CONSTRUCTION OF ELLIPTIC CURVES BASED SUBSTITUTION BOX WITH APPLICATIONS IN THE TEXT DATA ENCRYPTION

Abstract

Today, the design of secure substitution boxes (S-boxes) is a crucial issue in cryptography, especially considering the sophistication of the cryptanalytic attacks. In this study, a parameterized key-dependent Mordell elliptic curve construction approach to S-box is proposed over  using irreducible polynomials. Secret key is used to create key-dependent elliptic curves, adding extra randomness and creating even more security for encryption. The proposed method utilizes the algebraic properties of Mordell elliptic curve and the efficiency of the computation in finite fields to generate powerful S-boxes. The effectiveness of the generated S-box when it comes to the cryptographic properties is analyzed with some standard metrics such as nonlinearity, Strict Avalanche Criterion (SAC), Differential approximation Probability (DAP), Bit Independence Criterion (BIC), and Linear Approximation Probability (LAP). Moreover, the Avalanche effect analysis is performed for evaluating the effectiveness of encryption scheme. Analyses results showed excellent resistance to both differential and linear cryptanalysis, which demonstrates that the proposed dynamic S-box is an efficient component for modern cryptographic applications.