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

Naveed Ahmed AZAM; Umar HAYAT; Ikram ULLAH

doi:10.1631/FITEE.1800434

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

Regular Papers | Updated：2022-05-19

- Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field
- 高效构造基于有限域上莫德尔椭圆曲线的密码置换盒
- Frontiers of Information Technology & Electronic Engineering Vol. 20, Issue 10, Pages: 1378-1389(2019)
- Affiliations：
  
  Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
  Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
- Author bio：
  
  Naveed Ahmed AZAM, E-mail: azam@amp.i.kyoto-u.ac.jp
  [ "Umar HAYAT, E-mail: umar.hayat@qau.edu.pk" ]
- Funds：
- DOI：10.1631/FITEE.1800434
  CLC： TP309
- Received：18 July 2018，
  
  Revised：2019-10-10，
  
  Published：2019-10
- Accepted：
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Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH. Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1378-1389.
DOI：

Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH. Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1378-1389. DOI： 10.1631/FITEE.1800434.

摘要

椭圆曲线密码体制与其他密码体制相比有密钥小、安全性高等优点，被广泛应用于各种安全系统。在许多著名安全系统中，仅置换盒是非线性结构。最近研究表明，用动态置换盒代替静态置换盒可提高密码系统安全性，因此需构造新的安全置换盒。提出一种高效构造置换盒方法，该方法基于素数域上的一类莫德尔椭圆曲线，并通过定义不同总阶数实现。对于每个输入，该方法在线性时间与恒定空间内输出一个置换盒。因此，与现有基于椭圆曲线的置换盒生成方法相比，所提方法占用更少时间和空间。计算结果表明，所提方法能生成加密性强的置换盒，且其安全性与现有基于其他数学结构的置换盒相当。

Abstract

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 developed 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 proposed method is capable of generating cryptographically strong S-boxes with security comparable to some of the existing S-boxes constructed via different mathematical structures.

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references

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