Abstract:

Keccak has attracted many scientists since  it was announced new standard of Hash function SHA3 last year. θ and χ are the two most important and complex mappings in Keccak permutation. In this paper we first give the boolean function expression of χ, and then make a differential distribution table of χ by computing output differences from 32 input differences. We also make an analysis of the distribution pattern of χ from the distribution table. Double Kernel guarantees that the differences will not be diffused when passing θ mapping. With regard to this, we propose a new Double Kernel search algorithm with lower complexity compared with the algorithm in ［1］. In the end, theoretic derivation and experiments prove that the differences with Hamming Weight equal to or less than 4 do not exist.

Key words: Hash function;Keccak;SHA-3;boolean function expression;differential distribution;search algorithm