Identity-based multisignature and aggregate signature schemes from m-torsion groups

An identity-based multisignature scheme and an identity-based aggregate signature scheme are proposed in this paper. They are both from m-torsion groups on super-singular elliptic curves or hyper-elliptic curves and based on the recently proposed identity-based signature scheme of Cha and Cheon. Due to the sound properties of m-torsion groups and the base scheme, it turns out that our schemes are very simple and efficient. Both schemes are proven to be secure against adaptive chosen message attack in the random oracle model under the normal security notions with the assumption that the Computational Diffie-Hellman problem is hard in the m-torsion groups.