International Association for Cryptologic Research

International Association
for Cryptologic Research


Gaoli Wang


Efficient Collision Attack Frameworks for RIPEMD-160
RIPEMD-160 is an ISO/IEC standard and has been applied to generate the Bitcoin address with SHA-256. Due to the complex dual-stream structure, the first collision attack on reduced RIPEMD-160 presented by Liu, Mendel and Wang at Asiacrypt 2017 only reaches 30 steps, having a time complexity of $$2^{70}$$. Apart from that, several semi-free-start collision attacks have been published for reduced RIPEMD-160 with the start-from-the-middle method. Inspired from such start-from-the middle structures, we propose two novel efficient collision attack frameworks for reduced RIPEMD-160 by making full use of the weakness of its message expansion. Those two frameworks are called dense-left-and-sparse-right (DLSR) framework and sparse-left-and-dense-right (SLDR) framework. As it turns out, the DLSR framework is more efficient than SLDR framework since one more step can be fully controlled, though with extra $$2^{32}$$ memory complexity. To construct the best differential characteristics for the DLSR framework, we carefully build the linearized part of the characteristics and then solve the corresponding nonlinear part using a guess-and-determine approach. Based on the newly discovered differential characteristics, we provide colliding messages pairs for the first practical collision attacks on 30 and 31 (out of 80) steps of RIPEMD-160 with time complexity $$2^{35.9}$$ and $$2^{41.5}$$ respectively. In addition, benefiting from the partial calculation, we can attack 33 and 34 (out of 80) steps of RIPEMD-160 with time complexity $$2^{67.1}$$ and $$2^{74.3}$$ respectively. When applying the SLDR framework to the differential characteristic used in the Asiacrypt 2017 paper, we significantly improve the time complexity by a factor of $$2^{13}$$. However, it still cannot compete with the results obtained from the DLSR framework. To the best of our knowledge, these are the best collision attacks on reduced RIPEMD-160 with respect to the number of steps, including the first colliding message pairs for 30 and 31 steps of RIPEMD-160.
Cryptanalysis of 48-step RIPEMD-160
In this paper, we show how to theoretically compute the step differential probability of RIPEMD-160 under the condition that only one internal variable contains difference and the difference is a power of 2. Inspired by the way of computing the differential probability, we can do message modification such that a step differential hold with probability 1. Moreover, we propose a semi-free-start collision attack on 48-step RIPEMD-160, which improves the best semi-free start collision by 6 rounds. This is mainly due to that some bits of the chaining variable in the i-th step can be computed by adding some conditions in advance, even though some chaining variables before step i are unknown. Therefore, the uncontrolled probability of the differential path is increased and the number of the needed starting points is decreased. Then a semi-free-start collision attack on 48-step RIPEMD-160 can be obtained based on the differential path constructed by Mendel et al. at ASIACRYPT 2013. The experiments confirm our reasoning and complexity analysis.