Research Computer Center MSU
March 2016
GOST R 34.12-2015: Block Cipher "Kuznyechik"
Abstract
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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
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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
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Copyright © 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
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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
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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.
2. General Information
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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
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The following terms and their corresponding definitions are used in the standard.
3.1. Definitions
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Definitions
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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]),
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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]),
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Note:
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In GOST R 34.12-2015, the key must be a binary sequence.
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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]).
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3.2. Notations
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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
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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
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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
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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
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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
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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
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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)
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This section is for information only and is not a normative part of the standard.
5.1. Transformation S
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S(ffeeddccbbaa99881122334455667700) = b66cd8887d38e8d77765aeea0c9a7efc, S(b66cd8887d38e8d77765aeea0c9a7efc) = 559d8dd7bd06cbfe7e7b262523280d39, S(559d8dd7bd06cbfe7e7b262523280d39) = 0c3322fed531e4630d80ef5c5a81c50b, S(0c3322fed531e4630d80ef5c5a81c50b) = 23ae65633f842d29c5df529c13f5acda.
5.2. Transformation R
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R(00000000000000000000000000000100) = 94000000000000000000000000000001, R(94000000000000000000000000000001) = a5940000000000000000000000000000, R(a5940000000000000000000000000000) = 64a59400000000000000000000000000, R(64a59400000000000000000000000000) = 0d64a594000000000000000000000000.
5.3. Transformation L
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L(64a59400000000000000000000000000) = d456584dd0e3e84cc3166e4b7fa2890d, L(d456584dd0e3e84cc3166e4b7fa2890d) = 79d26221b87b584cd42fbc4ffea5de9a, L(79d26221b87b584cd42fbc4ffea5de9a) = 0e93691a0cfc60408b7b68f66b513c13, L(0e93691a0cfc60408b7b68f66b513c13) = e6a8094fee0aa204fd97bcb0b44b8580.
5.4. Key Schedule
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In this test example, the key is equal to:
K = 8899aabbccddeeff0011223344556677fedcba9876543210012345678
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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
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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
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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
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This entire document is about security considerations.
7. References
7.1. Normative References
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[GOST3412-2015]
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"Information technology. Cryptographic data security. Block ciphers", GOST R 34.12-2015, Federal Agency on Technical Regulating and Metrology, 2015.
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7.2. Informative References
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[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
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Vasily Dolmatov (editor) Research Computer Center MSU Leninskiye Gory, 1, Building 4, MGU NIVC Moscow 119991 Russian Federation Email: [email protected]