A Novel Undeniable (t, n)-Threshold Signature with Cheater Identification

Abstract

A digital signature is one of the most widely used cryptographic primitives in asymmetry cryptography. According to the security requirements in different symmetry or asymmetry network models, various digital signatures have been developed in the literature. To protect the right of the signer, Chaum and Antrepen first introduced the concept of an undeniable signature, where interactive protocols are needed for the verification process. Besides, a signer can, also, perform a disavowal protocol to prove that they did not sign the message. On the other hand, threshold cryptography is, usually, used to protect the system from a single point of failure. In a (t,n)-threshold signature scheme, as long as t people in the group of n people participate, the signature can be smoothly signed. By combining these two features, an undeniable threshold signature enjoys the advantages from both sides. After our survey, we found that the existing undeniable threshold signature schemes are either insecure or apply impractical assumptions. Thus, in this manuscript, we aim at designing a novel and provably secure undeniable threshold signature scheme. The proposed scheme is formally proven to be unforgeable and invisible. Besides, our scheme supports cheater identification, which allows one to find the cheater, when a signing protocol fails. Moreover, the proposed scheme can be performed without the help of trusted third parties or secure cryptographic modules, which would be more practical when our scheme is deployed in real-world applications.