Abstract
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.
Highlights
A lot of advancements have been made in the field of computation methods in the past few decades
Azam et al [22] used some typical type of orderings on a class of Mordell elliptic curve (MEC) over a finite field to design an 8 × 8 substitution box (S-box) in constant time
An efficient method for the generation of a large number of distinct, uncorrelated, and cryptographically secure injective m × n multiple S-boxes is presented in this paper
Summary
A lot of advancements have been made in the field of computation methods in the past few decades. Hayat et al [20, 21] proposed different methods for the generation of an 8 × 8 S-box by Security and Communication Networks using an elliptic curve (EC) over a prime field. Azam et al [22] used some typical type of orderings on a class of Mordell elliptic curve (MEC) over a finite field to design an 8 × 8 S-box in constant time. All these schemes can generate at most one S-box for a given EC.
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