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⋘S0⊞C0=(T⊞C1)⋘S1 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.
CITATION STYLE
Liu, F., Mendel, F., & Wang, G. (2017). Collisions and semi-free-start collisions for round-reduced RIPEMD-160. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10624 LNCS, pp. 158–186). Springer Verlag. https://doi.org/10.1007/978-3-319-70694-8_6
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