Collision attack on NaSHA-384/512

NaSHA is a family of hash functions submitted by Markovski and Mileva, it is accepted as one of the first SHA-3 round candidates. In this paper, we present a collision attack on NaSHA for the output sizes 384-bit and 512-bit. This attack is based on the the weakness in the generate course of the state words, and the fact that the quasigroup operation used in the compression function are determined by partial state words. The time complexity of this attack is about 2¹²⁸ with negligible memory. This is currently by far the best known cryptanalysis result on this hash function.