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{{Primary sources|date=November 2008}}
{{Infobox block cipher
| name          = Threefish
| designers     = [[Bruce Schneier]], [[Niels Ferguson]], [[Stefan Lucks]], [[Doug Whiting]], [[Mihir Bellare]], [[Tadayoshi Kohno]], [[Jon Callas]], [[Jesse Walker (programmer)|Jesse Walker]]
| publish date  = 2008
| related to    = [[Blowfish (cipher)|Blowfish]], [[Twofish]]
| key size      = 256, 512 or 1024 bits<br>(key size is equal to block size)
| block size    = 256, 512 or 1024 bits
| rounds        = 72 (80 for 1024-bit block size)
| speed         = 6.1 [[cycles per byte|cpb]] on [[Core 2]].<ref name=skein />
| cryptanalysis  = 
}}
'''Threefish''' is a [[Symmetric-key algorithm|symmetric-key]] [[tweakable block cipher]] designed as part of the [[Skein hash function]], an entry in the [[NIST hash function competition]]. Threefish uses no [[S-box]]es or other table lookups in order to avoid cache [[timing attack]]s;<ref name=skein>{{cite paper |date=2010-10-01 |author=Ferguson et al. |title=The Skein Hash Function Family |url=http://www.skein-hash.info/sites/default/files/skein1.3.pdf }} The paper in which Threefish was introduced.</ref> its nonlinearity comes from alternating additions with exclusive ORs.  In that respect, it is similar to [[Salsa20]], [[Tiny Encryption Algorithm|TEA]], and the SHA-3 candidates [[CubeHash]] and [[BLAKE (hash function)|BLAKE]].

Threefish and the Skein hash function were designed by [[Bruce Schneier]], [[Niels Ferguson]], [[Stefan Lucks]], [[Doug Whiting]], [[Mihir Bellare]], [[Tadayoshi Kohno]], [[Jon Callas]], and [[Jesse Walker (programmer)|Jesse Walker]].

==Security==
In October 2010, an attack that combines [[rotational cryptanalysis]] with the [[rebound attack]] was published. The attack mounts a [[known-key distinguisher]] against 53 of 72 rounds in Threefish-256, and 57 of 72 rounds in Threefish-512. It also affects the [[Skein (hash function)|Skein]] hash function.<ref name=rotational-rebound>{{cite paper |author=Dmitry Khovratovich, Ivica Nikolic, Christian Rechberger |date=2010-10-20 |title=Rotational Rebound Attacks on Reduced Skein |url=http://eprint.iacr.org/2010/538 }}</ref> This is a follow-up to the earlier attack published in February, which breaks 39 and 42 rounds respectively.<ref>{{cite paper |year=2010 |author=Dmitry Khovratovich and Ivica Nikolić |title=Rotational Cryptanalysis of ARX |publisher=University of Luxembourg |url=http://www.skein-hash.info/sites/default/files/axr.pdf }}</ref> In response to this attack, the Skein team tweaked the rotation constants used in Threefish and thereby the [[key schedule]] constants for round 3 of the NIST hash function competition.<ref name=skein />

In 2009, a related key [[boomerang attack]] against a reduced round Threefish version was published. For the 32-round version, the time complexity is <math>2^{226}</math> and the memory complexity is <math>2^{12}</math>; for the 33-round version, the time complexity is <math>2^{352.17}</math> with a negligible memory usage. The attacks also work against the tweaked version of Threefish: for the 32-round version, the time complexity is <math>2^{222}</math> and the memory complexity is <math>2^{12}</math>; for the 33-round version, the time complexity is <math>2^{355.5}</math> with a negligible memory usage.<ref>
{{Cite web
|author=Jiazhe Chen
|author2=Keting Jia
|date=2009-11-01
|title=Improved Related-key Boomerang Attacks on Round-Reduced Threeﬁsh-512
|url=http://eprint.iacr.org/2009/526
}}</ref>

==See also==
* [[Twofish]]
* [[Blowfish (cipher)]]

==References==
{{reflist}}

==External links==
* [http://www.skein-hash.info/ "The Skein Hash Function Family"] Homepage of the Skein Hash Function Family.

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