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This paper presents a new approach of group theory toward cryptosystem with its application of mathematical methods and functions for cryptographic regions. This new group theory in cryptographic paradigm is brought together with relation to existing functional groups, fields, rings, mathematical theorems, mathematical tools, etc. this study concentrated on semantic security solutions evaluation for cryptographic systems. Such cryptographic systems are mostly designed to use the group’s applications such as fields, ECC, functionality tests, cyclic groups, and Schnorr groups. In this paper, we discussed some possible applications of groups and group theory by introducing different forms of groups, fields, rings, theorems, etc. A brief description of some mathematical tools which include functionalities tests, methods, discrete logarithmic problems, ECC, factoring polynomials, and baby giant algorithm is also presented in this paper. Solutions for cryptographic problems inspired by group theory and its applications in this field are also described in the study. |
