A Group Action Method for Construction of Strong Substitution Box

Abstract

In this paper, the method to develop cryptographically strong substitution box is presented which can be used in multimedia security and data hiding techniques. The algorithm of construction depends on the action of a projective general linear group over the set of units of the finite commutative ring. The strength of substitution box and ability to create confusion is assessed with different available analyses. Moreover, the ability of resistance against malicious attacks is also evaluated. The substitution box is examined by bit independent criterion, strict avalanche criterion, nonlinearity test, linear approximation probability test and differential approximation probability test. This substitution box is equated with well-recognized substitution boxes such as AES, Gray, APA, S8, prime of residue, Xyi and Skipjack. The comparison shows encouraging results about the strength of the proposed box. The majority logic criterion is also calculated to analyze the strength and its practical implementation.