GOST R 34.12-2015: Block Cipher "Kuznyechik"
draft-dolmatov-kuznyechik-03
The information below is for an old version of the document.
Document | Type |
This is an older version of an Internet-Draft that was ultimately published as RFC 7801.
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Author | Vasily Dolmatov | ||
Last updated | 2015-11-11 | ||
RFC stream | Independent Submission | ||
Formats | |||
IETF conflict review | conflict-review-dolmatov-kuznyechik, conflict-review-dolmatov-kuznyechik, conflict-review-dolmatov-kuznyechik, conflict-review-dolmatov-kuznyechik, conflict-review-dolmatov-kuznyechik, conflict-review-dolmatov-kuznyechik | ||
Additional resources | |||
Stream | ISE state | Finding Reviewers | |
Consensus boilerplate | Unknown | ||
Document shepherd | (None) | ||
IESG | IESG state | Became RFC 7801 (Informational) | |
Telechat date | (None) | ||
Responsible AD | (None) | ||
Send notices to | (None) |
draft-dolmatov-kuznyechik-03
quot; and "block encryption algorithm" are synonyms. Dolmatov Expires May 14, 2016 [Page 3] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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), Dolmatov Expires May 14, 2016 [Page 4] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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 nabla, 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)): Dolmatov Expires May 14, 2016 [Page 5] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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 ). Dolmatov Expires May 14, 2016 [Page 6] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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, 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. Dolmatov Expires May 14, 2016 [Page 7] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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. Dolmatov Expires May 14, 2016 [Page 8] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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 = 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). Dolmatov Expires May 14, 2016 [Page 9] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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 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 Dolmatov Expires May 14, 2016 [Page 10] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 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. 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. Dolmatov Expires May 14, 2016 [Page 11] Internet-DraftGOST R 34.12-2015: Block Cipher "Kuznyechik" November 2015 [ISO-IEC18033-3] ISO-IEC, "Information technology - Security techniques - Encryption algorithms - Part 3: Block ciphers, ISO-IEC 18033-3", 2010. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", RFC 2119, BCP 14, March 1997. 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 Dolmatov Expires May 14, 2016 [Page 12]