## Cryptology ePrint Archive: Report 2007/086

Non-Interactive Proofs for Integer Multiplication

Ivan Damgard and Rune Thorbek

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.

Category / Keywords: cryptographic protocols

Publication Info: A shorter version appears in proc. of EUROCRYPT 07

Date: received 6 Mar 2007, last revised 7 Mar 2007

Contact author: thorbek at brics dk

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Short URL: ia.cr/2007/086

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