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

Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH

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PDF(780 KB)
Front. Inform. Technol. Electron. Eng ›› 2019, Vol. 20 ›› Issue (10) : 1378-1389. 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

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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 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.

Keywords

Substitution box / Finite field / Mordell elliptic curve / Total order / Computational complexity

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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. Front. Inform. Technol. Electron. Eng, 2019, 20(10): 1378‒1389 https://doi.org/10.1631/FITEE.1800434

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