Hybrid tabu search algorithm for excellent Boolean function

Weiqiong WANG; Haojie XU; Meng CUI; Qiong XIE

doi:10.11959/j.issn.1000-436x.2022096

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Hybrid tabu search algorithm for excellent Boolean function

Papers | 更新时间：2024-06-05

- Hybrid tabu search algorithm for excellent Boolean function
- Journal on Communications Vol. 43, Issue 5, Pages: 133-143(2022)
- 作者机构：
  
  长安大学理学院，陕西西安 710064
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(11901049);The Natural Science Basic Research Program of Shaanxi(2020JQ-343);Young Talent Fund of University Association for Science and Technology in Shaanxi(20200505)
- DOI：10.11959/j.issn.1000-436x.2022096
  CLC： TP301.6
- Online First：2022-05，
  
  Published：25 May 2022
- 稿件说明：
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Weiqiong WANG, Haojie XU, Meng CUI, et al. Hybrid tabu search algorithm for excellent Boolean function[J]. Journal on Communications, 2022, 43(5): 133-143.
DOI：

Weiqiong WANG, Haojie XU, Meng CUI, et al. Hybrid tabu search algorithm for excellent Boolean function[J]. Journal on Communications, 2022, 43(5): 133-143. DOI： 10.11959/j.issn.1000-436x.2022096.

摘要

为保障对称密码算法的安全性，其构成算法中所使用的布尔函数必须具有优良的密码学性质。结合禁忌搜索算法和爬山算法的优点，提出了一种新的优良布尔函数启发式生成算法——混合禁忌搜索算法。应用该算法，可以快速得到大量具有高非线性度、低自相关性、一阶弹性、最优代数次数、最优代数免疫度、最优（次优）抵抗快速代数攻击能力等的布尔函数。仿真结果表明，所提算法搜索能力强，运行速度快，且搜索出的布尔函数的密码学性质优于已知的优化算法的结果，也弥补了采用构造法构造布尔函数的一些缺陷。

Abstract

Boolean function in symmetric cryptographic algorithm must satisfy excellent cryptographic criteria to ensure the security of the algorithm.By combining the advantages of tabu search algorithm and hill climbing algorithm

a new heuristic generation algorithm called hybrid tabu search algorithm for excellent Boolean function was proposed.A large number of Boolean function with high nonlinearity

low autocorrelation

one-resilient

optimal algebraic degree

optimal algebraic immunity

optimal (suboptimal) resistance to fast algebraic attacks could be obtained quickly by applying the proposed algorithm.Simulation results demonstrate that the cryptographic properties of the Boolean function obtained by the proposed algorithm with strong search ability and fast running speed are better than the results of known optimization algorithm.Moreover

the algorithm also provides good Boolean function that cannot be obtained by using construction method.

关键词

Keywords

references

张卫国 , 肖国镇 . 具有偶数个变元的高非线性度平衡布尔函数的构造 [J ] . 电子学报 , 2011 , 39 ( 3 ): 727 - 728 .

ZHANG W G , XIAO G Z . Construction of balanced Boolean functions with high nonlinearity on even number variables [J ] . Acta Electronica Sinica , 2011 , 39 ( 3 ): 727 - 728 .

欧智慧 , 赵亚群 , 李旭 . 一类密码函数的构造与分析 [J ] . 通信学报 , 2013 , 34 ( 4 ): 106 - 113 .

OU Z H , ZHAO Y Q , LI X . Construction and analysis of one class of cryptographic functions [J ] . Journal on Communications , 2013 , 34 ( 4 ): 106 - 113 .

孙天锋 , 胡斌 , 杨阳 . Plateaued 函数的构造方法研究 [J ] . 电子与信息学报 , 2018 , 40 ( 10 ): 2352 - 2357 .

SUN T F , HU B , YANG Y . Research on the construction of Plateaued functions [J ] . Journal of Electronics ＆ Information Technology , 2018 , 40 ( 10 ): 2352 - 2357 .

杜蛟 , 刘春红 , 庞善起 . 4t-1 元旋转对称 2-弹性函数的构造 [J ] . 通信学报 , 2020 , 41 ( 11 ): 169 - 175 .

DU J , LIU C H , PANG S Q . Constructions of rotation symmetric 2-resilient functions with 4t-1 number of variables [J ] . Journal on Communications , 2020 , 41 ( 11 ): 169 - 175 .

ZHANG F R , PASALIC E , WEI Y Z . Constructions of balanced Boolean functions on even number of variables with maximum absolute value in autocorrelation spectra < 2 n/2 [J ] . Information Sciences , 2021 , 575 : 437 - 453 .

CARLET C , FENG K Q . An infinite class of balanced functions with optimal algebraic immunity,good immunity to fast algebraic attacks and good nonlinearity [C ] // 2008 International Conference on the Theory and Application of Cryptology and Information Security . Berlin:Springer , 2008 : 425 - 440 .

TU Z R , DENG Y P . A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity [J ] . Designs,Codes and Cryptography , 2011 , 60 ( 1 ): 1 - 14 .

TU Z R , DENG Y P . Boolean functions optimizing most of the cryptographic criteria [J ] . Discrete Applied Mathematics , 2012 , 160 ( 4/5 ): 427 - 435 .

ZHANG W G , PASALIC E . Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria [J ] . Information Sciences , 2017 , 376 : 21 - 30 .

SABER Z , UDDIN M F , YOUSSEF A . On the existence of (9,3,5,240) resilient functions [J ] . IEEE Transactions on Information Theory , 2006 , 52 ( 5 ): 2269 - 2270 .

LIU W M , YOUSSEF A . On the existence of (10,2,7,488) resilient functions [J ] . IEEE Transactions on Information Theory , 2009 , 55 ( 1 ): 411 - 412 .

YANG J P , ZHANG W G . Generating highly nonlinear resilient Boolean functions resistance against algebraic and fast algebraic attacks [J ] . Security and Communication Networks , 2015 , 8 ( 7 ): 1256 - 1264 .

贾少帅 , 张凤荣 . 基于引力搜索的布尔函数生成算法 [J ] . 计算机应用研究 , 2021 , 38 ( 2 ): 430 - 434 .

JIA S S , ZHANG F R . Boolean function generation algorithm based on gravitational search algorithm [J ] . Application Research of Computers , 2021 , 38 ( 2 ): 430 - 434 .

CLARK J A , JACOB J L . Two-stage optimisation in the design of Boolean functions [C ] // 2000 Australasian Conference on Information Security and Privacy . Berlin:Springer , 2000 : 242 - 254 .

李超 , 胡朋松 , 海昕 . 布尔函数设计中的爬山算法及其改进 [J ] . 通信学报 , 2007 , 28 ( 3 ): 130 - 133 .

LI C , HU P S , HAI X . Improved hill-climbing methods in the design of Boolean function [J ] . Journal on Communications , 2007 , 28 ( 3 ): 130 - 133 .

BEHERA P K , GANGOPADHYAY S . An improved hybrid genetic algorithm to construct balanced Boolean function with optimal cryptographic properties [J ] . Evolutionary Intelligence , 2022 , 15 ( 1 ): 639 - 653 .

JAKOBOVIC D , PICEK S , MARTINS M S R , et al . Toward more efficient heuristic construction of Boolean functions [J ] . Applied Soft Computing , 2021 ,107:107327.

CARLET C , JAKOBOVIC D , PICEK S . Evolutionary algorithms-assisted construction of cryptographic Boolean functions [C ] // Proceedings of the Genetic and Evolutionary Computation Conference .[S.l.:s.n. ] , 2021 : 565 - 573 .

MACWILLIAMS F J , SLOANE N J A . The theory of error correcting codes [M ] . Amsterdam : Elsevier , 1977 .

XIAO G Z , MASSEY J L . A spectral characterization of correlation-immune combining functions [J ] . IEEE Transactions on Information Theory , 1988 , 34 ( 3 ): 569 - 571 .

SIEGENTHALER T . Correlation-immunity of nonlinear combining functions for cryptographic applications [J ] . IEEE Transactions on Information Theory , 1984 , 30 ( 5 ): 776 - 780 .

ZHANG X M , ZHENG Y L . GAC-the criterion for global avalanche characteristics of cryptographic functions [J ] . Journal of Universal Computer Science , 1995 , 1 ( 5 ): 316 - 333 .

CARLET C . Partially-bent functions [J ] . Designs,Codes and Cryptography , 1993 , 3 ( 2 ): 135 - 145 .

COURTOIS N T , . Algebraic attacks on combiners with memory and several outputs [C ] // 2004 International Conference on Information Security and Cryptology . Berlin:Springer , 2004 : 3 - 20 .

MEIER W , PASALIC E , CARLET C . Algebraic attacks and decomposition of Boolean functions [C ] // 2004 International Conference on the Theory and Applications of Cryptographic Techniques . Berlin:Springer , 2004 : 474 - 491 .

COURTOIS N T , . Fast algebraic attacks on stream ciphers with linear feedback [C ] // 2003 Annual International Cryptology Conference . Berlin:Springer , 2003 : 176 - 194 .

GLOVER F . Future paths for integer programming and links to artificial intelligence [J ] . Computers ＆ Operations Research , 1986 , 13 ( 5 ): 533 - 549 .

GLOVER F . Tabu search—part I [J ] . ORSA Journal on Computing , 1989 , 1 ( 3 ): 190 - 206 .

GLOVER F . Tabu search—part II [J ] . ORSA Journal on Computing , 1990 , 2 ( 1 ): 4 - 32 .

GLOVER F . Tabu search:a tutorial [J ] . Interfaces , 1990 , 20 ( 4 ): 74 - 94 .

MAITRA S , PASALIC E . Further constructions of resilient Boolean functions with very high nonlinearity [C ] // Proceedings of Sequences and Their Applications . Berlin:Springer , 2002 : 265 - 280 .

CARLET C . On a weakness of the Tu-Deng function and its repair [R ] . Cryptology ePrint Archive , 2009 .

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