Improved zero-sum distinguisher for full round Keccak-f permutation

Keccak is one of the five hash functions selected for the final round of the SHA-3 competition and its inner primitive is a permutation called Keccakf . In this paper, we find that for the inverse of the only one nonlinear transformation of Keccak-f , the algebraic degrees of any output coordinate and of the product of any two output coordinates are both 3 and also 2 less than its size 5. Combining the observation with a proposition from an upper bound on the degree of iterated permutations, we improve the zerosum distinguisher of full 24 rounds Keccak-f permutation by lowering the size of the zero-sum partition from 2 to 2.