Active Security in Multiparty Computation over Black-Box Groups

  • Yvo Desmedt
  • Josef Pieprzyk
  • Ron Steinfeld
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7485)


Most previous work on unconditionally secure multiparty computation has focused on computing over a finite field (or ring). Multiparty computation over other algebraic structures has not received much attention, but is an interesting topic whose study may provide new and improved tools for certain applications. At CRYPTO 2007, Desmedt et al introduced a construction for a passive-secure multiparty multiplication protocol for black-box groups, reducing it to a certain graph coloring problem, leaving as an open problem to achieve security against active attacks.

We present the first n-party protocol for unconditionally secure multiparty computation over a black-box group which is secure under an active attack model, tolerating any adversary structure Δ satisfying the Q 3 property (in which no union of three subsets from Δ covers the whole player set), which is known to be necessary for achieving security in the active setting. Our protocol uses Maurer’s Verifiable Secret Sharing (VSS) but preserves the essential simplicity of the graph-based approach of Desmedt et al, which avoids each shareholder having to rerun the full VSS protocol after each local computation. A corollary of our result is a new active-secure protocol for general multiparty computation of an arbitrary Boolean circuit.


Multi-Party Computation General Adversary Structures Non-Abelian Group Black-Box Graph Colouring Active Security 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yvo Desmedt
    • 1
  • Josef Pieprzyk
    • 2
  • Ron Steinfeld
    • 3
  1. 1.Dept. of Computer ScienceUniversity College LondonUK
  2. 2.Centre for Advanced Computing - Algorithms and Cryptography (ACAC) Dept. of ComputingMacquarie UniversityNorth RydeAustralia
  3. 3.Clayton School of Information TechnologyMonash UniversityClaytonAustralia

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