Round Complexity of Authenticated Broadcast with a Dishonest Majority

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 < 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 < 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.