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

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