SOME VARIANTS OF THE SCHNORR SIGNATURE SCHEMA ON THE FINITE FIELD AND THE ELLIPTIC CURVE

Abstract

Schnorr signature schemas and the version on its elliptic curve (EC-Schnorr) are signature schemas that are not only highly secure but are also rated as having the highest performance among signature schemas based on discrete logarithm problems (on the Fp finite field and on the elliptic curve). The Schnorr and EC-Schnorr schemas have been incorporated into ISO/IEC 14888-3 and the BSI standard of the Federal Republic of Germany. Currently, the development of signature schemas based on Schnorr and EC-Schnorr schemas for BlockChain applications and digital currencies is of great interest. In this article the authors suggest several variations of the Schnorr schema on the finite field and the elliptic curve. The analyses in the article shows that the new schemas proposed here have the same security and performance as the Schnorr/EC-Schnorr signature schema in practical applications.