Difference between revisions of "CubeHash"

From The ECRYPT Hash Function Website
(tables split + designer's analysis)
(References sorted)
Line 116: Line 116:
  
  
−
 
+
<bibtex>
 +
@misc{cryptoeprint:2009:407,
 +
    author = {Benjamin Bloom and Alan Kaminsky},
 +
    title = {Single Block Attacks and Statistical Tests on CubeHash},
 +
    howpublished = {Cryptology ePrint Archive, Report 2009/407},
 +
    year = {2009},
 +
    note = {\url{http://eprint.iacr.org/}},
 +
    abstract = {This paper describes a second preimage attack on the CubeHash cryptographic one-way hash function. The attack finds a second preimage in less time than brute force search for these CubeHash variants: CubeHash $r$/$b$-224 for $b > 100$; CubeHash$r$/$b$-256 for $b > 96$; CubeHash$r$/$b$-384 for $b > 80$; and CubeHash$r$/$b$-512 for $b > 64$. However, the attack does not break the CubeHash variants recommended for SHA-3. The attack requires minimal memory and can be performed in a massively parallel fashion. This paper also describes several statistical randomness tests on CubeHash. The tests were unable to disprove the hypothesis that CubeHash behaves as a random mapping. These results support CubeHash's viability as a secure cryptographic hash function.},
 +
}
 +
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@inproceedings{cubehashAMPP09,
+
@misc{cubehashBKMP09b,
−
  author   = {Jean-Philippe Aumasson and Eric Brier and Willi Meier and María Naya-Plasencia and Thomas Peyrin},
+
    author = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
−
  title     = {Inside the Hypercube},
+
    title = {Linearization Framework for Collision Attacks: Application to CubeHash and MD6},
−
  booktitle = {ACISP},
+
    howpublished = {Cryptology ePrint Archive, Report 2009/382},
−
  publisher = {Springer},
+
    year = {2009},
−
  editor = {Colin Boyd and Juan Manuel Gonz{\'a}lez Nieto},
+
     url = {http://eprint.iacr.org/2009/382.pdf},
−
  series    = {LNCS},
+
    note = {\url{http://eprint.iacr.org/}},
−
  pages     = {202-213},
+
    abstract = {In this paper, an improved differential cryptanalysis framework for finding collisions in hash functions is provided. Its principle is based on linearization of compression functions in order to find low weight differential characteristics as initiated by Chabaud and Joux. This is formalized and refined however in several ways: for the problem of finding a conforming message pair whose differential trail follows a linear trail, a condition function is introduced so that finding a collision is equivalent to finding a preimage of the zero vector for the condition function. Then, the dependency table concept shows how much influence every input bit of the condition function has on its output bits. Careful analysis of the dependency table reveals degrees of freedom that can be exploited in accelerated preimage reconstruction of the condition function. These concepts are applied to an in-depth collision analysis of reduced-round versions of the two SHA-3 candidates CubeHash and MD6, and are demonstrated to give by far the best currently known collision attacks on these SHA-3 candidates.},
−
  volume    = {5594},
 
−
  url = {http://www.131002.net/data/papers/ABMNP08.pdf},
 
−
  year      = {2009},
 
−
  abstract = {Bernstein’s CubeHash is a hash function family that includes four functions submitted to the NIST Hash Competition. A CubeHash function is parametrized by a number of rounds r, a block byte size b, and a digest bit length h. The 1024-bit internal state of CubeHash is represented as a five-dimension hypercube. Submissions to NIST have r = 8, b = 1, and $h \in {224, 256, 384, 512}$.  
 
−
This paper gives the first external analysis of CubeHash, with
 
−
- improved standard generic attacks for collisions and preimages
 
−
- a multicollision attack that exploits fixed points
 
−
- a study of the round function symmetries
 
−
- a preimage attack that exploits these symmetries
 
−
- a practical collision attack on a weakened version of CubeHash
 
−
- high-probability truncated differentials over the 8-round transform
 
−
Our results do not contradict the security claims about CubeHash.},
 
 
}
 
}
 
</bibtex>
 
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashKNW08,
+
@misc{cubehashBKMP09a,
−
   author    = {Dmitry Khovratovich and Ivica Nikolic' and Ralf-Philipp Weinmann},
+
   author    = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
−
   title    = {Preimage attack on CubeHash512-r/4 and CubeHash512-r/8},
+
   title    = {Real Collisions for CubeHash-4/48},
−
   url       = {http://ehash.iaik.tugraz.at/uploads/6/6c/Cubehash.pdf},
+
   url = {http://ehash.iaik.tugraz.at/uploads/5/50/Bkmp_ch448.txt},  
−
   howpublished = {Available online},
+
   howpublished = {NIST mailing list (local link)},
−
   year     = {2008},
+
   year = {2009},
 
}
 
}
 
</bibtex>
 
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashA08,
+
@misc{cubehashBKMP09a,
−
   author    = {Jean-Philippe Aumasson},
+
   author    = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
−
   title    = {Collision for CubeHash2/120-512},
+
   title    = {Real Collisions for CubeHash-4/64},
−
   url = {http://ehash.iaik.tugraz.at/uploads/a/a9/Cubehash.txt},  
+
   url = {http://ehash.iaik.tugraz.at/uploads/9/93/Bkmp_ch464.txt},  
 
   howpublished = {NIST mailing list (local link)},
 
   howpublished = {NIST mailing list (local link)},
−
   year = {2008},
+
   year = {2009},
 
}
 
}
 
</bibtex>
 
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashD08,
+
@misc{cubehashBKMP09,
−
   author    = {Wei Dai},
+
   author    = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
−
   title    = {Collisions for CubeHash1/45 and CubeHash2/89},
+
   title    = {Attack for CubeHash-2/2 and collision for CubeHash-3/64},
−
   url = {http://www.cryptopp.com/sha3/cubehash.pdf},  
+
   url = {http://ehash.iaik.tugraz.at/uploads/3/3a/Peyrin_ch22_ch364.txt},  
−
   howpublished = {Available online},
+
   howpublished = {NIST mailing list (local link)},
−
   year = {2008},
+
   year = {2009},
−
  abstract = {Collisions were found for the hash functions CubeHash1/45-512 and CubeHash2/89-512. Attack code is included.},
 
 
}
 
}
 
</bibtex>
 
</bibtex>
Line 196: Line 192:
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashBKMP09,
+
@misc{cubehashD08,
−
   author    = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
+
   author    = {Wei Dai},
−
   title    = {Attack for CubeHash-2/2 and collision for CubeHash-3/64},
+
   title    = {Collisions for CubeHash1/45 and CubeHash2/89},
−
   url = {http://ehash.iaik.tugraz.at/uploads/3/3a/Peyrin_ch22_ch364.txt},  
+
   url = {http://www.cryptopp.com/sha3/cubehash.pdf},  
−
   howpublished = {NIST mailing list (local link)},
+
   howpublished = {Available online},
−
   year = {2009},
+
   year = {2008},
 +
  abstract = {Collisions were found for the hash functions CubeHash1/45-512 and CubeHash2/89-512. Attack code is included.},
 
}
 
}
 
</bibtex>
 
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashBKMP09a,
+
@misc{cubehashA08,
−
   author    = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
+
   author    = {Jean-Philippe Aumasson},
−
   title    = {Real Collisions for CubeHash-4/64},
+
   title    = {Collision for CubeHash2/120-512},
−
   url = {http://ehash.iaik.tugraz.at/uploads/9/93/Bkmp_ch464.txt},  
+
   url = {http://ehash.iaik.tugraz.at/uploads/a/a9/Cubehash.txt},  
 
   howpublished = {NIST mailing list (local link)},
 
   howpublished = {NIST mailing list (local link)},
−
   year = {2009},
+
   year = {2008},
 
}
 
}
 
</bibtex>
 
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashBKMP09a,
+
@misc{cubehashKNW08,
−
   author    = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
+
   author    = {Dmitry Khovratovich and Ivica Nikolic' and Ralf-Philipp Weinmann},
−
   title    = {Real Collisions for CubeHash-4/48},
+
   title    = {Preimage attack on CubeHash512-r/4 and CubeHash512-r/8},
−
   url = {http://ehash.iaik.tugraz.at/uploads/5/50/Bkmp_ch448.txt},  
+
   url       = {http://ehash.iaik.tugraz.at/uploads/6/6c/Cubehash.pdf},
−
   howpublished = {NIST mailing list (local link)},
+
   howpublished = {Available online},
−
   year = {2009},
+
   year     = {2008},
 
}
 
}
 
</bibtex>
 
</bibtex>
  
 
<bibtex>
 
<bibtex>
−
@misc{cubehashBKMP09b,
+
@inproceedings{cubehashAMPP09,
−
    author = {Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin},
+
  author   = {Jean-Philippe Aumasson and Eric Brier and Willi Meier and María Naya-Plasencia and Thomas Peyrin},
−
     title = {Linearization Framework for Collision Attacks: Application to CubeHash and MD6},
+
  title     = {Inside the Hypercube},
−
     howpublished = {Cryptology ePrint Archive, Report 2009/382},
+
  booktitle = {ACISP},
−
    year = {2009},
+
  publisher = {Springer},
−
    url = {http://eprint.iacr.org/2009/382.pdf},
+
  editor = {Colin Boyd and Juan Manuel Gonz{\'a}lez Nieto},
−
    note = {\url{http://eprint.iacr.org/}},
+
  series    = {LNCS},
−
    abstract = {In this paper, an improved differential cryptanalysis framework for finding collisions in hash functions is provided. Its principle is based on linearization of compression functions in order to find low weight differential characteristics as initiated by Chabaud and Joux. This is formalized and refined however in several ways: for the problem of finding a conforming message pair whose differential trail follows a linear trail, a condition function is introduced so that finding a collision is equivalent to finding a preimage of the zero vector for the condition function. Then, the dependency table concept shows how much influence every input bit of the condition function has on its output bits. Careful analysis of the dependency table reveals degrees of freedom that can be exploited in accelerated preimage reconstruction of the condition function. These concepts are applied to an in-depth collision analysis of reduced-round versions of the two SHA-3 candidates CubeHash and MD6, and are demonstrated to give by far the best currently known collision attacks on these SHA-3 candidates.},
+
  pages     = {202-213},
−
}
+
  volume    = {5594},
−
</bibtex>
+
  url = {http://www.131002.net/data/papers/ABMNP08.pdf},
−
 
+
  year      = {2009},
−
<bibtex>
+
  abstract = {Bernstein’s CubeHash is a hash function family that includes four functions submitted to the NIST Hash Competition. A CubeHash function is parametrized by a number of rounds r, a block byte size b, and a digest bit length h. The 1024-bit internal state of CubeHash is represented as a five-dimension hypercube. Submissions to NIST have r = 8, b = 1, and $h \in {224, 256, 384, 512}$.  
−
@misc{cryptoeprint:2009:407,
+
This paper gives the first external analysis of CubeHash, with
−
    author = {Benjamin Bloom and Alan Kaminsky},
+
- improved standard generic attacks for collisions and preimages
−
    title = {Single Block Attacks and Statistical Tests on CubeHash},
+
- a multicollision attack that exploits fixed points
−
    howpublished = {Cryptology ePrint Archive, Report 2009/407},
+
- a study of the round function symmetries
−
    year = {2009},
+
- a preimage attack that exploits these symmetries
−
    note = {\url{http://eprint.iacr.org/}},
+
- a practical collision attack on a weakened version of CubeHash
−
    abstract = {This paper describes a second preimage attack on the CubeHash cryptographic one-way hash function. The attack finds a second preimage in less time than brute force search for these CubeHash variants: CubeHash $r$/$b$-224 for $b > 100$; CubeHash$r$/$b$-256 for $b > 96$; CubeHash$r$/$b$-384 for $b > 80$; and CubeHash$r$/$b$-512 for $b > 64$. However, the attack does not break the CubeHash variants recommended for SHA-3. The attack requires minimal memory and can be performed in a massively parallel fashion. This paper also describes several statistical randomness tests on CubeHash. The tests were unable to disprove the hypothesis that CubeHash behaves as a random mapping. These results support CubeHash's viability as a secure cryptographic hash function.},
+
- high-probability truncated differentials over the 8-round transform
 +
Our results do not contradict the security claims about CubeHash.},
 
}
 
}
 
</bibtex>
 
</bibtex>

Revision as of 11:14, 15 February 2010

1 The algorithm


Daniel J. Bernstein - CubeHash specification (2.B.1)

,2009
http://cubehash.cr.yp.to/submission2/spec.pdf
Bibtex
Author : Daniel J. Bernstein
Title : CubeHash specification (2.B.1)
In : -
Address :
Date : 2009

Daniel J. Bernstein - CubeHash parameter tweak: 16 times faster

,2009
http://cubehash.cr.yp.to/submission/tweak.pdf
Bibtex
Author : Daniel J. Bernstein
Title : CubeHash parameter tweak: 16 times faster
In : -
Address :
Date : 2009

Daniel J. Bernstein - CubeHash Specification (2.B.1)

,2008
http://cubehash.cr.yp.to/submission/spec.pdf
Bibtex
Author : Daniel J. Bernstein
Title : CubeHash Specification (2.B.1)
In : -
Address :
Date : 2008


2 Cryptanalysis

We distinguish between two cases: results on the complete hash function, and results on underlying building blocks.

A description of the tables is given here.


2.1 Hash function

Here we list results on the actual hash function. The only allowed modification is to change the security parameter.

Recommended security parameters: r/b = 16/32 (n=224,256); 16/1 (n=384,512)

Type of Analysis Hash Size (n) Parameters/Variants Compression Function Calls Memory Requirements Reference
collision 512 7/64 2203 - Brier,Khazaei,Meier,Peyrin
collision all 4/48 example (237) - Brier,Khazaei,Meier,Peyrin
collision all 4/64 example (234) - Brier,Khazaei,Meier,Peyrin
collision all 3/64 example (224) - Brier,Khazaei,Meier,Peyrin
collision 512 2/2 2196 - Brier,Khazaei,Meier,Peyrin
collision 512 5/64 2231 - Brier,Peyrin
collision all 3/64 289 - Brier,Peyrin
collision 512 4/3 2207 - Brier,Peyrin
collision 384,512 4/4 2189 - Brier,Peyrin
collision all 2/3 246 - Brier,Peyrin
collision 512 2/4 example - Brier,Peyrin
collision 512 1/45, 2/89 example - Dai
collision 512 2/120 example - Aumasson
preimage 512 r/8 2480 - Khovratovich,Nikolic',Weinmann
preimage 512 r/4 2496 - Khovratovich,Nikolic',Weinmann
preimage 512 2511 2508 Khovratovich,Nikolic',Weinmann
preimage all 2513-4b - Aumasson,Meier,Naya-Plasencia,Peyrin
collision all 2521-4b-log b - submission document
preimage all 2522-4b-log b - submission document


2.2 Building blocks

Here we list results on underlying building blocks, and the hash function modified by other means than the security parameter.

Note that these results assume more direct control or access over some internal variables (aka. free-start, pseudo, compression function, block cipher, or permutation attacks).

Type of Analysis Hash Function Part Hash Size (n) Parameters/Variants Compression Function Calls Memory Requirements Reference
observations hash all Bloom,Kaminsky
multi-collision hash all 2513-4b - Aumasson,Meier,Naya-Plasencia,Peyrin
observations permutation all Aumasson,Meier,Naya-Plasencia,Peyrin


Benjamin Bloom, Alan Kaminsky - Single Block Attacks and Statistical Tests on CubeHash

,2009
Bibtex
Author : Benjamin Bloom, Alan Kaminsky
Title : Single Block Attacks and Statistical Tests on CubeHash
In : -
Address :
Date : 2009

Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin - Linearization Framework for Collision Attacks: Application to CubeHash and MD6

,2009
http://eprint.iacr.org/2009/382.pdf
Bibtex
Author : Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin
Title : Linearization Framework for Collision Attacks: Application to CubeHash and MD6
In : -
Address :
Date : 2009

Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin - Real Collisions for CubeHash-4/48

,2009
http://ehash.iaik.tugraz.at/uploads/5/50/Bkmp_ch448.txt
Bibtex
Author : Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin
Title : Real Collisions for CubeHash-4/48
In : -
Address :
Date : 2009

Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin - Real Collisions for CubeHash-4/64

,2009
http://ehash.iaik.tugraz.at/uploads/9/93/Bkmp_ch464.txt
Bibtex
Author : Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin
Title : Real Collisions for CubeHash-4/64
In : -
Address :
Date : 2009

Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin - Attack for CubeHash-2/2 and collision for CubeHash-3/64

,2009
http://ehash.iaik.tugraz.at/uploads/3/3a/Peyrin_ch22_ch364.txt
Bibtex
Author : Eric Brier, Shahram Khazaei, Willi Meier, Thomas Peyrin
Title : Attack for CubeHash-2/2 and collision for CubeHash-3/64
In : -
Address :
Date : 2009

Eric Brier, Thomas Peyrin - Cryptanalysis of CubeHash

,2009
http://thomas.peyrin.googlepages.com/BrierPeyrinCubehash.pdf
Bibtex
Author : Eric Brier, Thomas Peyrin
Title : Cryptanalysis of CubeHash
In : -
Address :
Date : 2009

Wei Dai - Collisions for CubeHash1/45 and CubeHash2/89

,2008
http://www.cryptopp.com/sha3/cubehash.pdf
Bibtex
Author : Wei Dai
Title : Collisions for CubeHash1/45 and CubeHash2/89
In : -
Address :
Date : 2008

Jean-Philippe Aumasson - Collision for CubeHash2/120-512

,2008
http://ehash.iaik.tugraz.at/uploads/a/a9/Cubehash.txt
Bibtex
Author : Jean-Philippe Aumasson
Title : Collision for CubeHash2/120-512
In : -
Address :
Date : 2008

Dmitry Khovratovich, Ivica Nikolic', Ralf-Philipp Weinmann - Preimage attack on CubeHash512-r/4 and CubeHash512-r/8

,2008
http://ehash.iaik.tugraz.at/uploads/6/6c/Cubehash.pdf
Bibtex
Author : Dmitry Khovratovich, Ivica Nikolic', Ralf-Philipp Weinmann
Title : Preimage attack on CubeHash512-r/4 and CubeHash512-r/8
In : -
Address :
Date : 2008

Jean-Philippe Aumasson, Eric Brier, Willi Meier, María Naya-Plasencia, Thomas Peyrin - Inside the Hypercube

ACISP 5594:202-213,2009
http://www.131002.net/data/papers/ABMNP08.pdf
Bibtex
Author : Jean-Philippe Aumasson, Eric Brier, Willi Meier, María Naya-Plasencia, Thomas Peyrin
Title : Inside the Hypercube
In : ACISP -
Address :
Date : 2009
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