Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes

This paper proposes to present a novel group theoretic approach of improvising the cryptographic features of substitution-boxes. The approach employs a proposed finite Abelian group of order 3720 with three generators and six relations. The pre and post-action of the new Abelian group on some nonlinear schemes is analyzed and investigated. It has been found that post-action is competent to construct substitution-boxes whose cryptographic strengths are quite better compared to them before the group action. The S-box strength improvisation has been perceived on multiple performance parameters including nonlinearity, differential uniformity, bits independent criteria, linear approximation probability, and auto-correlation functions along with the satisfaction of strict avalanche criteria. The suitability of proposed improved S-box is tested for image encryption applications under the majority logic criterions and differential analyses. The conducted statistical investigations demonstrated the proficiency of anticipated group action approach and its suitability for cryptographic usages.