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**2011/023**

**Title:**

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

**Authors:**
Ming Duan, 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}.

**ePrint:**
https://eprint.iacr.org/2011/023

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