Efficient and secure substitution box and random number generators over Mordell elliptic curves

Abstract

Elliptic curve cryptography has received great attention in recent years due to its high resistance against modern cryptanalysis. The aim of this article is to present efficient generators to generate substitution boxes (S-boxes) and pseudo random numbers which are essential for many well-known cryptosystems. These generators are based on a special class of ordered Mordell elliptic curves. Rigorous analyses are performed to test the security strength of the proposed generators. For a given prime, the experimental results reveal that the proposed generators are capable of generating a large number of distinct, mutually uncorrelated, cryptographically strong S-boxes and sequences of random numbers in low time and space complexity. Furthermore, it is evident from the comparison that the proposed schemes can efficiently generate secure S-boxes and random numbers as compared to some of the well-known existing schemes over different mathematical structures.