This report presents a weighted version of the Byzantine Agreement Problem and its solution under various conditions. In this version, each machine is assigned a weight depending on the application. Instead of assuming that at most $f$ out of $N$ machines fail, the algorithm assumes that the total weight of the machines that fail is at most $\rho < 1/3.$ When each machine has weight $1/N,$ this problem reduces to the standard Byzantine Generals Agreement Problem. By choosing weights appropriately, the weighted Byzantine Agreement Problem can be applied to situations where a subset of processes are more trusted. By using weights, the system can reach consensus in the presence of Byzantine failures, even when more than $N/3$ processes fail, so long as the total weight of the failed processes is less than $1/3.$ Some properties of the Weighted Byzantine Agreement algorithms when the weight vectors are not the same at every process are discussed. Also, a method to update the weights of the processes after execution of the weighted Byzantine Agreement is given. The update method guarantees that the weight of any correct process is never reduced and the weight of any faulty process, suspected by correct processes whose total weight is at least $1/4,$ is reduced to $0$ for future instances. A short discussion of some weight assignment strategies is also given. / text

In this thesis, we look into the problem of forming and maintaining good committees that can represent a distributed network. The solution to this problem can be used as a sub-routine for Byzantine Agreement that only costs sub-quadratic message complexity. Most importantly, we make no cryptographic assumptions such as the Random Oracle assumption and the existence of private channels. However, we do assume the network to be peer-to-peer, where a message receiver knows who the message sender is. Under the synchronous full information model, our solution is to utilize an approximating disperser for selecting a good next committee with high probability, repeatedly. We consider several existing theoretical constructions (randomized and deterministic) for approximating dispersers, and examine the practical applicability of them, while improving constants for some constructions. This algorithm is robust against a semi-adaptive adversary who can decide the set of nodes to corrupt periodically. Thus, a new committee should be selected before the current committee gets corrupted. We also prove some constructions that do not work practically for our scenario. / Graduate

Intrusion Detection & Countermeasure Systems (IDCS) and architectures commonly used in commercial, as well as research environments, suffer from a number of problems that limit their effectiveness. The most common shortcoming of current IDCSs is their inability to tolerate failures. These failures can occur naturally, such as hardware or software failures, or can be the result of attackers attempting to compromise the IDCS itself. Currently, the WPI System Security Laboratory at Worcester Polytechnic Institute is developing a Secure Architecture and Fault-Resilient Engine (S.A.F.E.), a system capable of tolerating failures. This system makes use of solutions to the Byzantine General's Problem, developed earlier by Lamport and others. Byzantine Agreement Protocols will be used to achieve consensus about which nodes have been compromised or failed, with a series of synchronized, secure rounds of message exchanges. Once a consensus has been reached, the offending nodes can be isolated and countermeasure actions can be initiated by the system. We consider the necessary and sufficient conditions for the application of Byzantine Agreement Protocols to the intrusion detection problem. Further, a first implementation of this algorithm will be embedded in the Distributed Trust Manager (DTM) module of S.A.F.E. The DTM is the key module responsible for assuring trust amongst the members of the system. Finally, we will evaluate the DTM, as a standalone unit, to ensure that it performs correctly.

<p>Cyber physical systems are deployed in a wide range of applications from sensor nodes in a factory setting to drones in defense applications. This distributed setting of nodes or processes often needs to reach agreement on a set of values. Byzantine Agreement protocols address this issue of reaching an agreement in an environment where a malicious entity can take control over a set of nodes and deviates the system from its normal operation. However these protocols do not consider the energy consumption of the nodes. We explore Byzantine Agreement protocols from an energy efficient perspective providing both <i>energy resilience</i> where the actions of the Byzantine nodes can not adversely effect the energy consumption of non-malicious nodes as well as <i>fairness</i> in energy consumption of nodes over multiple rounds of agreement.</p>

We present a partial implementation of King and Saia 2016’s expected polyno- mial time byzantine agreement algorithm, which which greatly speeds up Bracha’s Byzantine agreement algorithm by introducing a shared coin flip subroutine and a method for detecting adversarially controlled nodes. In addition to implementing the King-Saia algorithm, we detail a new version of the “blackboard” abstraction used to implement the shared coin flip, which improves the subroutine’s resilience from t < n/4 to t < n/3 and leads to an improvement of the resilience of the King-Saia Byzantine agreement algorithm overall. We test the King-Saia algorithm, and detail a series of adversarial attacks against it; we also create a Monte Carlo simulation to further test one particular attack’s level of success at biasing the shared coin flip / Graduate