Synthetic linear analysis: improved attacks on cubehash and rabbit

Authors:
Yi Lu;Serge Vaudenay;Willi Meier;Liping Ding;Jianchun Jiang
Affiliations:
National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China;EPFL, Lausanne, Switzerland;FHNW, Windisch, Switzerland;National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China;National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China
Venue:
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
Year:
2011

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Synthetic linear analysis with applications to CubeHash and Rabbit

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Abstract

It has been considered most important and difficult to analyze the bias and find a large bias regarding the security of crypto-systems, since the invention of linear cryptanalysis. The demonstration of a large bias will usually imply that the target crypto-system is not strong. Regarding the bias analysis, researchers often focus on 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. For CubeHash, the best linear attack on 11-round CubeHash with 2470 queries was proposed previously. 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 2513, which is sharply close to the security parameter 2512 of CubeHash. Rabbit is a stream cipher among the finalists of ECRYPT Stream Cipher Project (eSTREAM). For Rabbit, the best linear attack with complexity 2141 was recently presented. Our synthetic bias analysis yields the improved attack with complexity 2136. Moreover, it seems that our results might be further improved, according to our ongoing computations.