Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2012: Advances in Cryptology – EUROCRYPT 2012 pp 172-194

Robust Coin Flipping

  • Gene S. Kopp
  • John D. Wiltshire-Gordon
Conference paper

DOI: 10.1007/978-3-642-29011-4_12

Volume 7237 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Kopp G.S., Wiltshire-Gordon J.D. (2012) Robust Coin Flipping. In: Pointcheval D., Johansson T. (eds) Advances in Cryptology – EUROCRYPT 2012. EUROCRYPT 2012. Lecture Notes in Computer Science, vol 7237. Springer, Berlin, Heidelberg


Alice seeks an information-theoretically secure source of private random data. Unfortunately, she lacks a personal source and must use remote sources controlled by other parties. Alice wants to simulate a coin flip of specified bias α, as a function of data she receives from p sources; she seeks privacy from any coalition of r of them. We show: If p/2 ≤ r < p, the bias can be any rational number and nothing else; if 0 < r < p/2, the bias can be any algebraic number and nothing else. The proof uses projective varieties, convex geometry, and the probabilistic method. Our results improve on those laid out by Yao, who asserts one direction of the r = 1 case in his seminal paper [yao82]. We also provide an application to secure multiparty computation.


multiparty computationoutsourcing randomnessbiased coin flipalgebraic numberprojective dualityhyperdeterminant
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Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Gene S. Kopp
    • 1
  • John D. Wiltshire-Gordon
    • 1
  1. 1.University of MichiganUSA