Development, Implementation and Analysis of Cryptographic Protocol for Digital Signatures Based on Elliptic Curves

Abstract

Cryptographic primitives based on elliptic curves have become very popular recently. The main reason is that elliptic curves can build many examples of finite Abelian groups with good parameters suitable for cryptographic purposes. In addition, elliptical curves are easy to implement on a computer, and the cryptographic strength can be achieved by choosing the characteristics of the finite field. Software cryptographic protocol for digital signature based on elliptic curves is designed and implemented. The protocol encrypts messages, forming a digital signature, message transmission and decoding at the receiver. Resistant cryptographic protocol is analyzed by several methods. A diagram of dependence of cryptographic security of the protocol on finite field characteristic, over which the elliptic curve is built, is given in the paper. The program in C++ programming environment Visual C++ 2010 with the support of large numbers GMP library is written. The program allows you to encrypt and decrypt the messages according to the generated protocol. It is also the instrument for transmission and receiving the messages with high degree of cryptographic strength and at reasonable rate.