Quantum Secure Protocols for Multiparty Computations
Tapaswini Mohanty, Vikas Srivastava, Sumit Kumar Debnath, Pantelimon Stanica
TL;DR
The paper tackles the threat of quantum attacks on classical MPC by proposing quantum-information-theoretic protocols. It introduces qOLE, a three-party quantum oblivious linear evaluation built to compute $f(x)=ax+b$ over a finite field of order $p$ on Alice’s input alpha, using QKD for secret-key sharing and a quantum one-time pad for security, with phases qOLE.Kg, qOLE.Int, and qOLE.Comp. Building on qOLE, it then presents qMPSI for quantum-safe multiparty private set intersection among $m$ parties, leveraging polynomials and a trusted party to evaluate the intersection without exposing private data. The security analysis covers external eavesdropping, Trojan-horse risks, and internal threats, showing that nobody can learn more than the prescribed outputs without breaking qOTP. Efficiency results highlight low communication costs, with $\mathcal{O}(\log_2 p)$ qubits for qOLE and $\mathcal{O}(mn \log_2 p)$ for qMPSI, using single-photon resources and Pauli gates, suggesting a practical path toward quantum-secure MPC primitives.
Abstract
Secure multiparty computation (MPC) schemes allow two or more parties to conjointly compute a function on their private input sets while revealing nothing but the output. Existing state-of-the-art number-theoretic-based designs face the threat of attacks through quantum algorithms. In this context, we present secure MPC protocols that can withstand quantum attacks. We first present the design and analysis of an information-theoretic secure oblivious linear evaluation (OLE), namely ${\sf qOLE}$ in the quantum domain, and show that our ${\sf qOLE}$ is safe from external attacks. In addition, our scheme satisfies all the security requirements of a secure OLE. We further utilize ${\sf qOLE}$ as a building block to construct a quantum-safe multiparty private set intersection (MPSI) protocol.