Kuznyechik

Kuznyechik
General
Designers	InfoTeCS JSC[1]
First published	2015
Certification	GOST, and FSS
Cipher detail
Key sizes	256 bits Feistel network
Block sizes	128 bits
Structure	Substitution-permutation network
Rounds	10
Best public cryptanalysis
	A meet-in-the-middle attack on 5 rounds.[2]

Kuznyechik (Russian: Кузнечик, literally "grasshopper") is a symmetric block cipher. It has a block size of 128 bits and key length of 256 bits. It is defined in the National Standard of the Russian Federation GOST R 34.12-2015 in English^[3] and also in RFC 7801.

The name of the cipher can be translated from Russian as grasshopper, however, the standard explicitly says that the English name for the cipher is Kuznyechik (/kʊznˈɛtʃɪk/). The designers claim that by naming the cipher Kuznyechik they follow the trend of difficult to pronounce algorithm names set up by Rijndael and Keccak.^[4] There is also a rumor that the cipher was named after its creators: A.S.Kuzmin^[5], A.A.Nechaev^[6] and Company (Russian: Кузьмин, Нечаев и Компания).

The standard GOST R 34.12-2015 defines the new cipher in addition to the old GOST block cipher (now called Magma) one and does not declare the old cipher obsolete.^[7]

Kuznyechik is based on a substitution-permutation network, though the key schedule employs a Feistel network.

Designations

$\mathbb F$ — Finite field $GF(2^{8})$ $x^{8}+x^{7}+x^{6}+x+1$ .

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

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

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

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

Description

For encryption, decryption and key generation, the following functions:

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

$N(a)=S(a_{15})||$ … $||S(a_{0}).~~N^{-1}(a)$ is a reversed transformation of $N(a)$ .

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

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

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

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

The nonlinear transformation

Non-linear transformation is given by substituting S = Bin₈ S' Bin₈⁻¹.

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

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

Linear transformation

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

operations of addition and multiplication are carried out in the field $\mathbb F$ .

Key generation

key generation algorithm uses iterative constant $C_{i}=H(Bin_{128}(i))$ , i=1,2,…32. Sets the shared key $K=k_{255}||$ … $||k_{0}$ .

Iterated keys

$K_{1}=k_{255}||$ … $||k_{128}$

$K_{2}=k_{127}||$ … $||k_{0}$

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

Encryption algorithm

$E(a)=Add_{2}[K_{10}]HNAdd_{2}[K_{9}]$ … $HNAdd_{2}[K_{3}]HNAdd_{2}[K_{1}](a),$ where a — 128-bit string.

Decryption algorithm

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

Cryptanalysis

Riham AlTawy and Amr M. Youssef describe a meet-in-the-middle attack on the 5-round reduced Kuznyechik which allows to recover the key with time complexity of 2¹⁴⁰, memory complexity of 2¹⁵³, and data complexity of 2¹¹³.^[2]

Alex Biryukov, Leo Perrin, and Aleksei Udovenko published a paper in which they show that the S-Boxes of Kuznyechik and Streebog were not created pseudo-randomly but using a hidden algorithm which they were able to reverse engineer.^[8]

Later Leo Perrin and Aleksei Udovenko published two alternative decompositions of the S-Box and proved its connection to the S-Box of Belarusian cipher BelT.^[9]. The authors of the paper note that while the reason of using such a structure remains unclear, generating S-Boxes by a hidden algorithm contradicts the concept of nothing up my sleeve numbers which could prove that no weaknesses were intentionally introduced in their design.

Riham AlTawy, Onur Duman, and Amr M. Youssef published two fault attacks on Kuznyechik which show the importance of protecting the implementations of the cipher.^[10]

Adoption

VeraCrypt (a fork of TrueCrypt) included Kuznyechik as one of its supported encryption algorithms.^[11]

Source code

http://tc26.ru/standard/draft/PR_GOSTR-bch_v4.zip https://fossies.org/windows/misc/VeraCrypt_1.22_Source.zip/src/Crypto/kuznyechik.c (Alternative link for the case in which the first link is not working)

References

↑ http://tc26.ru/standard/draft/PR_GOSTR-bch_v4.zip
1 2 Riham AlTawy and Amr M. Youssef (2015-04-17). "A Meet in the Middle Attack on Reduced Round Kuznyechik" (PDF).
↑ http://tc26.ru/en/standard/gost/GOST_R_34_12_2015_ENG.pdf National Standard of the Russian Federation GOST R 34.12–2015 (English Version)
↑ https://mjos.fi/doc/rus/gh_ctcrypt.pdf Low-Weight and Hi-End: Draft Russian Encryption Standard
↑ https://www.researchgate.net/scientific-contributions/69696703_A_S_Kuzmin
↑ https://www.researchgate.net/profile/A_Nechaev
↑ http://www.itsec.ru/articles2/crypto/gost-r-chego-ozhidat-ot-novogo-standarta GOST R 34.12–2015: what to expect from a new standard? (Russian only)
↑ Alex Biryukov, Leo Perrin, and Aleksei Udovenko (2016-02-18). "Reverse-Engineering the S-Box of Streebog, Kuznyechik and STRIBOBr1 (Full Version)" (PDF).
↑ Léo Perrin, Aleksei Udovenko (2017). "Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog" (PDF).
↑ Riham AlTawy, Onur Duman, and Amr M. Youssef (2015-04-17). "Fault Analysis of Kuznyechik" (PDF).
↑ "Kuznyechik". VeraCrypt Documentation. IDRIX. Retrieved 2018-02-03.

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[1] ttp://tc26.ru/standard/draft/PR_GOSTR-bch_v4.zip

[mitm-2] 1 2 Riham AlTawy and Amr M. Youssef (2015-04-17). "A Meet in the Middle Attack on Reduced Round Kuznyechik" (PDF).

[3] ttp://tc26.ru/en/standard/gost/GOST_R_34_12_2015_ENG.pdf National Standard of the Russian Federation GOST R 34.12–2015 (English Version)

[4] ttps://mjos.fi/doc/rus/gh_ctcrypt.pdf Low-Weight and Hi-End: Draft Russian Encryption Standard

[5] ttps://www.researchgate.net/scientific-contributions/69696703_A_S_Kuzmin

[6] ttps://www.researchgate.net/profile/A_Nechaev

[7] ttp://www.itsec.ru/articles2/crypto/gost-r-chego-ozhidat-ot-novogo-standarta GOST R 34.12–2015: what to expect from a new standard? (Russian only)

[8] Alex Biryukov, Leo Perrin, and Aleksei Udovenko (2016-02-18). "Reverse-Engineering the S-Box of Streebog, Kuznyechik and STRIBOBr1 (Full Version)" (PDF).

[9] Léo Perrin, Aleksei Udovenko (2017). "Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog" (PDF).

[10] Riham AlTawy, Onur Duman, and Amr M. Youssef (2015-04-17). "Fault Analysis of Kuznyechik" (PDF).

[11] "Kuznyechik". VeraCrypt Documentation. IDRIX. Retrieved 2018-02-03.

General
Designers	InfoTeCS JSC^[1]
First published	2015
Certification	GOST, and FSS
Cipher detail
Key sizes	256 bits Feistel network
Block sizes	128 bits
Structure	Substitution-permutation network
Rounds	10
Best public cryptanalysis
A meet-in-the-middle attack on 5 rounds.^[2]