Polynomial Rabin Cryptosystem Based on the Operation of Addition

Abstract

The analysis of the existing asymmetric encryption / decryption algorithms is carried out, their advantages and disadvantages are determined on the basis of this analysis in the paper. Mathematical and algorithmic support for the implementation of a polynomial Rabin cryptosystem based on addition without computationally costly arithmetic operations is presented. This allows us to develop reliable and effective systems for protecting information flows by increasing the dimensions of input parameters (key size, message size), while improving the robustness of the cryptosystem. The encryption / decryption scheme of a polynomial Rabin cryptosystem applying addition is presented. Analytical expressions of time complexity of the classical and proposed approaches to the implementation of the Rabin cryptosystem in the polynomial ring are obtained. Graphical dependences of the found complexities on the degrees of polynomials are given, which show the advantages of the developed method.