A NOVEL ALGORITHM FOR S-BOX CONSTRUCTION USING TRIGONOMETRIC TOTAL ORDERS ON MORDELL ELLIPTIC CURVES OVER PRIME FIELDS

Abstract

The S-Box is the non-linear element of a cryptographic system and is applied to generate confusion and diffusion of a dataset. Generating confusion and diffusion in the data makes it difficult for adversaries to extract credential information. The generation of suitable S-boxes is one of the most important issues in any cryptographic algorithm. We design a new algorithm to generate suitable S-boxes by means of trigonometric orderings on Mordell elliptic curves (MECs) over the prime field Fp. The generated S-boxes possess excellent cryptographic properties and exhibit good resistance to various types of attacks namely algebraic, differential, and linear.

Keywords : Mordell Elliptic Curves, Total Orders, Substitution Box.