Finding Biaffine and Quadratic Equations for S-Boxes Based on Power Mappings

Gupta Kishan Chand; Ray Indranil Ghosh

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Finding Biaffine and Quadratic Equations for S-Boxes Based on Power Mappings

机译：基于功率映射查找S-Box的Biaffine和二次方程

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S-boxes having large number of linearly independent multivariate biaffine or quadratic equations may be susceptible to certain kinds of algebraic attacks. In a 2009 IEEE-IT paper, Nawaz provided a polynomial time algorithm to compute the number of such equations for finding S-boxes based on power mapping. Finding actual equations in polynomial time was still open. In this paper, techniques for finding a maximal set of linearly independent biaffine and quadratic equations are developed for S-boxes based on power mappings. Two algorithms to calculate the biaffine and quadratic equations for any S-box based on power mapping are presented. The time complexity of both the algorithms is .

机译：具有大量线性独立多元biaffine或二次方程的S-box可能易受某些代数攻击。在2009年IEEE-IT论文中，Nawaz提供了多项式时间算法来计算用于根据功率映射找到S盒的此类方程式的数量。在多项式时间内寻找实际方程仍然是开放的。在本文中，基于功率映射，为S盒开发了用于找到最大线性独立的仿射和二次方程组的技术。提出了两种基于功率映射来计算任何S盒的仿射方程和二次方程的算法。两种算法的时间复杂度均为。

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来源
《Information Theory, IEEE Transactions on》 |2015年第4期|2200-2209|共10页
作者
Gupta Kishan Chand; Ray Indranil Ghosh;
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作者单位

Applied Statistics Unit, Indian Statistical Institute, Kolkata, India;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Boolean functions; Ciphers; Mathematical model; Polynomials; Time complexity; Vectors; Algebraic attacks; Bi-affine equations; Power mapping; Quadratic equations; S-box; algebraic attacks; power mapping; quadratic equations;

机译：布尔函数;密码;数学模型;多项式;时间复杂度;向量;代数攻击;双仿射方程;幂映射;二次方程;S-box;代数攻击;幂映射;二次方程;

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2. Algebraic Immunity of S-Boxes Based on Power Mappings: Analysis and Construction [J] . Nawaz Y., Gupta K. C., Gong G. Information Theory, IEEE Transactions on . 2009,第9期

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4. Classifying 8-Bit to 8-Bit S-Boxes Based onPower Mappings from the Point of DDT and LAT Distributions [C] . Bora Asian, M. Tolga Sakalli, Ercan Bulus Arithmetic of Finite Fields . 2008

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Finding Biaffine and Quadratic Equations for S-Boxes Based on Power Mappings

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