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| research of lyapunov exponent of s-boxes | |
| Zang Hong-Yan; Fan Xiu-Bin; Min Le-Quan; Han Dan-Dan | |
| 2012 | |
| Source | ACTA PHYSICA SINICA
 |
| ISSN | 1000-3290 |
| Volume | 61Issue:20Pages:- |
| English Abstract | 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. |
| Indexed Type | SCI |
| Keyword | Finite Set Discrete Chaos Theory S-boxes Lyapunov Exponent |
| Department | 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. |
| Subject | Physics |
| Sponsorship | National Natural Science Foundation of China 61074192, 60833008 |
| Language | 中文 |
| WOS ID | WOS:000311525400018 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://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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