Improved preimage attack on 3-pass HAVAL

HAVAL is a hash function proposed by Zheng et al. in 1992, including 3-, 4- and 5-pass versions. We improve pseudo-preimage and preimage attacks on 3-pass HAVAL at the complexity of 2¹⁷² and 2^209.6, respectively, as compared to the previous best known results: 2¹⁹² and 2²²⁵ by Sasaki et al. in 2008. We extend the skip interval for partial-patching and apply the initial structure technique to find the better message chunks, and combine the indirect-partial-matching, partial-fixing and multi-neutral-word partial-fixing techniques to improve the attacks based on the meet-in-the-middle method. These are the best pseudo-preimage and preimage attacks on 3-pass HAVAL.