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

*Ming Duan and Xuajia Lai*

**Abstract: **K$\textsc{eccak}$ 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 K$\textsc{eccak}$-$f$. In this paper, we find that for the inverse of the only one nonlinear transformation of K$\textsc{eccak}$-$f$, 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 zero-sum distinguisher of full 24 rounds K$\textsc{eccak}$-$f$ permutation by lowering the size of the zero-sum partition from $2^{1590}$ to $2^{1579}$.

**Category / Keywords: **secret-key cryptography / hash functions, higher order differentials, algebraic degree, zero-sum, SHA-3.

**Date: **received 12 Jan 2011

**Contact author: **mduan at sjtu edu cn; lai-xj@cs sjtu edu cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20110114:041641 (All versions of this report)

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