Attacks for Finding Collision in Reduced Versions of 3-PASS and 4-PASS HAVAL

HAVAL is a hash function, which was proposed by Zheng et al. HAVAL has the first flexiable variable output lengths, namely 128, 160, 192, 224 or 256 bits, and consists of 3-pass, 4-pass and 5-pass. Differences of these types are the number of step, permutations order and boolean functions. P. R. Kasselman et al. and Park et al. found collisions of 3-pass HAVAL. In order to find a collision, they used two successive passes of 3-pass. To verify the security of HAVAL, we try to find a collision in two non-successive passes and 4-pass HAVAL. We can evaluate on the security of HAVAL through results of our attack. That is, we can know whether permutations order and boolean functions have an influence on the security of HAVAL or not. For this evaluation, we introduce the scheme of Park et al