Efficient Construction of S-boxes Based on a Mordell Elliptic Curve Over a Finite Field

Elliptic curve cryptography (ECC) is used in many security systems due to its small key size and high security as compared to the other cryptosystems. In many well-known security systems substitution box (S-box) is the only non-linear component. Recently, it is shown that the security of a cryptosystem can be improved by using dynamic S-boxes instead of static S-boxes. This fact necessitates the construction of new secure S-boxes. In this paper, we propose an efficient method for the generation of S-boxes based on a class of Mordell elliptic curves (MECs) over prime fields by defining different total orders. The proposed technique is developed carefully so that it output an S-box inheriting the properties of the underlying MEC for each input in constant time. Furthermore, it is shown by the computational results that the proposed method is capable of generating cryptographically strong S-boxes as compared to some of the existing S-boxes.

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