Internet Engineering Task Force V. Dolmatov, Ed.
Internet-Draft Research Computer Center MSU
Intended status: Informational November 11, 2015
Expires: May 14, 2016

GOST R 34.12-2015: Block Cipher "Kuznyechik"
draft-dolmatov-kuznyechik-03

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

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.

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:

3. Definitions and Notations

The following terms and their corresponding definitions are used in the standard.

3.1. Definitions

Definitions

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),
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)): 

 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,
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 = 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.

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 

	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.
[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