Achieving independence in logarithmic number of rounds
Benny Chor, Michael O. Rabin · 1987
Simultaneous broadcast [CGMAJ is a fundamental tool in designing secure protocols for fault tolerant distributed computing.A system that supports it enables n processes to globally commit to independently chosen values (a significantly harder task than mere agreement).It is also a basic building block in a recent %ompleteness" theorem of [GMWZ].In this paper we present a new protocol for simultaneous broadcast.Building upon past work, we introduce a novel method of concurrently alternating and interleaving n executions of verifiable secret sharing protocols.This approach greatly improves the time complexity (number of communication rounds) of simultaneous broadcast.Previous protocols (combination of [CGMA] and [GMW]) q re uired the complete serialization of the ra verifiable secret sharings, resulting in n(n) communication rounds.Our protocol is constructive, and requires only log n + log log n serial executions of verifiable secret sharings.It preserves maximum fault tolerance (t < n/2 faults), and polynomial resource bounds (internal computation and communication bits).The same improvement appiies to the general simulation in [GMWX].In light of its improved performance, it is significant that our our protocol has a fairly simple correctness proof.In the slippery business of distributed cryptographic protocols, simpler proofs are important.