Digital Signature Authentication Scheme with Message Recovery Based on the Use of Elliptic Curves

Abstract

Digital signature authentication scheme provides secure communication between users. Digital signatures guarantee message integrity and authentication information about the origin of a message. In the present paper we describe existing algorithms for the formation and verification of the digital signature. The conducted studies made it possible to determine that the schemes with message recovery differ from the schemes with the addition that they do not completely hash messages, but instead use masking functions and redundancy of the message. It was determined that the most effective and optimal for further use is the Nyrberg-Rueppel scheme, which is based on elliptical curves (ECNR). In this paper, we present a new digital signature scheme with message recovery based on elliptic curve cryptograph on the base of the State standart 4145-2002. Elliptic curve cryptosystem provides greater security compared to integer factorization system and discrete logarithm system, for any given key size and bandwidth. The main difference between the proposed scheme was the replacement of the hash function with the hash token function, which makes the signature and verification procedure reversed and allows you to recove messages from the signature r-component.