摘要
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 permu- tation 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-fpermutation with full 24 rounds by lowering the size of the zero-sum partition from 2^1590 to 2^1575.
基金
supported by the National Natural Science Foundation of China (60573032,60773092 and 61073149)
Research Fund for the Doctoral Program of Higher Education of China (20090073110027)
关键词
置换
非线性变换
哈希函数
坐标
输出
排列
迭代
hash functions, higher order differentials, algebraic degree, zero-sum, SHA-3
