Non-interactive Proofs for Integer Multiplication

Abstract. We present two universally composable and practical protocols by which a dealer can, verifiably and non-interactively, secret-share an integer among a set of players. Moreover, at small extra cost and using a distributed verifier proof, it can be shown in zero-knowledge that three shared integers a, b, c satisfy ab = c. This implies by known reductions non-interactive zero-knowledge proofs that a shared integer is in a given interval, or that one secret integer is larger than another. Such primitives are useful, e.g., for supplying inputs to a multiparty computation protocol, such as an auction or an election. The protocols use various set-up assumptions, but do not require the random oracle model.

• Type: Conference
• Year: 2007
• Where: EUROCRYPT
• Authors: Ivan Damgård, Rune Thorbek
• Keywords: Cryptography, EUROCRYPT 2007, Integer, Reductions Non-interactive Zero-knowledge, Shared Integer