## Cryptology ePrint Archive: Report 2012/164

On Secure Two-party Integer Division

Morten Dahl, Chao Ning, Tomas Toft

Abstract: We consider the problem of {\it secure integer division}: given two Paillier encryptions of $\ell$-bit values $n$ and $d$, determine an encryption of \intdiv{n}{d} without leaking any information about $n$ or $d$. We propose two new protocols solving this problem.

The first requires $\Oh(\ell)$ arithmetic operation on encrypted values (secure addition and multiplication) in $\Oh(1)$ rounds. This is the most efficient constant-rounds solution to date. The second protocol requires only $\Oh \left( (\log^2 \ell)(\kappa + \loglog \ell) \right)$ arithmetic operations in $\Oh(\log^2 \ell)$ rounds, where $\kappa$ is a correctness parameter. Theoretically, this is the most efficient solution to date as all previous solutions have required $\Omega(\ell)$ operations. Indeed, the fact that an $o(\ell)$ solution is possible at all is highly surprising.

Category / Keywords: cryptographic protocols / Secure two-party computation, Secure integer division, Constant-rounds, Bit-Length

Publication Info: A shorten version can be seen in Proc. FC' 2012

Date: received 28 Mar 2012, last revised 21 Mar 2013

Contact author: mdahl at cs au dk, ttoft@cs au dk, ncnfl@mail tsinghua edu cn

Available format(s): PDF | BibTeX Citation

Note: This is the full version of the paper which was accepted to FC 2012.

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