Secure Multi-Party Computation with a Dishonest Majority via Quantum Means

We introduce a scheme for secure multi-party computation utilising the quantum correlations of entangled states. First we present a scheme for two-party computation, exploiting the correlations of a Greenberger-Horne-Zeilinger state to provide, with the help of a third party, a near-private computation scheme. We then present a variation of this scheme which is passively secure with threshold t=2, in other words, remaining secure when pairs of players conspire together provided they faithfully follow the protocol. We show that this can be generalised to computations of n-party polynomials of degree 2 with a threshold of n-1. The threshold achieved is significantly higher than the best known classical threshold, which satisfies the bound t<n/2.