### 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.

Available format(s)
Publication info
Published elsewhere. A shorter version appears in proc. of EUROCRYPT 07
Keywords
cryptographic protocols
Contact author(s)
thorbek @ brics dk
History
2007-03-07: revised
See all versions
Short URL
https://ia.cr/2007/086

CC BY

BibTeX

@misc{cryptoeprint:2007/086,
author = {Ivan Damgard and Rune Thorbek},
title = {Non-Interactive Proofs for Integer Multiplication},
howpublished = {Cryptology ePrint Archive, Paper 2007/086},
year = {2007},
note = {\url{https://eprint.iacr.org/2007/086}},
url = {https://eprint.iacr.org/2007/086}
}

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