International Association
for Cryptologic Research

We develop a distributed service for generating correlated randomness (e.g. permutations) for multiple parties, where each party’s output is private but publicly verifiable. This service provides users with a low-cost way to play online poker in real-time, without a trusted party. Our service is backed by a committee of compute providers, who run a multi-party computation (MPC) protocol to produce an (identity-based) encrypted permutation of a deck of cards, in an offline phase well ahead of when the players’ identities are known. When the players join, what we call the online phase, they decrypt their designated cards immediately after deriving the identity-based decryption keys, a much simpler computation. In addition, the MPC protocol also generates a publicly-verifiable proof that the output is a permutation. In our construction, we introduce a new notion of succinctly verifiable multi-identity based encryption (SVME), which extends the existing notion of verifiable encryption to a multi-identity-based setting, but with a constant sized proof – this may be of independent interest. We instantiate this for a permutation relation (defined over a small set) along with identity-based encryption, polynomial commitments and succinct proofs – our choices are made to enable a distributed computation when the card deck is always secret shared. Moreover, we design a new protocol to efficiently generate a secret-sharing of random permutation of a small set, which is run prior to distributed SVME. Running these protocols offline simplifies the online phase substantially, as parties only derive their identity-specific keys privately via secure channels with the MPC committee, and then decrypt locally to obtain their decks. We provide a rigorous UC-based formalization in a highly modularized fashion. Finally, we demonstrate practicality with an implementation that shows that for 8 MPC parties, gen- erating a secret publicly-verifiable permutation of 64 cards takes under 3 seconds, while accessing cards for a player takes under 0.3 seconds.