Significance of Certain Algebraic Structures in Cryptography

First chapter is based on fascinating introduction of basic group theory. Introduction of cryptography is provided in second chapter. In third chapter, a novel group theoretic approach of improvising the cryptographic features of substitution-boxes is used. The approach employs the action of a proposed finite Abelian group of order 3720 with three generators and six relations over four different algebraic schemes. The S-box strength improvisation has been perceived on multiple performance parameters including nonlinearity, differential uniformity, bit independence criteria, linear approximation probability, and autocorrelation 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.