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This paper, for the first time, presents a provably secure signature scheme with message recovery based on the (elliptic-curve) discrete logarithm. The proposed scheme can be proven to be secure in the strongest sense (i.e., existentially unforgeable against adaptively chosen message attacks) in the random oracle model under the (elliptic-curve) discrete logarithm assumption. We give the concrete analysis of the security reduction. When practical hash functions are used in place of truly random functions, the proposed scheme is almost as efficient as the (elliptic-curve) Schnorr signature scheme and the existing schemes with message recovery such as (elliptic-curve) Nyberg-Rueppel and Miyaji schemes.

A Signature Scheme with Message Recovery as Secure as Discrete Logarithm