Global, unpredictable bit generation without broadcast

Abstract

We investigate the problem of generating a global, unpredictable coin in a distributed system. A fast, efficient solution is of fundamental importance to distributed protocols, especially those that rely on broadcast channels. We present two unpredictable bit generators, based on the Blum-Blum-Shub generator, that can be evaluated non-interactively; that is, each bit (or group of bits) requires each processor merely to send one message to the other processors, without requiring a broadcast or Byzantine Agreement. The unpredictability of our generators (and the security of our protocols) are based provably on the QRA or the intractability of factoring. Remarkably, their structure seems to violate an impossibility result of [8], but our generators escape that lower bound because they achieve a slightly weaker goal: producing unpredictable bits directly, rather than producing “shares” of random bits. In doing so, they avoid the extra machinery (eg., “sharing shares”) of similar results discovered independently in [8].