Preimage Attack on the Parallel FFT-Hashing Function

Abstract

The parallel FFT-Hashing function 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 the parallel FFT-Hashing function using 2^t + 64 + 2^{128 − t} time complexity and 2^t memory, which is less than the generic complexity 2¹²⁸. Specifically, when t = 32 , we can find a preimage using 2⁹⁷ time and 2³² memory. Our method can be described as “disseminative-meet-in-the-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 the parallel FFT-Hashing function has some weaknesses when preimage attack is considered (and relevant). To the best of our knowledge,this is the first attack on the parallel FFT-Hashing function.

This research was supported by the MIC(Ministry of Information and Communication), Korea, under the ITRC(Information Technology Research Center) support program supervised by the IITA(Institute of Information Technology Advancement) (IITA-2006-(C1090-0603-0025)). Part of this work was done while the first author visited Columbia University.