A subexponential construction of graph coloring for multiparty computation

  • 1 National ICT Australia (NICTA), Sydney, Australia
  • 2 Department of Computer Science, University College London, UK; and Department of Computer Science, University of Texas at Dallas, USA
  • 3 School of Electrical Engineering and Computer Science, Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD 4000, Australia
  • 4 Clayton School of Information Technology, Faculty of Information Technology, Monash University, Clayton, Australia


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 t<n2 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.

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JMC is a forum for original research articles in the area of mathematical cryptology. Works in the theory of cryptology and articles linking mathematics with cryptology are welcome. Submissions from all areas of mathematics significant for cryptology are published, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes.