Kuznyechik

Kuznyechik (Russian: Кузнечик, literally: "grasshopper") is a symmetrical block cipher . It has a block size of 128-bit and a key length of 256-bit. The cipher is defined in the national standard of Russia GOST R 34.12-2015 in English and also in RFC 7801 .

The name of the cipher comes from the Russian word for grasshopper, although the standard explicitly mentions that the English name is Kuznyechik . The developers said they wanted to follow the trend of hard-to-pronounce names for algorithms like Rijndael and Keccak .

The GOST R 34.12-2015 standard defines the new cipher as an addition to the old GOST block cipher.

Kuznyechik is based on the substitution-permutation network , with the key schedule using the Feistel network .

VeraCrypt (descendant of TrueCrypt ) offers Kuznyechik as one of the encryption algorithms.

Designation

${\displaystyle \mathbb {F} }$- Finite body . ${\displaystyle GF(2^{8})}$ ${\displaystyle x^{8}+x^{7}+x^{6}+x+1}$

${\displaystyle Bin_{8}:\mathbb {Z} _{p}\rightarrow V_{8}}$- ( ) ${\displaystyle \mathbb {Z} _{p}}$ ${\displaystyle p=2^{8}}$

${\displaystyle {Bin_{8}}^{-1}:V_{8}\rightarrow \mathbb {Z} _{p}}$- . ${\displaystyle Bin_{8}}$

${\displaystyle \delta :V_{8}\rightarrow \mathbb {F} }$- . ${\displaystyle \mathbb {F} }$

${\displaystyle \delta ^{-1}:\mathbb {F} \rightarrow V_{8}}$ - ${\displaystyle \delta }$

description

The following is specified for encryption, decryption and key generation:

${\displaystyle Add_{2}[k](a)=k\oplus a}$, where , are binary strings of the form ... ( is string concatenation ). ${\displaystyle k}$ ${\displaystyle a}$ ${\displaystyle a=a_{15}||}$ ${\displaystyle ||a_{0}}$ ${\displaystyle ||}$

${\displaystyle N(a)=S(a_{15})||}$... is an inverted transformation of . ${\displaystyle ||S(a_{0}).~~N^{-1}(a)}$ ${\displaystyle N(a)}$

${\displaystyle G(a)=\delta (a_{15},}$... ... ${\displaystyle ,a_{0})||a_{15}||}$ ${\displaystyle ||a_{1}.}$

${\displaystyle G^{-1}(a)}$- inverted transformation of , ... ... ${\displaystyle G(a)}$ ${\displaystyle G^{-1}(a)=a_{14}||a_{13}||}$ ${\displaystyle ||a_{0}||\delta (a_{14},a_{13},}$ ${\displaystyle ,a_{0},a_{15}).}$

${\displaystyle H(a)=G^{16}(a)}$, where - composition of the transformations of and etc. ${\displaystyle G^{16}}$ ${\displaystyle G^{15}}$ ${\displaystyle G}$

${\displaystyle F[k](a_{1},a_{0})=(HNAdd_{2}[k](a_{1})\oplus a_{0},a_{1}).}$

The nonlinear transformation

The nonlinear transformation is given by substituting the following:

S = Bin ₈ S 'Bin ₈ ⁻¹ .

Values ​​of the substitution S ' are given as an array S' = (S '(0), S' (1), ..., S '(255)) :

${\displaystyle S'=(252,238,221,17,207,110,49,22,251,196,250,218,35,197,4,77,233,}$ ${\displaystyle 119,240,219,147,46,153,186,23,54,241,187,20,205,95,193,249,24,101,}$ ${\displaystyle 90,226,92,239,33,129,28,60,66,139,1,142,79,5,132,2,174,227,106,143,}$ ${\displaystyle 160,6,11,237,152,127,212,211,31,235,52,44,81,234,200,72,171,242,42,}$ ${\displaystyle 104,162,253,58,206,204,181,112,14,86,8,12,118,18,191,114,19,71,156,}$ ${\displaystyle 183,93,135,21,161,150,41,16,123,154,199,243,145,120,111,157,158,178,}$ ${\displaystyle 177,50,117,25,61,255,53,138,126,109,84,198,128,195,189,13,87,223,}$ ${\displaystyle 245,36,169,62,168,67,201,215,121,214,246,124,34,185,3,224,15,236,}$ ${\displaystyle 222,122,148,176,188,220,232,40,80,78,51,10,74,167,151,96,115,30,0,}$ ${\displaystyle 98,68,26,184,56,130,100,159,38,65,173,69,70,146,39,94,85,47,140,163,}$ ${\displaystyle 165,125,105,213,149,59,7,88,179,64,134,172,29,247,48,55,107,228,136,}$ ${\displaystyle 217,231,137,225,27,131,73,76,63,248,254,141,83,170,144,202,216,133,}$ ${\displaystyle 97,32,113,103,164,45,43,9,91,203,155,37,208,190,229,108,82,89,166,}$ ${\displaystyle 116,210,230,244,180,192,209,102,175,194,57,75,99,182).}$

Linear transformation

${\displaystyle \gamma }$: ... ${\displaystyle \gamma (a_{15},}$ ${\displaystyle ,a_{0})=\delta ^{-1}~(148*\delta (a_{15})+32*\delta (a_{14})+133*\delta (a_{13})+16*\delta (a_{12})+}$ ${\displaystyle 194*\delta (a_{11})+192*\delta (a_{10})+1*\delta (a_{9})+251*\delta (a_{8})+1*\delta (a_{7})+192*\delta (a_{6})+}$ ${\displaystyle 194*\delta (a_{5})+16*\delta (a_{4})+133*\delta (a_{3})+32*\delta (a_{2})+148*\delta (a_{1})+1*\delta (a_{0})),}$

Operations of addition and multiplication are performed in the field . ${\displaystyle \mathbb {F} }$

Key generation

The key generation algorithm uses the iterative constant t , i = 1,2,… 32 and sets the shared keys as: … . ${\displaystyle C_{i}=H(Bin_{128}(i))}$ ${\displaystyle K=k_{255}||}$ ${\displaystyle ||k_{0}}$

Iterated keys

${\displaystyle K_{1}=k_{255}||}$... ${\displaystyle ||k_{128}}$

${\displaystyle K_{2}=k_{127}||}$... ${\displaystyle ||k_{0}}$

${\displaystyle (K_{2i+1},K_{2i+2})=F[C_{8(i-1)+8}]}$... ${\displaystyle F[C_{8(i-1)+1}](K_{2i+1},K_{2i}),i=1,2,3,4.}$

Encryption algorithm

${\displaystyle E(a)=Add_{2}[K_{10}]HNAdd_{2}[K_{9}]}$... where a - 128-bit string. ${\displaystyle HNAdd_{2}[K_{2}]HNAdd_{2}[K_{1}](a),}$

Decryption algorithm

${\displaystyle D(a)=Add_{2}[K_{1}]H^{-1}N^{-1}Add_{2}[K_{2}]}$... ${\displaystyle H^{-1}N^{-1}Add_{2}[K_{9}]H^{-1}N^{-1}Add_{2}[K_{10}](a).}$

Adaptation

VeraCrypt , the encryption software known worldwide, uses Kuznyechik as one of the popular encryption algorithms.

See also

• Source code
• Alternative link

Individual evidence

1. ↑ Vasily Dolmatov <[e-mail]>: GOST R 34.12-2015: Block Cipher "Kuznyechik". Retrieved May 25, 2020 (English). 
2. ↑ Groteck Business Media: ГОСТ Р 34.12–2015: чего ожидать от нового стандарта? | ITSec.Ru. Retrieved May 25, 2020 (English). 
3. ↑ VeraCrypt - Free Open Source Disk Encryption with Strong Security for the Paranoid. Retrieved May 25, 2020 .