基于均匀化混沌系统生成S盒的算法研究

臧鸿雁; 黄慧芳

doi:10.11999/JEIT160535

基于均匀化混沌系统生成S盒的算法研究

doi: 10.11999/JEIT160535

臧鸿雁¹,
黄慧芳²

1.
(北京科技大学数理学院北京 100083) ②(厦门大学嘉庚学院信息科学与技术学院漳州 363105)

基金项目:

国家自然科学基金(61170037)

计量
- 文章访问数: 1322
- HTML全文浏览量: 240
- PDF下载量: 366
- 被引次数: 0
出版历程
- 收稿日期: 2016-05-26
- 修回日期: 2016-10-27
- 刊出日期: 2017-03-19

Research on Algorithm of Generating S-box Based on Uniform Chaotic System

ZANG Hongyan¹,
HUANG Huifang²

1.
(School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China)
2.
(School of Information Science and Technology, Xiamen University Tan Kah Kee College, Zhangzhou 363105, China)

Funds:

The National Natural Science Foundation of China (61170037)

摘要

摘要: 该文给出了一个新的二次多项式混沌系统，并利用系统与Tent映射拓扑共轭的性质，给出了系统的概率密度函数，基于概率密度的形式，进一步设计了一个变换函数，实现了系统的均匀化。针对均匀化前后的混沌系统构造了S盒生成算法，对该算法产生的300个S盒进行差分概率(DP)和线性概率(LP)的统计分析，结果表明均匀化后混沌系统产生的S盒的DP和LP略优于均匀化前的值。
- 混沌系统 /
- 均匀化 /
- 拓扑共轭 /
- S盒
Abstract: A new quadratic polynomial chaotic system is given and homogenized based on its probability density function. Then, based on the chaotic systems before and after homogenization, an S-box generation algorithm is constructed. By numerical simulation, the algorithm dynamically generates 300 S-boxes and then analyses their Differential Probability (DP) and Linear Probability (LP). The statistical results show that the uniform chaotic system can produce better performance of S-boxes.
- Chaotic system /
- Homogenization /
- Topological conjugation /
- S-box

HTML全文

参考文献(21)

LI Tienyien and YORKE J A. Period three implies chaos[J]. American Mathematical Monthly, 1975(82): 985-992.

MATTHEWS R. On the serivation of a chaotic encryption algorithm[J]. Cryptologia, 1989, 13(1): 29-42.

GOTZ M, KELBER K, and SCHWARZ W. Discrete-time chaotic coders for information encryptionPart 1: Systematic structural design[C]. Workshop on Nonlinear Dynamics of Electronic Systems, Moscow, Russia, 1997: 21-26.

KOCAREV L, JAKIMOSKI G, STOJANOVSKI T, et al. From chaotic maps to encryption schemes[C]. IEEE International Symposium on Circuits, Systems. Monterey, USA, 1998: 514-517.

何振亚, 李克, 杨绿溪. 具有良好安全性能的混沌映射二进制序列[J]. 电子与科学学刊, 1999, 21(5): 646-651.

HE Zhenya, LI Ke, and YANG Luxi. Chaotic Map Binary Sequences with Good Security[J]. Journal of Electronics, 1999, 21(5): 646-651.

曹光辉, 胡凯, 佟维. 基于Logistic均匀分布图像置乱方法[J]. 物理学报, 2011, 60(11): 125-132.

CAO Guanghui, HU Kai, and TONG Wei. Image scrambling based on logistic uniform distribution[J]. Acta Physica Sinica, 2011, 60(11): 125-132.

TERRY R. Substitution cipher with pseudo-random shuffling: The dynamic substitution combiner[J]. Cryptologia, 1990, 14(4): 289-303.

WONG K W, HO S W, and YUNG C K. A chaotic cryptography scheme for generating short cipher text[J]. Physics Letters A, 2003, 310(1): 67-73.

周海玲, 宋恩彬. 二次多项式映射的3-周期点判定[J]. 四川大学学报(自然科学版), 2009, 46(3): 561-564. doi: 103969/j. issn. 0490-6756.2009.03-009.

ZHOU H L and SONG E B. Discrimination of the 3-periodic points of a quadratic polynomial[J]. Journal of Sichuan University(Natural Science Edition), 2009, 46(3): 561-564. doi: 103969/j.issn.0490-6756.2009.03-009.

郝柏林. 从抛物线谈起混沌动力学引论[M]. 第2版, 北京: 北京大学出版社, 2013, 114-118.

HAO B L. Starting with Parabola: An Introduction to Chaotic Dynamics[M]. 2nd Edition, Beijing: Peking University Press, 2013, 114-118.

AMIGO J M, KOCAREV L, and TOMOVSKI I. Discrete entropy[J]. Physica D, 2007, 228(1): 77-85.

KHAN M, SHAH T, and BATOOL S I. Construction of S-box based on chaotic Boolean functions and its application in image encryption[J]. Neural Computing Applications, 2016, 27(3): 677-685.

韩丹丹, 闵乐泉, 赵耿, 等. 一维鲁棒混沌映射及S盒的设计[J]. 电子学报, 2015, 43(9): 1770-1775. doi: 10.3969/j.issn. 0372-2112.2015.09.014.

HAN D, MIN L, ZHAO G, et al. One-dimensional robust chaotic map and the construction of S-box[J]. Acta Electronica Sinica, 2015, 43(9): 1770-1775. doi: 10.3969/j. issn.0372-2112.2015.09.014.

LIU G, YANG W, LIU W, et al. Designing S-boxes based on 3-D four-wing autonomous chaotic system[J]. Nonlinear Dynamics, 2015, 82(4): 1867-1877. doi: 10.1007/s11071-015- 2283-y.

臧鸿雁, 范修斌, 闵乐泉, 等. S-盒的 Lyapunov 指数研究[J]. 物理学报, 2012, 61(20): 200508.

ZANG H, FAN X, MIN L, et al. Research of Lyapunov exponent of S-boxes[J]. Acta Physica Sinica, 2012, 61(20): 200508.

施引文献

资源附件(0)

访问统计