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

  • Naveed Ahmed AzamEmail author
  • Umar Hayat
  • Ikram Ullah
Article
  • 11 Downloads

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.

Key words

Substitution box Finite field Mordell elliptic curve Total order Computational complexity 

CLC number

TP309 

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Notes

Compliance with ethics guidelines

Naveed Ahmed AZAM, Umar HAYAT, and Ikram ULLAH declare that they have no conflict of interest.

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Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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