Security Proof of Single-Source Shortest Distance Protocols Built on Secure Multiparty Computation Protocols

Secure secret-sharing Single-Source Shortest Distance (SSSD) protocols, based on secure multiparty computation (SMC), offer a promising solution for securely distributing and managing sensitive information among multiple parties. However, formal security proofs for these protocols have largely been unexplored. This paper addresses this gap by providing the first security proof for the SSSD protocols using the privacy-preserving Bellman–Ford protocols. These new protocols offer significant enhancements in efficiency, particularly in handling large-scale graphs due to parallel computation. In our previous work, published in MDPI Cryptography, we introduced these protocols and presented extensive experiments on the Sharemind system that demonstrated their efficiency. However, that work did not include security proofs. Building on this foundation, the current paper rigorously proves the security of these protocols, offering valuable insights into their robustness and reliability. Furthermore, we discuss the adversarial model, security definitions, cryptographic assumptions, and sophisticated reduction techniques employed in the proof. This paper not only validates the security of the proposed protocols but also provides a detailed comparison of their performance with existing methods, highlighting their strengths and potential for future research in the field.