Information geometry

2013-06-05T22:42:59Z

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{{Infobox encryption method
|name = GOST 28147-89
|image = [[File:GOSTDiagram.png|240px|center]]
|caption = Diagram of GOST
|designers = [[USSR]]
|publish date = 1994-05-23 (declassified)
|series =
|derived from =
|derived to = [[GOST (hash function)|GOST hash function]]
|related to =
|certification = [[GOST|GOST standard]]
|key size = 256 bits
|security claim =
|block size = 64 bits
|structure = [[Feistel network]]
|rounds = 32
|cryptanalysis =
}}

The '''GOST block cipher''', defined in the standard '''GOST 28147-89''', is a Soviet and Russian government standard [[symmetric key]] [[block cipher]]. Also based on this block cipher is the [[GOST (hash function)|GOST hash function]].

Developed in the 1970s, the standard had been marked "Top Secret" and then downgraded to "Secret" in 1990. Shortly after the dissolution of the [[USSR]], it was declassified and it was released to the public in 1994. GOST 28147 was a Soviet alternative to the [[United States]] standard algorithm, [[Data Encryption Standard|DES]].<ref name=fleischmann2009>
{{cite journal
|last=Fleischmann
|first=Ewan
|coauthors=Gorski, Michael; Hühne, Jan-Hendrik; Lucks, Stefan
|title=Key Recovery Attack on Full GOST Block Cipher with Zero Time and Memory
|journal=Published as ISO/IEC JTC
|year=2009
|volume=1}}
</ref> Thus, the two are very similar in structure.

==The algorithm==

GOST has a 64-bit [[block size (cryptography)|block size]] and a [[key length]] of 256 bits. Its [[S-box]]es can be secret, and they contain about 354 (log2(16!8)) bits of secret information, so the effective key size can be increased to 610 bits; however, a chosen-key attack can recover the contents of the S-Boxes in approximately 232 encryptions.<ref>{{
cite journal
|last=Saarinen
|first=Markku-Juhani
|title=A chosen key attack against the secret S-boxes of GOST
|year=1998
|url=http://citeseer.ist.psu.edu/rd/96002585%2C277448%2C1%2C0.25%2CDownload/http://citeseer.ist.psu.edu/compress/0/papers/cs/13215/http:zSzzSzwww.jyu.fizSz~mjoszSzgost_cka.ps.gz/saarinen98chosen.ps
|quote=We show that a simple "black box" chosen-key attack against GOST can recover secret S-boxes with approximately 2^32 encryptions}}
</ref>

GOST is a [[Feistel network]] of 32 rounds. Its round function is very simple: add a 32-bit subkey [[modular arithmetic|modulo]] 232, put the result through a layer of S-boxes, and rotate that result left by 11 bits. The result of that is the output of the round function. In the diagram to the right, one line represents 32 bits.

The subkeys are chosen in a pre-specified order. The key schedule is very simple: break the 256-bit key into eight 32-bit subkeys, and each subkey is used four times in the algorithm; the first 24 rounds use the key words in order, the last 8 rounds use them in reverse order.

The S-boxes accept a four-bit input and produce a four-bit output. The S-box substitution in the round function consists of eight 4 × 4 S-boxes. The S-boxes are implementation-dependent – parties that want to secure their communications using GOST must be using the same S-boxes. For extra security, the S-boxes can be kept secret. In the original standard where GOST was specified, no S-boxes were given, but they were to be supplied somehow. This led to speculation that organizations the government wished to spy on were given weak S-boxes. One GOST chip manufacturer reported that he generated S-boxes himself using a [[pseudorandom number generator]].<ref name=schneier1996>
{{cite book
|last=Schneier
|first=Bruce
|title=Applied cryptography : protocols, algorithms, and source code in C
|year=1996
|publisher=Wiley
|location=New York [u.a.]
|isbn=0-471-11709-9
|edition=2. ed., [Nachdr.]}}</ref>

For example, the [[Central Bank of Russia|Central Bank of Russian Federation]] uses the following S-boxes: 

{|class="wikitable"
!#
!S-Box
|-
!1
|4 10 9 2 13 8 0 14 6 11 1 12 7 15 5 3
|-
!2
|14 11 4 12 6 13 15 10 2 3 8 1 0 7 5 9
|-
!3
|5 8 1 13 10 3 4 2 14 15 12 7 6 0 9 11
|-
!4
|7 13 10 1 0 8 9 15 14 4 6 12 11 2 5 3
|-
!5
|6 12 7 1 5 15 13 8 4 10 9 14 0 3 11 2
|-
!6
|4 11 10 0 7 2 1 13 3 6 8 5 9 12 15 14
|-
!7
|13 11 4 1 3 15 5 9 0 10 14 7 6 8 2 12
|-
!8
|1 15 13 0 5 7 10 4 9 2 3 14 6 11 8 12
|}

==Cryptanalysis of GOST==

Compared to DES, GOST has a very simple round function. However, the designers of GOST attempted to offset the simplicity of the round function by specifying the algorithm with 32 rounds and secret S-boxes.

Another concern is that the [[avalanche effect]] is slower to occur in GOST than in DES. This is because of GOST's lack of an expansion permutation in the round function, as well as its use of a rotation instead of a permutation. Again, this is offset by GOST's increased number of rounds.

There is not much published cryptanalysis of GOST, but a cursory glance says that it seems secure.<ref name=schneier1996 /><ref>
{{cite journal
|last=Shorin
|first=Vitaly V.
|coauthors=Jelezniakov, Vadim V.; Gabidulin, Ernst M.
|title=Linear and Differential Cryptanalysis of Russian GOST
|journal=Electronic Notes in Discrete Mathematics
|date=April 2001
|volume=6
|pages=538–547
|doi=10.1016/S1571-0653(04)00206-9
|quote=In this paper the linear cryptanalysis and the differential cryptanalysis of the Russian GOST encryption algorithm are carried out [2]. It is shown that GOST is secure against the linear cryptanalysis after five rounds and against the differential cryptanalysis after seven rounds. The differential analysis algorithm of the three round GOST is given. Also criteria for selection of the substitution boxes with provable security against linear cryptanalysis are given.}}
</ref> The large number of rounds and secret S-boxes makes both [[linear cryptanalysis|linear]] and [[differential cryptanalysis]] difficult. Its avalanche effect may be slower to occur, but it can propagate over 32 rounds very effectively.

However, GOST is not fully defined by its standard: It does not specify the S-boxes (replacement tables). On the one hand, this can be additional secure information (in addition to key). On the other hand, the following problems arise:
* different algorithm implementations can use different replacement tables, and thus, can be incompatible to each other
* possibility of deliberate weak replacement table usage
* possibility (standard does not forbid it) to use replacement tables in which nodes are not commutation, that may lead to extreme security downfall

Despite its apparently strong construction, GOST is vulnerable to generic attacks based on its short (64-bit) block size, and should therefore never be used in contexts where more than 232 blocks could be encrypted with the same key.

Since 2007, several attacks were developed against GOST implementations with reduced number of rounds and/or keys with additional special properties.<ref>
{{cite news
|url=http://www.iacr.org/archive/fse2007/45930152/45930152.pdf
|title=Improved Slide Attacks
|year=2007
|author=Eli Biham, Orr Dunkelman, Nathan Keller}}
</ref><ref>
{{cite news
|url=http://dl.acm.org/citation.cfm?id=1484903.1484932
|title=Reflection Cryptanalysis of Some Ciphers
|year=2008
|author=Orhun Kara}}</ref>

In 2011 several authors discovered more significant flaws in GOST cipher, being able to attack full 32-round GOST with arbitrary keys for the first time. It has been even called "a deeply flawed cipher" by [[Nicolas Courtois]].<ref>
{{cite web
|last=Courtois
|first=Nicolas T.
|title=Security Evaluation of GOST 28147-89 In View Of International Standardisation
|url=http://eprint.iacr.org/2011/211
|work=Cryptology ePrint Archive
|publisher=[[International Association for Cryptologic Research|IACR]]
|date=9 May 2011
|quote=Until 2011 researchers unanimously agreed that GOST could or should be very secure, which was summarized in 2010 in these words: despite considerable cryptanalytic efforts spent in the past 20 years, GOST is still not broken". Unhappily, it was recently discovered that GOST can be broken and is a deeply flawed cipher}}
</ref> First attacks were able to reduce time complexity from <math>2^{256}</math> to <math>2^{228}</math> at the cost of huge memory requirements,<ref>
{{cite news
|url=http://eprint.iacr.org/2011/312
|title=Differential Cryptanalysis of GOST
|year=2011
|publisher=[[International Association for Cryptologic Research|IACR]]
|author=Nicolas T. Courtois, Michał Miształ}}
</ref> and soon they were improved up to <math>2^{178}</math> time complexity (at the cost of <math>2^{70}</math> memory and <math>2^{64}</math> data).<ref>
{{cite news
|url=http://eprint.iacr.org/2012/138.pdf
|title=An Improved Differential Attack on Full GOST
|year=2012
|publisher=[[International Association for Cryptologic Research|IACR]]
|author=Nicolas T. Courtois}}</ref>

As of December 2012 the best known attack on GOST (<math>2^{101}</math>) is on par with the best known attack (<math>2^{100}</math>, based on [[XSL attack|another weakness noted by Nicolas Courtois]]) on widely used [[AES-256|Advanced Encryption Standard]].

GOST has been submitted to ISO standardization in 2010.

== See also ==
*[[GOST|GOST standards]]

==References==
{{reflist}}

==Further reading==
* {{cite web |date=March 2010 |url=http://tools.ietf.org/html/rfc5830 |title=RFC 5830: GOST 28147-89 encryption, decryption and MAC algorithms |publisher=IETF }}
* {{cite web |date=January 2006 |url=http://tools.ietf.org/html/rfc4357 |title=RFC 4357: Additional Cryptographic Algorithms for Use with GOST |publisher=IETF }}
* Alex Biryukov, David Wagner, [http://now.cs.berkeley.edu/~daw/papers/advslide-ec00.ps Advanced Slide Attacks], EUROCRYPT 2000, LNCS, pp 589–606, 2000.

== External links ==
* [http://vipul.net/gost/ GOST — The Soviet Encryption Algorithm]
* [http://textop.us/Encryption/GOST Online GOST encrypt and decrypt tool]
* [http://textop.us/Hashing/Gost Online GOST hashing tool]
* [http://www.users.zetnet.co.uk/hopwood/crypto/scan/cs.html#GOST SCAN's entry for GOST]
* [http://sourceforge.net/p/atoken/ An open source implementation of PKCS#11 software device with Russian GOST cryptography standards capabilities]

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