On Complete Primitives for Fairness

Abstract. For secure two-party and multi-party computation with abort, classification of which primitives are complete has been extensively studied in the literature. However, for fair secure computation, where (roughly speaking) either all parties learn the output or none do, the question of complete primitives has remained largely unstudied. In this work, we initiate a rigorous study of completeness for primitives that allow fair computation. We show the following results: – No “short” primitive is complete for fairness. In surprising contrast to other notions of security for secure two-party computation, we show that for fair secure computation, no primitive of size O(log k) is complete, where k is a security parameter. This is the case even if we can enforce parallelism in calls to the primitives (i.e., the adversary does not get output from any primitive in a parallel call until it sends input to all of them). This negative result holds regardless of any computational assum...

• Type: Conference
• Year: 2010
• Where: TCC
• Authors: S. Dov Gordon, Yuval Ishai, Tal Moran, Rafail Ostrovsky, Amit Sahai
• Keywords: Cryptography, Fair Secure Computation, Fairness Hierarchy, Secure Two-party Computation, TCC 2010