%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(k^{2}) 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