Secure multi-party computation with a quantum manner

Abstract

Quantum information processing protocols have great advantages over their classical counterparts, especially on cryptography. Secure multi-party computation is one of the most important issues and has been extensively studied in cryptography. It is of both theoretical and practical significance to develop the quantum information processing protocols for secure multi-party computation. In this paper, we consider the secure multi-party computation for n-variable polynomial functions over the finite field GF(d). We propose two protocols using quantum resources to compute the function within a one-time execution. One is based on d-level mutually unbiased (orthonormal) bases with cyclic property and the other takes advantage of quantum Fourier transform. Analytical results show that the proposed protocols are secure against a passive adversary with unlimited computing power, including colluding attack mounted by n − 2 parties. We also implement the second protocol of the special case d = 2 on the IBM Q Experience. In principle, our proposals can be experimentally realized in the arbitrary d dimension with the advances in realizations and controls of high-dimensional quantum computation.