Improved Cryptanalysis of APOP-MD4 and NMAC-MD4 using New Differential Paths

In case of security analysis of hash functions, finding a good collision-inducing differential paths has been only focused on. However, it is not clear how differential paths of a hash function influence the securities of schemes based on the hash function. In this paper, we show that any differential path of a hash function can influence the securities of schemes based on the hash function. We explain this fact with the MD4 hash function. We first show that APOP-MD4 with a nonce of fixed length can be analyzed efficiently with a new differential path. Then we improve the result of the key-recovery attack on NMAC-MD4 described by Fouque et al. [4] by combining new differential paths. Our results mean that good hash functions should have the following property : It is computationally infeasible to find differential a path of hash functions with a high probability.