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research of lyapunov exponent of s-boxes
Zang Hong-Yan; Fan Xiu-Bin; Min Le-Quan; Han Dan-Dan
2012
SourceACTA PHYSICA SINICA
ISSN1000-3290
Volume61Issue:20Pages:-
English AbstractIn 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.
Indexed TypeSCI
KeywordFinite Set Discrete Chaos Theory S-boxes Lyapunov Exponent
DepartmentZang 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.
SubjectPhysics
SponsorshipNational Natural Science Foundation of China 61074192, 60833008
Language中文
WOS IDWOS:000311525400018
Citation statistics
Content Type期刊论文
URIhttp://ir.iscas.ac.cn/handle/311060/15059
Collection中国科学院软件研究所
Recommended Citation
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):-.
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