Welcome to the resource topic for
**2017/800**

**Title:**

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

**Authors:**
Fukang Liu, Florian Mendel, Gaoli Wang

**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^{70}. 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 Daumâ€™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}.

**ePrint:**
https://eprint.iacr.org/2017/800

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