RSA-Based Generalized Signature Scheme

Threshold signatures, while valuable, are often constrained by rigidity due to the requirement of a fixed threshold of signers and also the signers are treated as equals. This rigidity can hinder real-world applications where nuanced authorization requirements are crucial. We propose a novel RSA-based threshold signature scheme that surpasses the limitations of traditional threshold signature schemes by offering enhanced flexibility and adaptability. The proposed scheme leverages generalized secret sharing for non-monotone access structures to enable flexible signing policies, which allows any subset of signers to sign. It allows for the specification of arbitrary signing groups, including non-monotone access structures, where the inclusion or exclusion of specific signers can influence the signing capability. The signing keys of the signers can be chosen independent of the public key without any interaction among the signers. The signature does not reveal anything about who all generated it. A single public key is required for verification. The correctness, complexity and security analysis of the scheme are given.