Single-Round Zero-Knowledge Proof for the Square-Root Problem in Cloud Systems.

Zero-knowledge proofs (ZKPs) enable a prover to convince a verifier of knowledge of a secret without revealing it. The ZKP for the square-root problem has many applications in network and cloud security, such as user authentication and privacy-preserving cloud storage auditing. Classical protocols for the quadratic residuosity (square-root) relation require multiple iterations to reach negligible soundness error, incurring latency and communication costs that are critical in cloud settings. This paper proposes a new single-round zero-knowledge proof (SR-ZKP) for the square-root problem that achieves the same soundness as iterative schemes by increasing the challenge length. The protocol requires only one execution of a 4-message protocol (request, commit, challenge, response) and can be transformed into a one-message non-interactive ZKP via the Fiat-Shamir heuristic. The completeness, soundness, and zero-knowledge properties of the proposed scheme are formally proven. The results of this study show that the proposed protocol can achieve approximately 97% reduction in communication overhead and latency, when compared to an 80-round iterative ZKPs with RSA modulus.. of size 2048 bits. This provides a substantial advantage for cloud applications.