An Anonymous Proxy Multi-signature with Accountablility

A proxy signature scheme enables a signer to delegate its signing rights to any other user, called the proxy signer, to produce a signature on its behalf. In a proxy multi-signature scheme, the proxy signer can produce one single signature on behalf of multiple original signers. [18] proposed an efficient and provably secure threshold-anonymous identity-based proxy multi-signature (IBPMS) scheme which provides anonymity to the proxy signer while also providing a threshold mechanism to the original signers to expose the identity of the proxy signer in case of misuse. The scheme in [18] provided proxy anonymity using a verifiable secret sharing scheme. We propose an anonymous proxy multi-signature without the need of the verifiable secret sharing scheme when the threshold is 1. Thus we reduce the reliance on a secret sharing scheme and reduce the corresponding computation. We also save one round of communication from the original signers to the proxy signer. Thus our scheme requires significantly less operation time in the practical implementation and also increases the actual security by reducing the components available to an adversary to attack. Finally, we compare our scheme with a recently proposed anonymous proxy multi-signature scheme and other ID-based proxy multi-signature schemes, and show that our scheme requires significantly less operation time in the practical implementation and thus it is more efficient in computation than the existing schemes.