%0 Conference Paper %B Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on %D 2007 %T Round Complexity of Authenticated Broadcast with a Dishonest Majority %A Garay,J. A %A Katz, Jonathan %A Koo,Chiu-Yuen %A Ostrovsky,R. %K broadcast %K complexity;cryptographic %K complexity;deterministic %K cryptography; %K key %K majority;randomized %K PKI;authenticated %K protocols;broadcasting;computational %K protocols;digital %K round %K signatures;dishonest %K signatures;public %X 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. %B Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on %P 658 - 668 %8 2007/10// %G eng %R 10.1109/FOCS.2007.44