Round Complexity of Authenticated Broadcast with a Dishonest Majority

TitleRound Complexity of Authenticated Broadcast with a Dishonest Majority
Publication TypeConference Papers
Year of Publication2007
AuthorsGaray JA, Katz J, Koo C-Y, Ostrovsky R
Conference NameFoundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on
Date Published2007/10//
Keywordsbroadcast, complexity;cryptographic, complexity;deterministic, cryptography;, key, majority;randomized, PKI;authenticated, protocols;broadcasting;computational, protocols;digital, round, signatures;dishonest, signatures;public

Broadcast among n parties in the presence of t ges n/3 malicious parties is possible only with some additional setup. The most common setup considered is the existence of a PKI and secure, digital signatures, where so-called authenticated broadcast is achievable for any t lt; n. It is known that t + 1 rounds are necessary and sufficient for deterministic protocols achieving authenticated broadcast. Recently, however, randomized protocols running in expected constant rounds have been shown for the case of t lt; n/2. It has remained open whether randomization can improve the round complexity when an honest majority is not present. We address this question and show upper/lower bounds on how much randomization can help: ldr For t les n/2 + k, we. show a randomized broadcast protocol that runs in expected O(k2) rounds. In particular, we obtain expected constant-round pivtocols for t = n/2 + O(1). ldr On the negative side, we show that even randomized protocols require Omega(2n/(n-t)) rounds. This in particular rules out expected constant-round protocols when the fraction of honest parties is sub-constant.