An Efficient and Provably-secure Digital signature Scheme based on Elliptic Curve Bilinear Pairings

Abstract

We proposed an efficient and secure digital signature scheme using elliptic curve cryptography (ECC) and bilinear pairings in this paper. The proposed scheme employs the general cryptographic hash function (i.e., SHA-1) instead of map-to-point function, because the map-to-point is a cost-intensive operation and it is usually implemented as a probabilistic algorithm. Further, our scheme is computationally efficient as one bilinear paring and three elliptic curve scalar point multiplication operations are executed for signature generation and verification, and thus the scheme requires much lesser computation cost than other related schemes. In addition, in the random oracle model, our scheme is proven to be existential unforgeable against the adaptive chosen message and identity attacks (EUF-CMA) based on a variation of the collusion attack algorithm with ktraitors (k-CAA3) problem.