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 t2) 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.

We study the problem of achieving global broadcast in a radio network where a node can multicast messages to all of its neighbors (that is, nodes within some given distance r), and up to t nodes in any single neighborhood may be corrupted. Previous work assumes that corrupted nodes can neither cause collisions nor spoof addresses of honest nodes. In this work, we eliminate these assumptions and allow each faulty node to cause a (known) bounded number of collisions and spoof the addresses of arbitrary other nodes. We show that the maximum tolerable t in this case is identical to the maximum tolerable t when collisions and address spoofing are not allowed. Thus, by causing collisions and spoofing addresses an adversary may be able to degrade the efficiency of achieving broadcast, but it cannot affect the feasibility of this task.

Much work has focused on the Byzantine Generals (or secure broadcast) problem in the standard model in which pairwise communication is available between all parties in the network. Some research has also explored the problem when pairwise channels exist only between selected pairs of players, or under the assumption of "k-cast channels" shared by all subsets of players of size k. However, none of these models are appropriate for radio networks in which a player can communicate only by multicasting a message which is then received by all players within some radius r (i.e., the neighbors of the transmitting node). Yet, as far as we are aware, obtaining secure broadcast in radio networks in the presence of a Byzantine adversary has not been studied before.This paper corrects this omission, and provides the first analysis of secure broadcast in radio networks for the case of Byzantine adversaries. We note that secure broadcast is impossible in the presence of an omnipotent adversary. To bypass this barrier, we make the following assumption: there exists a prefixed schedule for players to communicate and everyone (including corrupted ones) adheres to this schedule. Under this assumption, we give a simple broadcast protocol which is provably secure whenever the adversary corrupts at most 1 4 r(r+√rover2 + 1)-3 neighbors (roughly a 1/4π fraction) of any honest player. On the other hand, we show that it is impossible to achieve secure broadcast when the adversary corrupts ⌈1/2 r(2r+1)⌉ (roughly a 1/π fraction) neighbors of any honest player.

This paper is concerned with the extra-resource analysis of online scheduling algorithms. In particular, it studies how to make use of multiple processors to counteract the lack of future information in online deadline scheduling. Our results extend the previous work that are primarily based on using a faster processor to obtain a performance guarantee. The challenge arises from the fact that jobs are sequential in nature and cannot be executed on more than one processor at the same time. Thus, a faster processor can speed up a job while multiple unit-speed processors cannot help.