A SCHNORR-BASED ZERO-KNOWLEDGE PROOF SCHEME ON ELLIPTIC CURVE

Abstract

A cryptographic method known as Zero-Knowledge Proof, or ZKP for short, was introduced to the public for the first time in the 1990s. ZKP has been extensively implemented in practice over the past decade, such as in blockchain technology and authentication systems, as well as incorporated into other cryptographic algorithms. The majority of these ZKP schemes are mathematically founded on finite fields. In this paper, we propose a Schnorr-based ZKP scheme on Elliptic curves. This approach has high security and better performance than the Schnorr-based ZKP scheme on the finite field. Moreover, its security enhancements are superior to those of other Schnorr-based ZKP algorithms on the Elliptic curve. These results are argued on the basis of the mathematical theory of published and experimental works in the Python programming language. Therefore, it can be concluded that this ZKP scheme has tremendous potential for implementation in client-side authentication systems and in Blockchain technology.