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Collisions and Semi-Free-Start Collisions for Round-Reduced RIPEMD-160

  • Fukang Liu
  • Florian Mendel
  • Gaoli WangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10624)

Abstract

In this paper, we propose an improved cryptanalysis of the double-branch hash function RIPEMD-160 standardized by ISO/IEC. Firstly, we show how to theoretically calculate the step differential probability of RIPEMD-160, which was stated as an open problem by Mendel et al. at ASIACRYPT 2013. Secondly, based on the method proposed by Mendel et al. to automatically find a differential path of RIPEMD-160, we construct a 30-step differential path where the left branch is sparse and the right branch is controlled as sparse as possible. To ensure the message modification techniques can be applied to RIPEMD-160, some extra bit conditions should be pre-deduced and well controlled. These extra bit conditions are used to ensure that the modular difference can be correctly propagated. This way, we can find a collision of 30-step RIPEMD-160 with complexity \(2^{67}\). This is the first collision attack on round-reduced RIPEMD-160. Moreover, by a different choice of the message words to merge two branches and adding some conditions to the starting point, the semi-free-start collision attack on the first 36-step RIPEMD-160 from ASIACRYPT 2013 can be improved. However, the previous way to pre-compute the equation \(T^{\lll S_0}\boxplus C_0=(T\boxplus C_1)^{\lll S_1}\) costs too much. To overcome this obstacle, we are inspired by Daum’s et al. work on MD5 and describe a method to reduce the time complexity and memory complexity to pre-compute that equation. Combining all these techniques, the time complexity of the semi-free-start collision attack on the first 36-step RIPEMD-160 can be reduced by a factor of \(2^{15.3}\) to \(2^{55.1}\).

Keywords

RIPEMD-160 Semi-free-start collision Collision Hash function Compression function 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions. Fukang Liu and Gaoli Wang are supported by the National Natural Science Foundation of China (Nos. 61572125, 61632012, 61373142), and Shanghai High-Tech Field Project (No. 16511101400). Florian Mendel has been supported by the Austrian Science Fund (FWF) under grant P26494-N15.

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Trustworthy Computing, School of Computer Science and Software EngineeringEast China Normal UniversityShanghaiChina
  2. 2.Graz University of TechnologyGrazAustria

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