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International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2003: Advances in Cryptology — EUROCRYPT 2003 pp 596–613Cite as

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Efficient Multi-party Computation over Rings

Efficient Multi-party Computation over Rings

  • Ronald Cramer5,
  • Serge Fehr5,
  • Yuval Ishai6 &
  • …
  • Eyal Kushilevitz6 
  • Conference paper
  • First Online: 01 January 2003
  • 3745 Accesses

  • 44 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2656)

Abstract

Secure multi-party computation (MPC) is an active research area, and a wide range of literature can be found nowadays suggesting improvements and generalizations of existing protocols in various directions. However, all current techniques for secure MPC apply to functions that are represented by (boolean or arithmetic) circuits over finite fields. We are motivated by two limitations of these techniques:

  • Generality. Existing protocols do not apply to computation over more general algebraic structures (except via a brute-force simulation of computation in these structures).

  • Efficiency. The best known constant-round protocols do not efficiently scale even to the case of large finite fields.

Our contribution goes in these two directions. First, we propose a basis for unconditionally secure MPC over an arbitrary ginite ring, an algebraic object with a much less nice structure than a field, and obtain efficient MPC protocols requiring only a black-box access to the ring operations and to random ring elements. Second, we extend these results to the constant-round setting, and suggest efficiency improvements that are relevant also for the important special case of fields. We demonstrate the usefulness of the above results by presenting a novel application of MPC over (non-field) rings to the round-efficient secure computation of the maximum function.

Keywords

  • Access Structure
  • Secure Computation
  • Homomorphic Encryption
  • Arithmetic Circuit
  • Arithmetic Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Basic Research in Computer Science (www.brics.dk), funded by the Danish National Research Foundation.

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Author information

Authors and Affiliations

  1. BRICS, Department of Computer Science, Århus University, Denmark

    Ronald Cramer & Serge Fehr

  2. Computer Science Department, Technion, Israel

    Yuval Ishai & Eyal Kushilevitz

Authors
  1. Ronald Cramer
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  2. Serge Fehr
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  3. Yuval Ishai
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  4. Eyal Kushilevitz
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, Haifa, 32000, Israel

    Eli Biham

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© 2003 International Association for Cryptologic Research

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Cite this paper

Cramer, R., Fehr, S., Ishai, Y., Kushilevitz, E. (2003). Efficient Multi-party Computation over Rings. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_37

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  • DOI: https://doi.org/10.1007/3-540-39200-9_37

  • Published: 13 May 2003

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14039-9

  • Online ISBN: 978-3-540-39200-2

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