A variant of Schnorr signature scheme with tight security reduction

In 1990, Schnorr proposed a signature scheme that is suitable for smart card interactions. The original Schnorr signature was based on the Discrete Logarithm assumption with a loose security reduction. In 2003, Katz-Wang then proposed a variant of Schnorr's signature scheme based on the Decisional Diffie-Hellman assumption with a tight security reduction. In this paper, we further improve Katz-Wang's work by reducing the number of public keys used, while maintaining the tight security properties of the scheme based on Decisional Square Computational Diffie-Hellman assumption.