## 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

**Version: **20070307:154128 (All versions of this report)

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