A Provably Secure and Practical Signature Scheme for Smart Cards

By "secure", we mean that some well-defined computational assumption can be shown to be sufficient for the scheme not to be existentially forgeable, even under an adaptive chosen message attack. Most, if not all, signature schemes used in practice are based on a computational assumption that is certainly necessary for this kind of security, not known to be sufficient. Since the work of Goldwasser, Micali and Rivest[?], many researches have been done for the secure signature schemes. We modify the Cramer-Damg$\dot{a}$rd scheme to implement a practical and secure signature scheme for smart cards.