International Association
for Cryptologic Research

The SHA-2 family including SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224 and SHA512/256 is a U.S. federal standard published by NIST. Especially, there is no doubt that SHA-256 is one of the most important hash functions used in real-world applications. Due to its complex design compared with SHA-1, there is almost no progress in collision attacks on SHA-2 after ASIACRYPT 2015. In this work, we retake this challenge and aim to significantly improve collision attacks on the SHA-2 family. First, we observe from many existing attacks on SHA-2 that the current advanced tool to search for SHA-2 characteristics has reached the bottleneck. Specifically, longer differential characteristics could not be found, and this causes that the collision attack could not reach more steps. To address this issue, we adopt Liu et al.’s MILP-based method and implement it with SAT/SMT for SHA-2, where we also add more techniques to detect contradictions in SHA-2 characteristics. This answers an open problem left in Liu et al.’s paper to apply the technique to SHA-2. With this SAT/SMT-based tool, we search for SHA-2 characteristics by controlling its sparsity in a dedicated way. As a result, we successfully find the first practical semi-free-start (SFS) colliding message pair for 39-step SHA-256, improving the best 38-step SFS collision attack published at EUROCRYPT 2013. In addition, we also report the first practical free-start (FS) collision attack on 40-step SHA-224, while the previously best theoretic 40-step attack has time complexity 2^{110}. Moreover, for the first time, we can mount practical and theoretic collision attacks on 28-step and 31-step SHA-512, respectively, which improve the best collision attack only reaching 27 steps of SHA-512 at ASIACRYPT 2015. In a word, with new techniques to find SHA-2 characteristics, we have made some notable progress in the analysis of SHA-2 after the major achievements made at EUROCRYPT 2013 and ASIACRYPT 2015.

The hash function RIPEMD-160 is an ISO/IEC standard and is being used to generate the bitcoin address together with SHA-256. Despite the fact that many hash functions in the MD-SHA hash family have been broken, RIPEMD-160 remains secure and the best collision attack could only reach up to 34 out of 80 rounds, which was published at CRYPTO 2019. In this paper, we propose a new collision attack on RIPEMD-160 that can reach up to 36 rounds with time complexity $2^{64.5}$. This new attack is facilitated by a new strategy to choose the message differences and new techniques to simultaneously handle the differential conditions on both branches. Moreover, different from all the previous work on RIPEMD-160, we utilize a MILP-based method to search for differential characteristics, where we construct a model to accurately describe the signed difference transitions through its round function. As far as we know, this is the first model targeting the signed difference transitions for the MD-SHA hash family. Indeed, we are more motivated to design this model by the fact that many automatic tools to search for such differential characteristics are not publicly available and implementing them from scratch is too time-consuming and difficult. Hence, we expect that this can be an alternative easy tool for future research, which only requires to write down some simple linear inequalities.

As an ISO/IEC standard, the hash function RIPEMD-160 has been used to generate the Bitcoin address with SHA-256. However, due to the complex doublebranch structure of RIPEMD-160, the best collision attack only reaches 36 out of 80 steps of RIPEMD-160, and the best semi-free-start (SFS) collision attack only reaches 40 steps. To improve the 36-step collision attack proposed at EUROCRYPT 2023, we explored the possibility of using different message differences to increase the number of attacked steps, and we finally identified one choice allowing a 40-step collision attack. To find the corresponding 40-step differential characteristic, we re-implement the MILP-based method to search for signed differential characteristics with SAT/SMT. As a result, we can find a colliding message pair for 40-step RIPEMD-160 in practical time, which significantly improves the best collision attack on RIPEMD-160. For the best SFS collision attack published at ToSC 2019, we observe that the bottleneck is the probability of the right-branch differential characteristics as they are fully uncontrolled in the message modification. To address this issue, we utilize our SAT/SMT-based tool to search for high-probability differential characteristics for the right branch. Consequently, we can mount successful SFS collision attacks on 41, 42 and 43 steps of RIPEMD-160, thus significantly improving the SFS collision attacks. In addition, we also searched for a 44-step differential characteristic, but the differential probability is too low to allow a meaningful SFS collision attack.