research of lyapunov exponent of s-boxes

ISCAS OpenIR

	research of lyapunov exponent of s-boxes
	Zang Hong-Yan; Fan Xiu-Bin; Min Le-Quan; Han Dan-Dan
	2012
发表期刊	ACTA PHYSICA SINICA
ISSN	1000-3290
卷号	61 期号:20 页码:-
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.; 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.
收录类别	SCI
关键词	Finite Set Discrete Chaos Theory S-boxes Lyapunov Exponent
部门归属	Zang Hong-Yan; Min Le-Quan; Han Dan-Dan Univ Sci & Technol Beijing Math & Phys Sch Beijing 100083 Peoples R China. Fan Xiu-Bin Chinese Acad Sci Inst Software Beijing 100190 Peoples R China.
学科领域	Physics
资助者	National Natural Science Foundation of China 61074192, 60833008
语种	中文
WOS记录号	WOS:000311525400018
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/15059
专题	中国科学院软件研究所
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):-.