Algorithm of the electronic sign-code signature on the basis of the composition of existing complexities

Abstract

The article developed a new algorithm for electronic digital signature in the composition of existing difficulties: discrete logarithm in a finite field, addition of points with rational coordinates of the elliptic curve. Based on a combination of the complexities of a discrete logarithm on a finite field with a large number characteristic, decomposition of a sufficiently large odd number into prime factors, and addition of points of an elliptic curve, an electronic digital signature algorithm is developed for generating. The generally recognized model of electronic sign-code signature covers three processes: generation of digital signature keys; ESS formation; confirmation of authenticity of electronic sign-code signature. Firmness offered AESS is based on several complexities: calculations of the discrete logarithming in a finite field, decisions of the task of expansion of enough big odd number on simple factors, executions of operation of addition of points of the elliptic curve set in a finite field. It considerably raises crypto algorithm strength.