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International Conference on Financial Cryptography and Data Security

FC 2012: Financial Cryptography and Data Security pp 164–178Cite as

On Secure Two-Party Integer Division

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 7397)

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.

Keywords

  • Secure two-party computation
  • Secure integer division

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Author information

Authors and Affiliations

  1. Aarhus University, Denmark

    Morten Dahl & Tomas Toft

  2. IIIS, Tsinghua University, Beijing, China

    Chao Ning

  3. School of Computer Science and Technology, Shandong University, Jinan, China

    Chao Ning

Authors
  1. Morten Dahl
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  2. Chao Ning
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  3. Tomas Toft
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Columbia University, 1214 Amsterdam Avenue, 10027-7003, New York, NY, USA

    Angelos D. Keromytis

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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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