A variable threshold ring signature scheme for privacy protection in smart city blockchain applications

In smart city deployments, blockchain offers decentralized control over services and data, yet it also introduces stringent privacy and scalability challenges. Ring signatures can authenticate transactions while preserving signer anonymity, but existing schemes seldom provide both unconditional strong anonymity and robust collusion resistance, and they often incur burdensome key management and costly verification. To overcome these limitations, we present a distributed, attribute-based ring signature scheme with a flexible threshold policy. Our approach leverages (n, t)-threshold distributed key-generation protocol to eliminate any single point of trust and to simplify key distribution. By encoding user identity attributes directly into signature keys, the construction guarantees provable unforgeability, unconditional anonymity, and resistance to collusion among malicious users. We further introduce an optimized batch-verification algorithm that cuts the number of expensive pairing checks per signature from O(n) to $$O(1) + n$$ , dramatically improving throughput. Security proofs in the random-oracle model and detailed performance evaluations confirm that our scheme is both practical and scalable for privacy-critical blockchain applications in smart cities.