Construction of an S-Box Using Suppersingular Elliptic Curve over Finite Field

Iqrar Ali Pali, Muhammad Afzal Soomro, Muhammad Memon, Asgher Ali Maitlo, Sanaullah Dehraj, Naveed Ahmed Umrani


This research aims to develop an S-box using elliptic curve cryptography (ECC) that provides higher security than other cryptographic schemes with equivalent key size. In this paper, a supersingular elliptic curve  has been taken of characteristic more than three.  The generated S-box depends on the values of a and b used in the supersingular elliptic curve. The robustness of the recently constructed S-box is thoroughly evaluated against prevalent attacks, including linear, differential, and algebraic attacks, through an analysis of its nonlinearity, linear approximation, differential branch number, and other established properties. The achieved findings are additionally contrasted with some well-known S-boxes.


Keywords: finite fields, supersingular elliptic curves, group law, rational points, substitution boxes.

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