We present pseudo-preimage attacks on Davis-Meyer mode of reduced rounds of the block ciphers ARIA, Camellia, and Serpent by using Sasaki's framework. They yield preimage or second-preimage attacks on PGV hashing modes. We develop proper initial structures for applying meet-in-the-middle techniques to the block ciphers, by considering their diffusion layers, and propose a method to find matching-check equations for indirect partial matching technique with a binary matrix. These works enable us to attack 5 rounds of ARIA, 7 rounds of Camellia, and 4 rounds of Serpent faster than brute force attack.

MDC-4 is the enhanced version of MDC-2, which is a well-known hash mode of block ciphers. However, it does not guarantee sufficient securities required for a cryptographic hash function. In the ideal cipher model, the MDC-4 compression function has the collision security bound close to 25n/8 and the preimage security bound close to 25n/4, where the underlying block cipher has the block size of n bits. We have studied how to improve MDC-4 with simple modification to strengthen its security. It is meaningful work because users often want to improve their familiar systems with low cost. In this paper, we achieve it by proposing MDC-4+, which is a light variation of MDC-4. We prove that MDC-4+ is much more secure than MDC-4 by showing that it has the collision security bound close to optimal 2n and the preimage security bound close to 24n/3. We also discuss its efficiency by comparing existing hash modes.