A hashing algorithm based on a one-way function in the symmetric group Sn

Abstract: We have found an operation between permutations in the symmetric group Sn upon which we have experimentally derived results that can be linked to desirable properties in cryptography, mainly in the domain of one-way functions. From it, we have implemented a beta version of an algorithm for a hashing function by exploiting the operation’s low computational cost for speed and its properties for security. Its design makes it resistant to length extension attacks and the encoding of blocks into permutations suggests that any differential cryptanalysis technique that is based on bit conditions should be useless against it. More precisely, when measuring the evolution of differences in the compression function, bit-based distances such as the exclusive-or distance should be replaced by another type of distance, still to be determined in future research. In this work we will present the algorithm and introduce a new framework of cryptanalysis for collision and preimage attacks in order to somehow measure its security. Once this is done, we will run comparison tests against MD5 and SHA256 in order to externally evaluate our algorithm in terms of speed, weaknesses and strength.