On the Round Complexity of Randomized Byzantine Agreement

We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)]. 2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1). 3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI). The third bound essentially matches the recent protocol of Micali (ITCS\u2717) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability

Lower Bounds on Implementing Robust and Resilient Mediators

We consider games that have (k,t)-robust equilibria when played with a mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by coalitions of size up to k and deviations by up to $t$ players with unknown utilities. We prove lower bounds that match upper bounds on the ability to implement such mediators using cheap talk (that is, just allowing communication among the players). The bounds depend on (a) the relationship between k, t, and n, the total number of players in the system; (b) whether players know the exact utilities of other players; (c) whether there are broadcast channels or just point-to-point channels; (d) whether cryptography is available; and (e) whether the game has a $k+t)-punishment strategy; that is, a strategy that, if used by all but at most$k+t$ players, guarantees that every player gets a worse outcome than they do with the equilibrium strategy

ARPA Whitepaper

We propose a secure computation solution for blockchain networks. The correctness of computation is verifiable even under malicious majority condition using information-theoretic Message Authentication Code (MAC), and the privacy is preserved using Secret-Sharing. With state-of-the-art multiparty computation protocol and a layer2 solution, our privacy-preserving computation guarantees data security on blockchain, cryptographically, while reducing the heavy-lifting computation job to a few nodes. This breakthrough has several implications on the future of decentralized networks. First, secure computation can be used to support Private Smart Contracts, where consensus is reached without exposing the information in the public contract. Second, it enables data to be shared and used in trustless network, without disclosing the raw data during data-at-use, where data ownership and data usage is safely separated. Last but not least, computation and verification processes are separated, which can be perceived as computational sharding, this effectively makes the transaction processing speed linear to the number of participating nodes. Our objective is to deploy our secure computation network as an layer2 solution to any blockchain system. Smart Contracts\cite{smartcontract} will be used as bridge to link the blockchain and computation networks. Additionally, they will be used as verifier to ensure that outsourced computation is completed correctly. In order to achieve this, we first develop a general MPC network with advanced features, such as: 1) Secure Computation, 2) Off-chain Computation, 3) Verifiable Computation, and 4)Support dApps' needs like privacy-preserving data exchange

Scalable and Robust Distributed Algorithms for Privacy-Preserving Applications

We live in an era when political and commercial entities are increasingly engaging in sophisticated cyber attacks to damage, disrupt, or censor information content and to conduct mass surveillance. By compiling various patterns from user data over time, untrusted parties could create an intimate picture of sensitive personal information such as political and religious beliefs, health status, and so forth. In this dissertation, we study scalable and robust distributed algorithms that guarantee user privacy when communicating with other parties to either solely exchange information or participate in multi-party computations. We consider scalability and robustness requirements in three privacy-preserving areas: secure multi-party computation (MPC), anonymous broadcast, and blocking-resistant Tor bridge distribution. We propose decentralized algorithms for MPC that, unlike most previous work, scale well with the number of parties and tolerate malicious faults from a large fraction of the parties. Our algorithms do not require any trusted party and are fully load-balanced. Anonymity is an essential tool for achieving privacy; it enables individuals to communicate with each other without being identified as the sender or the receiver of the information being exchanged. We show that our MPC algorithms can be effectively used to design a scalable anonymous broadcast protocol. We do this by developing a multi-party shuffling protocol that can efficiently anonymize a sequence of messages in the presence of many faulty nodes. Our final approach for preserving user privacy in cyberspace is to improve Tor; the most popular anonymity network in the Internet. A current challenge with Tor is that colluding corrupt users inside a censorship territory can completely block user\u27s access to Tor by obtaining information about a large fraction of Tor bridges; a type of relay nodes used as the Tor\u27s primary mechanism for blocking-resistance. We describe a randomized bridge distribution algorithm, where all honest users are guaranteed to connect to Tor in the presence of an adversary corrupting an unknown number of users. Our simulations suggest that, with minimal resource costs, our algorithm can guarantee Tor access for all honest users after a small (logarithmic) number of rounds

On the coherence of a duty to surrender with just war theory and the laws of war

This thesis conducts an interdisciplinary analysis of the obligation for states and individuals to surrender as an emerging phenomenon in just war theory and international law. It seeks to establish the humanitarian value of a duty to surrender and extrapolate it from the principles of these two disciplines, arguing that the lack of a previous in-depth analysis of surrender is not just an absence, but an oversight. After conducting a historical analysis of surrender it explores the doctrinal basis of such a duty in related bodies of international law: the law on the use of force, international humanitarian law, human rights law, aggression and international criminal law, and peace treaties in international law. This thesis then explores the orthodox and revisionist schools of just war theory gradually assessing the themes which coalesce around the determination of justice in surrender. It argues that the duty to surrender must, in order to avoid the pitfalls of empire and appeasement, draw its normative force from popular sovereignty and the right of self-determination. It establishes the value of referenda and conscientious objection as important mechanisms in the duty to surrender. Equipped with these ideas, the thesis finally turns to a discussion of the parameters of the right of self-determination in international law. Ultimately, it fully theorises the source and requirements of the duty to surrender for individuals and states, and how they interact. It positions the duty to surrender as an obligation with the potential to not only be coherent with just war theory and international law, but which allows them to better achieve their humanitarian promise