A Linkable Ring Signature Based on Polar Codes with Reusable Authorization

Post-quantum digital signatures are needed to protect authentication against quantum attacks. Code-based techniques offer a promising foundation for this goal. Linkable ring signatures additionally provide signer anonymity and public linkage, but repeated membership proofs can incur substantial communication costs. We propose a linkable ring signature based on polar codes with reusable anonymous authorization. The scheme supports independently verifiable messages, public linking across rings, and repeated signing. Under the stated primitive assumptions and honest registration, we prove unforgeability, restricted anonymity, linkability, and non-frameability in the classical random oracle model. For parameters selected against a 128-bit classical generic-attack target, the authorization proof is 98.52% shorter than the selected-matrix implementation of the same relation for a 32-member ring, and each cached online packet occupies 807 bytes. Compared with a direct-proof baseline using the same parameters, certificate reuse reduces total communication from the second message onward for all evaluated ring sizes. A prototype executes key generation, authorization, certificate installation, and online signing and verification with actual polar-code keys. For a 1024-member ring, the authorization certificate occupies 189.5 MB. For a single verifier with pre-distributed rings, total communication is lower than that of a reference linkable ring signature scheme for workloads of at least 6561 messages.