Communication Complexity of Key Agreement on Small Ranges

Abstract This paper studies a variation on classical key-agreement and consensus problems in which the set S of possible keys is the range of a random variable that can be sampled. We give tight upper and lower bounds ofdlog2ke bits on the communication complexity of agreement on some key in S, using a form of Sperner’s Lemma, and give bounds on other problems. In the case where keys are generated by a probabilistic polynomial-time Turing machine, agreement is shown to be possible with zero communication if every fully polynomial-time approximation scheme (fpras) has a certain symmetry-breaking property. Topics Computational complexity, cryptography.