MarriageTheoremのこと

_ プレプリント確認状況：arXiv:math 1月29日分まで、arXiv:quant-ph 5月31日分まで、IACR ePrint：2012/164まで

_ 気になった論文：On Secure Two-party Integer Division（Morten Dahl, Chao Ning, Tomas Toft, IACR ePrint 2012/164）

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.