Multiparty Computation to Generate Secret Permutations

We make use of a universal re-encryption mixnet to efficiently perform a secure multiparty computation to generate a secret permutation. When complete, the permutation is shared among the players in such a way that each player knows his share of the permutation but no others. Such a permutation is useful in dining cryptographers networks (DC-nets) to determine in which slot each player should transmit. We also see this primitive as being useful in online gaming for either shuffling cards or ordering players without the need for a trusted dealer or other third party.