Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field

作     者：Naveed Ahmed AZAM Umar HAYAT Ikram ULLAH 

作者机构：Department of Applied Mathematics and PhysicsGraduate School of InformaticsKyoto UniversityKyoto 606-8501Japan Department of MathematicsQuaid-i-Azam UniversityIslamabad 44000Pakistan 

出 版 物：《Frontiers of Information Technology & Electronic Engineering》 (信息与电子工程前沿（英文版）)

年 卷 期：2019年第20卷第10期

页      面：1378-1389页

核心收录：

学科分类：0839[工学-网络空间安全] 08[工学] 081201[工学-计算机系统结构] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Project supported by the JSPS KAKENHI(No.18J23484) 

主　　题：Substitution box Finite field Mordell elliptic curve Total order Computational complexity 

摘      要：Elliptic curve cryptography has been used in many security systems due to its small key size and high security compared with other cryptosystems. In many well-known security systems, a substitution box (S-box) is the only non-linear component. Recently, it has been shown that the security of a cryptosystem can be improved using dynamic S-boxes instead of a static S-box. This necessitates the construction of new secure S-boxes. We propose an efficient method to generate S-boxes that are based on a class of Mordell elliptic curves over prime fields and achieved by defining different total orders. The proposed scheme is devel-oped in such a way that for each input it outputs an S-box in linear time and constant space. Due to this property, our method takes less time and space than the existing S-box construction methods over elliptic curves. Computational results show that the pro-posed method is capable of generating cryptographically strong S-boxes with security comparable to some of the existing S-boxes constructed via different mathematical structures.