Journal of Cryptology

, Volume 18, Issue 1, pp 37–61 | Cite as

Minimal Complete Primitives for Secure Multi-Party Computation



The study of minimal cryptographic primitives needed to implement secure computation among two or more players is a fundamental question in cryptography. The issue of complete primitives for the case of two players has been thoroughly studied. However, in the multi-party setting, when there are n > 2 players and t of them are corrupted, the question of what are the simplest complete primitives remained open for t ≥ n/3. (A primitive is called complete if any computation can be carried out by the players having access only to the primitive and local computation.) In this paper we consider this question, and introduce complete primitives of minimal cardinality for secure multi-party computation. The cardinality issue (number of players accessing the primitive) is essential in settings where primitives are implemented by some other means, and the simpler the primitive the easier it is to realize. We show that our primitives are complete and of minimal cardinality possible for most cases.

Multi-party computation Secure function evaluation Unconditional security Complete functions Oblivious cast 


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Computer Science, University of California, Davis, CA 95616USA
  2. 2.Bell Labs – Lucent Technologies, 600 Mountain Ave., Murray Hill, NJ 07974USA
  3. 3.Department of Computer Science, ETH, CH-8096 ZurichSwitzerland
  4. 4.Telcordia Technologies Inc., 445 South Street, Morristown, NJ 07960-6438USA

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