International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2000: Advances in Cryptology — EUROCRYPT 2000 pp 316-334

General Secure Multi-party Computation from any Linear Secret-Sharing Scheme

  • Ronald Cramer
  • Ivan Damgård
  • Ueli Maurer
Conference paper

DOI: 10.1007/3-540-45539-6_22

Volume 1807 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Cramer R., Damgård I., Maurer U. (2000) General Secure Multi-party Computation from any Linear Secret-Sharing Scheme. In: Preneel B. (eds) Advances in Cryptology — EUROCRYPT 2000. EUROCRYPT 2000. Lecture Notes in Computer Science, vol 1807. Springer, Berlin, Heidelberg


We show that verifiable secret sharing (VSS) and secure multi-party computation (MPC) among a set of n players can efficiently be based on any linear secret sharing scheme (LSSS) for the players, provided that the access structure of the LSSS allows MPC or VSS at all. Because an LSSS neither guarantees reconstructability when some shares are false, nor verifiability of a shared value, nor allows for the multiplication of shared values, an LSSS is an apparently much weaker primitive than VSS or MPC.

Our approach to secure MPC is generic and applies to both the information-theoretic and the cryptographic setting. The construction is based on 1) a formalization of the special multiplicative property of an LSSS that is needed to perform a multiplication on shared values, 2) an efficient generic construction to obtain from any LSSS a multiplicative LSSS for the same access structure, and 3) an efficient generic construction to build verifiability into every LSSS (always assuming that the adversary structure allows for MPC or VSS at all).

The protocols are efficient. In contrast to all previous information-theoretically secure protocols, the field size is not restricted (e.g, to be greater than n). Moreover, we exhibit adversary structures for which our protocols are polynomial in n while all previous approaches to MPC for non-threshold adversaries provably have super-polynomial complexity.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ronald Cramer
    • 1
  • Ivan Damgård
    • 1
  • Ueli Maurer
    • 2
  1. 1.BRICSAarhus UniversityAarhus
  2. 2.ETH ZürichZürich