research of lyapunov exponent of s-boxes

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	research of lyapunov exponent of s-boxes
	Zang Hong-Yan ; Fan Xiu-Bin ; Min Le-Quan ; Han Dan-Dan
刊名	ACTA PHYSICA SINICA
	2012
卷号	61 期号:20 页码:-
关键词	finite set discrete chaos theory S-boxes Lyapunov exponent
ISSN号	1000-3290
中文摘要	In the design of cryptographic algorithms, S-boxes provide the cryptosystems with the information confusion function. The traditional cryptography indexes of the S-boxes generally include linear deviation, differential characteristics, algebraic immunity, fixed point mumber, snowslide effect, and so on. In 2006, Kocarev et al. (Kocarev L, Szczepanski J, Amigo J M and Tomovski I 2006 IEEE Transactions on Circuits and Systems-I: regular papers 53 6 1300) set up a discrete chaos theory based on the finite set. In light of the theory in this paper, we introduce the definition of the Lyapunov exponent with Hamming distance, calculate and compare the Lyapunov exponent values of the S-boxes in several cryptographic algorithms. In this paper we prove that a map defined on the Euclidean distance has a maximal Lyapunov exponent value of 0. In this paper it is shown that the relationship between the Lyapunov exponent and the snowslide effect of the S-box is the relationship between the butterfly effect in chaos theory and the snowslide effect in cryptography. The definition of the Lyapunov exponent of the proposed S-boxes may be complementary to the traditional cryptography indexes of the S-box.
英文摘要	In the design of cryptographic algorithms, S-boxes provide the cryptosystems with the information confusion function. The traditional cryptography indexes of the S-boxes generally include linear deviation, differential characteristics, algebraic immunity, fixed point mumber, snowslide effect, and so on. In 2006, Kocarev et al. (Kocarev L, Szczepanski J, Amigo J M and Tomovski I 2006 IEEE Transactions on Circuits and Systems-I: regular papers 53 6 1300) set up a discrete chaos theory based on the finite set. In light of the theory in this paper, we introduce the definition of the Lyapunov exponent with Hamming distance, calculate and compare the Lyapunov exponent values of the S-boxes in several cryptographic algorithms. In this paper we prove that a map defined on the Euclidean distance has a maximal Lyapunov exponent value of 0. In this paper it is shown that the relationship between the Lyapunov exponent and the snowslide effect of the S-box is the relationship between the butterfly effect in chaos theory and the snowslide effect in cryptography. The definition of the Lyapunov exponent of the proposed S-boxes may be complementary to the traditional cryptography indexes of the S-box.
学科主题	Physics
收录类别	SCI
资助信息	National Natural Science Foundation of China 61074192, 60833008
语种	中文
WOS记录号	WOS:000311525400018
公开日期	2013-09-17
内容类型	期刊论文
源URL	[http://ir.iscas.ac.cn/handle/311060/15059]
专题	软件研究所_软件所图书馆_期刊论文
推荐引用方式 GB/T 7714	Zang Hong-Yan,Fan Xiu-Bin,Min Le-Quan,et al. research of lyapunov exponent of s-boxes[J]. ACTA PHYSICA SINICA,2012,61(20):-.
APA	Zang Hong-Yan,Fan Xiu-Bin,Min Le-Quan,&Han Dan-Dan.(2012).research of lyapunov exponent of s-boxes.ACTA PHYSICA SINICA,61(20),-.
MLA	Zang Hong-Yan,et al."research of lyapunov exponent of s-boxes".ACTA PHYSICA SINICA 61.20(2012):-.