Hybrid proxy multisignature: A new type multi-party signature

In this paper, we introduce a new type of multi-party signature: hybrid proxy multisignature (HPM). An HPM is collaboratively generated by some signers themselves and some proxy signers on behalf of their original signers. We describe the syntax of general HPM schemes and formalize a notion of security for them. We also construct a concrete HPM scheme and prove its security in the Random Oracle Model, assuming the Co-Diffie-Hellman problem in the underlying groups equipped with a pairing is hard. The size of an HPM in our scheme is independent of the number of the actual signers. Further, the scheme has accountability, that is the signers of an HPM can be identified. Comparing with other types of multi-party signatures such as multisignature, proxy multisignature and multiproxy multisignature, HPM has more flexibility.