The Lower Bound Estimation of Order of a Class of Transitive Permutation Groups and Instantiation

被引：0
|
作者：
Zhou C.-W. [1 ]
Hu B. [1 ]
Guan J. [1 ]
机构：
[1] PLA SSF Information Engineering University, Zhengzhou
来源：
Tien Tzu Hsueh Pao/Acta Electronica Sinica | 2021年 / 49卷 / 12期
关键词：
Element order; Finite group; Lower bound; Order of group; Post quantum cryptography; Transitive permutation group;
D O I：
10.12263/DZXB.20201412
中图分类号：
学科分类号：
摘要：
Post quantum cryptography based on non-commutative group is a hot topic in cryptography. The order of the group ensures the difficulty of inverse operation to some extent. We mainly study the algebraic proposition of order of transitive permutation groups <g1,g2> generated by two elements g1,g2, give a necessary and sufficient conditions of transitive permutation group, and get a lower bound estimation of order of transitive permutation groups generated by two elements. In the process of the instantiation for generating g1,g2 which enables the order of transitive permutation groups <g1,g2> to satisfy the corresponding lower bound value, we give a method expressing a class of special n‑order cycles as the product of two n‑ary permutations and a corresponding design algorithm on transitive permutation groups <g1,g2> generated by two elements. In the end, this paper describes the application of transitive permutation group in symmetric cryptography. © 2021, Chinese Institute of Electronics. All right reserved.
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页码：2366 / 2371
页数：5
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