International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Non-Interactive Proofs for Integer Multiplication

Ivan Damgård
Rune Thorbek
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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.
  title={Non-Interactive Proofs for Integer Multiplication},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols},
  note={A shorter version appears in proc. of EUROCRYPT 07 13579 received 6 Mar 2007, last revised 7 Mar 2007},
  author={Ivan Damgård and Rune Thorbek},