Compact Identity-Based Signature and Puncturable Signature from SQISign

Puncturable signature (PS) offers a fine-grained revocation of signing ability by updating its signing key for a given message m such that the resulting punctured signing key can produce signatures for all messages except for m. In light of the applications of PS in proof-of-stake blockchain protocols, disappearing signatures and asynchronous transaction data signing services, this paper addresses the need for designing practical and efficient PS schemes. Existing proposals pertaining to PS suffer from various limitations, including computational inefficiency, false-positive errors, vulnerability to quantum attacks and large key and signature sizes. To overcome these challenges, we aim to design a PS from isogenies. We first propose an Identity-Based Signature (IBS) by employing the Short Quaternion and Isogeny Signature (SQISign). We provide a rigorous security analysis of our IBS and prove it is secure against unforgeability under chosen identity and chosen message attacks. More interestingly, our IBS achieves the most compact key and signature size compared to existing isogeny-based IBS schemes. Leveraging our proposed IBS, we introduce the first Short Quaternion and Isogeny Puncturable Signature (SQIPS) which allows for selective revocation of signatures and is supported by a comprehensive security analysis against existential forgery under chosen message attacks with adaptive puncturing. Our PS scheme SQIPS provides resistance from quantum attacks, enjoys small signature size and is free from false-positive errors.