Abstract
We consider the problem of secure integer division: given two Paillier encryptions of ℓ-bit values n and d, determine an encryption of \(\lfloor \frac{n}{d}\rfloor\) without leaking any information about n or d. We propose two new protocols solving this problem.
The first requires \(\ensuremath{\mathcal{O}}(\ell)\) arithmetic operations on encrypted values (secure addition and multiplication) in \(\ensuremath{\mathcal{O}}(1)\) rounds. This is the most efficient constant-rounds solution to date. The second protocol requires only \(\ensuremath{\mathcal{O}} \left( (\log^2 \ell)(\kappa + \operatorname{loglog} \ell) \right)\) arithmetic operations in \(\ensuremath{\mathcal{O}}(\log^2 \ell)\) rounds, where κ is a correctness parameter. Theoretically, this is the most efficient solution to date as all previous solutions have required Ω(ℓ) operations. Indeed, the fact that an o(ℓ) solution is possible at all is highly surprising.
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Dahl, M., Ning, C., Toft, T. (2012). On Secure Two-Party Integer Division. In: Keromytis, A.D. (eds) Financial Cryptography and Data Security. FC 2012. Lecture Notes in Computer Science, vol 7397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32946-3_13
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DOI: https://doi.org/10.1007/978-3-642-32946-3_13
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