Provably secure identity-based threshold signature on access structure

The existing provably secure threshold signature schemes based on the Lagrange interpolation can only be applied to the (t, n) threshold structure. Through introducing the concept of access structure into the provably secure threshold signature, the first provably secure identity-based threshold signature scheme on access structure is proposed. The formal security proof under the adaptive chosen message attack is provided. Compared to the existing schemes, the proposed scheme is more flexible in practice. Besides, it is easier to design because that the troublesome Lagrange interpolation is not needed.