A Verifiable Secret Sharing Protocol Based on Isogenies for Post-Quantum Cryptography

—We propose a novel Verifiable Secret Sharing (VSS) protocol utilizing isogenies of supersingular elliptic curves to ensure robust security in a post-quantum environment. By exploiting the computational hardness of the Supersingular Isogeny Problem (SIP), our protocol achieves resistance against quantum attacks. We integrate Zero-Knowledge Proofs (ZKP) to enable participants to verify share validity without compromising the secret. Through rigorous mathematical proofs and performance analysis, we demonstrate that our protocol not only enhances security but also maintains computational efficiency compared to existing schemes, making it highly suitable for applications requiring long-term security such as blockchain technologies and secure multi-party computations.