一类新的基于元胞自动机的S盒的密码学性质研究

doi:10.11959/j.issn.1000-436x.2019101

通信学报 ›› 2019, Vol. 40 ›› Issue (5): 192-200.doi: 10.11959/j.issn.1000-436x.2019101

一类新的基于元胞自动机的S盒的密码学性质研究

关杰,黄俊君

解放军战略支援部队信息工程大学密码工程学院，河南郑州 450001

修回日期:2019-04-01 出版日期:2019-05-25 发布日期:2019-05-30
作者简介:关杰（1974– ），女，河南郑州人，博士，解放军战略支援部队信息工程大学教授、博士生导师，主要研究方向为密码理论和密码算法分析。|黄俊君（1995– ），男，浙江上虞人，解放军战略支援部队信息工程大学硕士生，主要研究方向为对称密码设计与分析。
基金资助:
国家自然科学基金资助项目(61572516);国家自然科学基金资助项目(61272041);国家自然科学基金资助项目(61272488)

Research on cryptographic properties of a new S-box based on cellular automaton

Jie GUAN,Junjun HUANG

Institute of Cryptography Engineering,Information Engineering University,Zhengzhou 450001,China

Revised:2019-04-01 Online:2019-05-25 Published:2019-05-30
Supported by:
The National Natural Science Foundation of China(61572516);The National Natural Science Foundation of China(61272041);The National Natural Science Foundation of China(61272488)

摘要/Abstract

摘要：

通过实验找到了一类新的基于元胞自动机的S盒，分析了该S盒的置换性质，证明了其仅在规模为5时是一个置换。通过构造差分矩阵的方法给出了该S盒的非平凡差分转移概率与差分矩阵的秩之间的关系，从而得到其取值范围。证明了对输入差分进行循环移位不改变其对应的非平凡差分转移概率，从而给出其在规模为5时取最大和最小非平凡差分转移概率的充要条件，彻底解决了此时该S盒的差分对应的结构和计数问题。

关键词: 元胞自动机, S盒, 置换性质, 差分分析

Abstract:

A new S-box based on cellular automata was found by experiments.The permutation properties of the S-box were analyzed,which proved that the S-box was a permutation only when the size of lattice was 5.Then the relation between the nontrivial difference transition probability of the S-box and the rank of the difference matrix was proved by constructing the difference matrix.And it was proved that the cyclic shift of input differential would not change the corresponding nontrivial differential transition probability,and obtained the sufficient and necessary conditions about the maximum and minimum nontrivial differential transition probabilities when the size of lattice was 5.Then the problem of the difference distribution of the S-box in this situation is completely solved.

Key words: cellular automaton, S-box, permutation property, differential analysis

中图分类号:

TN918.1

关杰,黄俊君. 一类新的基于元胞自动机的S盒的密码学性质研究[J]. 通信学报, 2019, 40(5): 192-200.

Jie GUAN,Junjun HUANG. Research on cryptographic properties of a new S-box based on cellular automaton[J]. Journal on Communications, 2019, 40(5): 192-200.

图/表 2

图1

表1

F new 5 和 F K 5 的差分转移概率计数"

差分转移概率	$_{F_{new}^{5}}$	$F_{K}^{5}$
1	1	1
$\frac{1}{4}$	0	20
$\frac{1}{8}$	120	120
$\frac{1}{16}$	256	176
0	647	707

表1

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一类新的基于元胞自动机的S盒的密码学性质研究

Research on cryptographic properties of a new S-box based on cellular automaton

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