . . . . . . . . . 9
5. Examples (Informative) . . . . . . . . . . . . . . . . . . . 9
5.1. Transformation S . . . . . . . . . . . . . . . . . . . . 9
5.2. Transformation R . . . . . . . . . . . . . . . . . . . . 9
5.3. Transformation L . . . . . . . . . . . . . . . . . . . . 9
5.4. Key schedule . . . . . . . . . . . . . . . . . . . . . . 9
5.5. Test encryption . . . . . . . . . . . . . . . . . . . . . 11
5.6. Test decryption . . . . . . . . . . . . . . . . . . . . . 11
6. Security Considerations . . . . . . . . . . . . . . . . . . . 12
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 12
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.1. Normative References . . . . . . . . . . . . . . . . . . 12
8.2. Informative References . . . . . . . . . . . . . . . . . 12
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 12
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 developing, operation, and modernization of
the information systems of various purposes.
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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 19.06.2015.
Terms and concepts in the standard comply with the following
international standards:
o ISO/IEC 10116 [ISO-IEC10116],
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 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.
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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 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 set 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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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 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),
delta: V_8 -> Q bijective mapping which 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,
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)):
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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)):
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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,
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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,
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:
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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:
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K = 8899aabbccddeeff0011223344556677fedcba98765432100123456789abcdef.
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.
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5.5. Test encryption
In this test example, encryption is performed on the round keys
specified in clause 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 clause 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
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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. IANA Considerations
This document has no IANA considerations.
8. References
8.1. Normative References
[GOST3412-2015]
Federal Agency on Technical Regulating and Metrology,
"Information technology. Cryptographic data security.
Block ciphers.GOST R 34.12-2015", 2015.
8.2. 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",
2013.
[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
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