Cryptography and Communications

, Volume 4, Issue 3–4, pp 259–276 | Cite as

Synthetic linear analysis with applications to CubeHash and Rabbit

  • Yi Lu
  • Serge Vaudenay
  • Willi Meier


In linear cryptanalysis, it has been considered most important and difficult to analyze the bias and find a large bias. The demonstration of a large bias will usually imply that the target crypto-system is not strong. Regarding the bias analysis, researchers tend to look for a theoretical solution for a specific problem. In this paper, we take a first step towards the synthetic approach on bias analysis. We successfully apply our synthetic analysis to improve the most recent linear attacks on CubeHash and Rabbit respectively. CubeHash was selected to the second round of SHA-3 competition. The best linear attack on 11-round CubeHash with 2470 queries was proposed in Ashur and Dunkelman (2011). We present an improved attack for 11-round CubeHash with complexity 2414.2. Based on our 11-round attack, we give a new linear attack for 12-round CubeHash with complexity 2509. It is the first known attack on 12 rounds with complexity below the security parameter 2512 of CubeHash. Rabbit is a stream cipher among the finalists of ECRYPT Stream Cipher Project (eSTREAM). It has also been published as informational RFC 4503 with the Internet Engineering Task Force (IETF), which is the main standardization body for Internet technology. For Rabbit, the best linear attack with complexity 2141 was recently presented in [9]. Our synthetic bias analysis yields the improved attack with complexity 2136.


Bias Linear cryptanalysis Synthetic analysis Conditional dependence CubeHash  Rabbit 



We gratefully thank the anonymous reviewers for many helpful and valuable comments. The first author is supported by the National Science and Technology Major Project No. 2010ZX01036-001-002 and the Knowledge Innovation Key Directional Program of Chinese Academy of Sciences under Grant No. KGCX2-YW-125, and the National Natural Science Foundation of China under Grant No. 90818012.


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Copyright information

© Springer Science + Business Media, LLC 2012

Authors and Affiliations

  1. 1.National Engineering Research Center of Fundamental SoftwareInstitute of Software, Chinese Academy of SciencesBeijingChina
  2. 2.EPFLLausanneSwitzerland
  3. 3.FHNWWindischSwitzerland

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