On the Algebraic Immunity of Symmetric Boolean Functions

机译：关于对称布尔函数的代数免疫

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In this paper, we analyze the algebraic immunity of symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. We identify a set of lowest degree annihilators for symmetric functions and propose an efficient algorithm for computing the algebraic immunity of a symmetric function. The existence of several symmetric functions with maximum algebraic immunity is proven. In this way, we have found a new class of functions which have good implementation properties and maximum algebraic immunity.

机译：在本文中，我们分析了对称布尔函数的代数免疫性。代数免疫性是一种测量对称密码对代数攻击的抵抗力的性质。我们为对称函数确定了一组最低度的hil灭子，并提出了一种有效的算法来计算对称函数的代数免疫力。证明了几个具有最大代数免疫力的对称函数的存在。这样，我们发现了一类新的函数，它们具有良好的实现属性和最大的代数免疫性。

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来源
《International Conference on Cryptology in India(INDOCRYPT 2005); 20051210-12; Bangalore(IN)》|2005年|P.35-48|共14页
会议地点 Bangalore(IN)
作者
An Braeken; Bart Preneel;
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作者单位

Katholieke Universiteit Leuven, Dept. Elect. Eng.-ESAT/SCD-COSIC, Kasteelpark Arenberg 10, 3001 Heverlee, Belgium;

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原文格式 PDF
正文语种 eng
中图分类密码、密码机;
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1. Balanced 2p-variable rotation symmetric Boolean functions with optimal algebraic immunity, good nonlinearity, and good algebraic degree [J] . Li X., Zhou Q., Qian H., Journal of Mathematical Analysis and Applications . 2013,第1期

机译：平衡的2p变量旋转对称布尔函数，具有最佳的代数免疫性，良好的非线性和良好的代数度
2. The algebraic immunity and the optimal algebraic immunity functions of a class of correlation immune H Boolean functions [J] . Jinglian Huanga, Zhuo Wang MATEC Web of Conferences . 2016,第6期

机译：一类相关免疫H布尔函数的代数免疫和最优代数免疫函数
3. A construction method of balanced rotation symmetric Boolean functions on arbitrary even number of variables with optimal algebraic immunity [J] . Mesnager Sihem, Su Sihong, Zhang Hui Designs, Codes and Crytography . 2021,第1期

机译：具有最佳代数免疫的任意偶数变量的平衡旋转对称布尔函数的施工方法
4. The algebraic immunity and the optimal algebraic immunity functions of a class of correlation immune H Boolean functions [C] . Huang Jinglian, Wang Zhuo International Seminar on Applied Physics, Optoelectronics and Photonics . 2016

机译：一类相关性免疫HOOLEAN函数的代数免疫和最佳代数免疫功能
5. Rotation Symmetric Boolean Functions [D] . Sanger, Ellyn M. 2018

机译：旋转对称布尔函数
6. Plethystic algebras and vector symmetric functions. [O] . G C Rota, J A Stein 1994

机译：多变代数和矢量对称函数。
7. On Algebraic Immunity of Weight Symmetric H Boolean Functions [O] . Jinglian Huanga, Zhuo Wangb, Juan Lic 2016

机译：关于权重对称H布尔函数的代数免疫
8. Computing the Algebraic Immunity of Boolean Functions on the SRC-6 Reconfigurable Computer. [R] . M. E. McCay 2012

机译：计算sRC-6可重构计算机上布尔函数的代数免疫性。

On the Algebraic Immunity of Symmetric Boolean Functions

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