Distinguishers on Double-Branch Compression Function and Applications to Round-Reduced RIPEMD-128 and RIPEMD-160

or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. SUMMARY This paper presents differential-based distinguishers against double-branch compression functions and applies them to ISO standard hash functions RIPEMD-128 and RIPEMD-160. A double-branch compression function computes two branch functions to update a chaining variable and then merges their outputs. For such a compression function, we observe that second-order differential paths will be constructed by finding a sub-path in each branch independently. This leads to 4-sum attacks on 47 steps (out of 64 steps) of RIPEMD-128 and 40 steps (out of 80 steps) of RIPEMD-160. Then new properties called a (partial) 2-dimension sum and a q-multi-second-order collision are considered. The partial 2-dimension sum is generated on 48 steps of RIPEMD-128 and 42 steps of RIPEMD-160, with complexities of 2 35 and 2 36 , respectively. Theoretically, the 2-dimension sum is generated faster than the brute force attack up to 52 steps of RIPEMD-128 and 51 steps of RIPEMD-160, with complexities of 2 101 and 2 158 , respectively. The results on RIPEMD-128 can also be viewed as q-multi-second-order collision attacks. The practical attacks have been implemented and examples are presented. We stress that our results do not impact to the security of full RIPEMD-128 and RIPEMD-160 hash functions. key words: RIPEMD-128, RIPEMD-160, double-branch structure, 2-dimension sum, q-multi-second-order collision