Randomness in distribution protocols

Abstract

In this paper we give a systematic analysis of the amount of randomness needed by Secret Sharing Schemes and Secure Key Distribution Schemes. We give both upper and lower bounds on the number of random bits needed by secret sharing schemes; such bounds match for several classes of secret sharing schemes. For secure key distribution schemes we provide a lower bound on the amount of randomness needed, thus showing the optimality of a recently proposed key distribution protocol.