A subexponential construction of graph coloring for multiparty computation

Hassan Jameel Asghar, Yvo Desmedt, Josef Pieprzyk, Ron Steinfeld

Research output: Contribution to journalArticlepeer-review


We show the first deterministic construction of an unconditionally secure multiparty computation (MPC) protocol in the passive adversarial model over black-box non- Abelian groups which is both optimal (secure against an adversary who possesses any < inputs) and has subexponential complexity of construction based on coloring of planar graphs. More specifically, following the result of Desmedt et al. (2012) that the problem of MPC over non-Abelian groups can be reduced to finding a t -reliable n-coloring of planar graphs, we show the construction of such a graph which allows a path from the input nodes to the output nodes when any t -party subset is in the possession of the adversary. Unlike the deterministic constructions from Desmedt et al. (2012) our construction has subexponential complexity and is optimal at the same time, i.e., it is secure for any t < n2 .

Original languageEnglish
Pages (from-to)363-403
Number of pages41
JournalJournal of Mathematical Cryptology
Issue number4
Publication statusPublished - 1 Dec 2014
Externally publishedYes


  • Graph coloring
  • Multiparty computation
  • Non-Abelian group
  • Planar graph


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