Proxy signatures for delegating signing operation
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In this paper, we first show that a previous proxy signature scheme by delegation with certificate is not provably secure under adaptive-chosen message attacks and adaptive-chosen warrant attacks. The scheme does not provide the strong undeniability. Then we construct a proxy signature scheme by delegation with certificate based on Co-GDH group from bilinear map. Our proxy signature scheme is existentially unforgeable against adaptive-chosen message attacks and adaptive-chosen warrant attacks in random oracle model. We adopt a straight method of security reduction in which our scheme's security is reduced to hardness of the computational co-Diffie-Hellem problem. The proposed signature scheme is the first secure delegation-by-certificate proxy signature based on co-GDH groups from bilinear maps under the formal security model in random oracle model.