Secure multiparty computation with a dishonest majority via quantum means

We introduce a scheme for secure multiparty computation utilizing 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. Furthermore, we show that the passively secure variant can be modified to be secure when cheating parties are allowed to deviate from the protocol. We show that this can be generalized 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. Our schemes, each complying with a different definition of security, shed light on which physical assumptions are necessary in order to achieve quantum secure multiparty computation.