优良布尔函数的混合禁忌搜索算法

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

摘要/Abstract

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。

关键词: 布尔函数, 禁忌搜索算法, 弹性, 非线性度

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.

Key words: Boolean function, tabu search algorithm, resiliency, nonlinearity

中图分类号:

TP301.6

王维琼, 许豪杰, 崔萌, 谢琼. 优良布尔函数的混合禁忌搜索算法[J]. 通信学报, 2022, 43(5): 133-143.

Weiqiong WANG, Haojie XU, Meng CUI, Qiong XIE. Hybrid tabu search algorithm for excellent Boolean function[J]. Journal on Communications, 2022, 43(5): 133-143.

图/表 6

图1

表1

表2

表3

表4

HTS cost 1 算法与 HTS cost 2 算法的结果对比"

n	${HTS}_{{cost}_{1}}$	${HTS}_{{cost}_{2}}$
8	(116,24,6,4,7)	(116,24,6,4,7)
9	(236,48,7,5,8)	(236,48,7,5,8)
10	(484,80,8,5,10)	(488,72,8,5,9)
11	(984,112,9,6,10)	(988,104,9,6,10)
12	(1 988,144,10,6,11)	(1 996,152,10,6,11)
13	(4 012,216,11,7,12)	(4 020,232,11,7,12)
14	(8 072,320,12,7,13)	(8 080,320,12,7,13)

表4

表5

一阶弹性布尔函数的密码学性质对比"

n	文献[8]	文献[9]	文献[12]	文献[13]	${HTS}_{{cost}_{2}}$
8	(112,-,6,4,-)	(116,32,6,4,7)	(116,48,6,4,7)	(112,48,6,4,7)	(116,24,6,4,7)
9	—	—	(236,48,7,4,8)	(232,80,7,4,8)	(236,48,7,5,8)
10	(484,-,8,5,-)	(488,-,8,5,8)	(484,96,8,5,9)	—	(488,72,8,5,9)
11	—	—	(984,136,9,5,10)	—	(988,104,9,6,10)
12	(1996,-,10,6,-)	(2 008,96,9,6,9)	(1988,184,10,6,11)	—	(1996,152,10,6,11)
13	—	—	(4 012,288,11,6,12)	—	(4 020,232,11,7,12)
14	(8100,-,12,7,-)	(8112,-,11,-,-)	(8 072,368,12,7,13)	—	(8 080,320,12,7,13)

表5

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n	K
8	8.6
9	9.8
10	10.7
11	11.7
12	12.6
13	13.7
14	14.6

n		运行时间/s
n	改进前		改进后
8	2.41		1.66
9	3.51		2.52
10	10.28		6.14
11	28.39		12.58
12	176.42		40.36
13	556.82		126.62
14	1 864.96		415.16