Collision attack on the full extended MD4 and pseudo-Preimage attack on RIPEMD

The cryptographic hash functions Extended MD4 and RIPEMD are double-branch hash functions, which consist of two parallel branches. Extended MD4 was proposed by Rivest in 1990, and RIPEMD was devised in the framework of the RIPE project (RACE Integrity Primitives Evaluation, 1988 ~ 1992). On the basis of differential analysis and meet-in-the-middle attack principle, this paper proposes a collision attack on the full Extended MD4 and a pseudo-preimage attack on the full RIPEMD respectively. The collision attack on Extended MD4 holds with a complexity of 2³⁷, and a collision instance is presented. The pseudo-preimage attack on RIPEMD holds with a complexity of 2^125:4, which optimizes the complexity order for brute-force attack. The results in this study will also be beneficial to the analysis of other double-branch hash functions such as RIPEMD-160.