Broadcast amplification

Abstract

A d-broadcast primitive is a communication primitive that allows a sender to send a value from a domain of size d to a set of parties. A broadcast protocol emulates the d-broadcast primitive using only point-to-point channels, even if some of the parties cheat, in the sense that all correct recipients agree on the same value v (consistency), and if the sender is correct, then v is the value sent by the sender (validity). A celebrated result by Pease, Shostak and Lamport states that such a broadcast protocol exists if and only if t < n), which can be possible only if, in addition to point-to-point channels, another primitive is available. Broadcast amplification is the problem of achieving d-broadcast when d′-broadcast can be used once, for d′ 3 no broadcast amplification is possible, i.e.,n (d) = d for any d. However, if other parties than the sender can also broadcast some short messages, then broadcast amplification is possible for any n. Let denote the minimal d′ such that d-broadcast can be constructed from primitives d′1- broadcast,., d′ k-broadcast, where d′ = â̂ i d′ i (i.e., logd′ = Σ i logd′ i ). Note that. We show that broadcasting 8nlogn bits in total suffices, independently of d, and that at least n-2 parties, including the sender, must broadcast at least one bit. Hence. © 2014 International Association for Cryptologic Research.