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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 Keccak-f.In this paper,we observe that for the inverse of the only nonlinear transformation in Keccak-f,the algebraic degree of any output coordinate and the one of the product of any two output coordinates are both 3,which is 2 less than its size of 5.Combining this observation with a proposition on the upper bound of the degree of iterated permutations,we improve the zero-sum distinguisher for the Keccak-f permutation with full 24 rounds by lowering the size of the zero-sum partition from 21590 to 21575.
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 Keccak-f.In this paper, we observe that for the inverse of the only nonlinear transformation in Keccak- f, the algebraic degree of any output coordinate and the one of the product of any two output coordinates are both 3, which is 2 less than its size of 5. Combining this observation with a proposition on the upper bound of the degree of iterated permutations , we improve the zero-sum distinguisher for the Keccak-f permutation with full 24 rounds by lowering the size of the zero-sum partition from 21590 to 21575.