Results on the Immunity of Boolean Functions against Probabilistic Algebraic Attacks

被引：0
|
作者：
Liu, Meicheng [1 ]
Lin, Dongdai [1 ]
Pei, Dingyi [2 ]
机构：
[1] Chinese Acad Sci, Inst Software, State Key Lab Informat Secur, Beijing 100190, Peoples R China
[2] Guangzhou Univ, Coll Math & Infroma Sci, Guangzhou 510006, Peoples R China
来源：
INFORMATION SECURITY AND PRIVACY | 2011年 / 6812卷
基金：
中国国家自然科学基金;
关键词：
Boolean functions; algebraic attacks; algebraic immunity; algebraic immunity distance; k-error algebraic immunity; high order nonlinearity; STREAM CIPHERS; CONSTRUCTION; VARIABLES;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we study the immunity of Boolean functions against probabilistic algebraic attacks. We first show that there are functions, using as filters in a linear feedback shift register based nonlinear filter generator, such that probabilistic algebraic attacks outperform deterministic ones. Then we introduce two notions, algebraic immunity distance and k-error algebraic immunity, to measure the ability of Boolean functions resistant to probabilistic algebraic attacks. We analyze both lower and upper bounds on algebraic immunity distance, and also present the relations among algebraic immunity distance, k-error algebraic immunity, algebraic immunity and high order nonlinearity.
引用
收藏
页码：34 / +
页数：3
相关论文
共 50 条
  • [1] On Computing the Immunity of Boolean Power Functions Against Fast Algebraic Attacks
    Du, Yusong
    Wei, Baodian
    [J]. INFORMATION SECURITY AND CRYPTOLOGY - ICISC 2016, 2017, 10157 : 304 - 316
  • [2] On the immunity of rotation symmetric Boolean functions against fast algebraic attacks
    Zhang, Yin
    Liu, Meicheng
    Lin, Dongdai
    [J]. DISCRETE APPLIED MATHEMATICS, 2014, 162 : 17 - 27
  • [3] Some results on the algebraic immunity of Boolean functions
    XU Li-qing
    [J]. The Journal of China Universities of Posts and Telecommunications, 2011, 18 (02) : 102 - 105
  • [4] New Results on the Algebraic Immunity of Boolean Functions
    Rizomiliotis, Panagiotis
    [J]. ENHANCING CRYPTOGRAPHIC PRIMITIVES WITH TECHNIQUES FROM ERROR CORRECTING CODES, 2009, 23 : 192 - 202
  • [5] Highly Nonlinear Boolean Functions With Optimal Algebraic Immunity and Good Behavior Against Fast Algebraic Attacks
    Tang, Deng
    Carlet, Claude
    Tang, Xiaohu
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (01) : 653 - 664
  • [6] On the security of the Feng–Liao–Yang Boolean functions with optimal algebraic immunity against fast algebraic attacks
    Panagiotis Rizomiliotis
    [J]. Designs, Codes and Cryptography, 2010, 57 : 283 - 292
  • [7] Results on highly nonlinear Boolean functions with provably good immunity to fast algebraic attacks
    Liu, Meicheng
    Lin, Dongdai
    [J]. INFORMATION SCIENCES, 2017, 421 : 181 - 203
  • [8] On the security of the Feng-Liao-Yang Boolean functions with optimal algebraic immunity against fast algebraic attacks
    Rizomiliotis, Panagiotis
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2010, 57 (03) : 283 - 292
  • [9] Results on algebraic immunity for cryptographically significant Boolean functions
    Dalai, DK
    Gupta, KC
    Maitra, S
    [J]. PROGRESS IN CRYPTOLOGY - INDOCRYPT 2004, PROCEEDINGS, 2004, 3348 : 92 - 106
  • [10] A CLASS OF 1-RESILIENT BOOLEAN FUNCTIONS WITH OPTIMAL ALGEBRAIC IMMUNITY AND GOOD BEHAVIOR AGAINST FAST ALGEBRAIC ATTACKS
    Tang, Deng
    Carlet, Claude
    Tang, Xiaohu
    [J]. INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, 2014, 25 (06) : 763 - 780
12345