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Improved zero-sum distinguisher for full round Keccak-f permutation
  • ISSN号：1001-6538
  • 期刊名称：Chinese Science Bulletin
  • 时间：2012.2.2
  • 页码：694-697
  • 分类：O175.29[理学—数学;理学—基础数学] TP301.6[自动化与计算机技术—计算机系统结构;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China, [2]Basic Courses Department, University of Foreign Language, Luoyang 471003, China
  • 相关基金：The authors express their great thanks to C. Boura and the anonymous reviewers for their helpful comments. This work was supported by the National Natural Science Foundation of China （60573032, 60773092 and 61073149）, and Research Fund for the Doctoral Program of Higher Education of China （20090073110027）.
  • 相关项目：密码算法的高阶差分分析与可证明安全性
作者： Duan Ming|Lai XueJia|
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
中文摘要：

Keccak 是 SHA-3 比赛周围为决赛选择的五个哈希函数之一，并且它的内部原语是称为 Keccak-f 的排列。在这份报纸，我们在 Keccak-f 为唯一的非线性的转变的逆观察那，任何产量坐标的代数学的度并且任何二个产量坐标的一个产品两个都是 3，它是 2 不到它 5 的尺寸。在重申的排列的度的上面的界限上把这观察与一项提议相结合，我们为 Keccak-f 排列改进零和的 distinguisher 与完整由从 21590 ～ 21575 降低零和的分区的尺寸的 24 个回合。

英文摘要：

Keccak is one of the five hash functions selected for the final round of the SHA-3 competition, and its inner primitive is a 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.

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