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Elliptic curves (ECs) are considered as one of the highly secure structures against modern computational attacks. In this paper, we present an efficient method based on an ordered isomorphic EC for the generation of a large number of distinct, mutually uncorrelated, and cryptographically strong injective S-boxes. The proposed scheme is characterized in terms of time complexity and the number of the distinct S-boxes. Furthermore, rigorous analysis and comparison of the newly developed method with some of the existing methods are conducted. Experimental results reveal that the newly developed scheme can efficiently generate a large number of distinct, uncorrelated, and secure S-boxes when compared with some of the well-known existing schemes.

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 a static S-box. 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 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 as compared to all existing S-box construction methods over elliptic curve. Furthermore, it is shown by the computational results that the proposed method is capable of generating cryptographically strong S-boxes with comparable security to some of the existing S-boxes constructed over different mathematical structures.