Collision Attack on 4 Secure PGV Hash Function Schemes based on 4-Round PRESENT-80 with Iterative Differential Approach

Preneel-Govaerts-Vandewalle (PGV) hash function schemes is a single-block-length hash function based on block cipher introduced by Preneel et al. in 1993. They proposed 64 basic ways to construct a (collision-resistant) hash functions from a block cipher. They regarded 12 of these 64 schemes are secure, though no proofs or formal claims were given. We take 4 schemes from those 12 schemes to analyzed. In this paper, we show different approach to find collisions in four secure PGV hash function schemes. The use of block cipher that has iterative differential such as PRESENT can let us to find collisions. In 2007, Wang found four iterative characteristics for 4-round PRESENT-80. Based on the analysis, we indicate that those four secure PGV schemes based on 4-round PRESENT-80 are not fulfilled collision resistance property.