Integral distinguishers for Grøstl‐512 and Kupyna‐512 permutation functions

Abstract

Grøstl is one of the SHA-3 finalist hash functions. Kupyna is the new Ukrainian hash standard, which is structurally very similar to Grøstl. The authors investigate the randomness of the two permutations used in Grøstl-512 and one of the two permutations used in Kupyna-512, in this study. New integral distinguishers of the three permutations are constructed. First, using an automatic search tool of division property, they find improved integral distinguishers of the permutations in both the forward and backward directions. Then, subspace trails are utilised to extend the length of the backward integral distinguishers by one round. Finally, the forward and backward integral distinguishers are combined using the inside-out method. As far as they know, they decrease the computational cost of 8, 9 and 10-round distinguishers and their 12-round distinguishers are the longest distinguishers for the three permutations.