Preimage Attack on Parallel FFT-Hashing

Parallel FFT-Hashing was designed by C. P. Schnorr and S. Vaudenay in 1993. The function is a simple and light weight hash algorithm with 128-bit digest. Its basic component is a multi-permutation which helps in proving its resistance to collision attacks. In this work we show a preimage attack on Parallel FFT-Hashing with complexity 2 + 2 and memory 2 which is less than the generic complexity 2. When t = 32, we can find a preimage with complexity 2 and memory 2. Our method can be described as “disseminative-meet-inthe-middle-attack” we actually use the properties of multi-permutation (helpful against collision attack) to our advantage in the attack. Overall, this type of attack (beating the generic one) demonstrates that the structure of Parallel FFT-Hashing has some weaknesses when preimage attack is considered. To the best of our knowledge, this is the first attack on Parallel FFT-Hashing.