Optimal Gossip with Direct Addressing

Gossip algorithms spread information by having nodes repeatedly forward information to a few random contacts. By their very nature, gossip algorithms tend to be distributed and fault tolerant. If done right, they can also be fast and message-efficient. A common model for gossip communication is the random phone call model, in which in each synchronous round each node can PUSH or PULL information to or from a random other node. For example, Karp et al. [FOCS 2000] gave algorithms in this model that spread a message to all nodes in $\Theta(\log n)$ rounds while sending only $O(\log \log n)$ messages per node on average. Recently, Avin and Els\"asser [DISC 2013], studied the random phone call model with the natural and commonly used assumption of direct addressing. Direct addressing allows nodes to directly contact nodes whose ID (e.g., IP address) was learned before. They show that in this setting, one can "break the $\log n$ barrier" and achieve a gossip algorithm running in $O(\sqrt{\log n})$ rounds, albeit while using $O(\sqrt{\log n})$ messages per node. We study the same model and give a simple gossip algorithm which spreads a message in only $O(\log \log n)$ rounds. We also prove a matching $\Omega(\log \log n)$ lower bound which shows that this running time is best possible. In particular we show that any gossip algorithm takes with high probability at least $0.99 \log \log n$ rounds to terminate. Lastly, our algorithm can be tweaked to send only $O(1)$ messages per node on average with only $O(\log n)$ bits per message. Our algorithm therefore simultaneously achieves the optimal round-, message-, and bit-complexity for this setting. As all prior gossip algorithms, our algorithm is also robust against failures. In particular, if in the beginning an oblivious adversary fails any $F$ nodes our algorithm still, with high probability, informs all but $o(F)$ surviving nodes

FairLedger: A Fair Blockchain Protocol for Financial Institutions

Financial institutions are currently looking into technologies for permissioned blockchains. A major effort in this direction is Hyperledger, an open source project hosted by the Linux Foundation and backed by a consortium of over a hundred companies. A key component in permissioned blockchain protocols is a byzantine fault tolerant (BFT) consensus engine that orders transactions. However, currently available BFT solutions in Hyperledger (as well as in the literature at large) are inadequate for financial settings; they are not designed to ensure fairness or to tolerate selfish behavior that arises when financial institutions strive to maximize their own profit. We present FairLedger, a permissioned blockchain BFT protocol, which is fair, designed to deal with rational behavior, and, no less important, easy to understand and implement. The secret sauce of our protocol is a new communication abstraction, called detectable all-to-all (DA2A), which allows us to detect participants (byzantine or rational) that deviate from the protocol, and punish them. We implement FairLedger in the Hyperledger open source project, using Iroha framework, one of the biggest projects therein. To evaluate FairLegder's performance, we also implement it in the PBFT framework and compare the two protocols. Our results show that in failure-free scenarios FairLedger achieves better throughput than both Iroha's implementation and PBFT in wide-area settings

On Byzantine Broadcast in Loosely Connected Networks

We consider the problem of reliably broadcasting information in a multihop asynchronous network that is subject to Byzantine failures. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the authentic message and nothing else), but they require a highly connected network. An approach giving only probabilistic guarantees (correct nodes deliver the authentic message with high probability) was recently proposed for loosely connected networks, such as grids and tori. Yet, the proposed solution requires a specific initialization (that includes global knowledge) of each node, which may be difficult or impossible to guarantee in self-organizing networks - for instance, a wireless sensor network, especially if they are prone to Byzantine failures. In this paper, we propose a new protocol offering guarantees for loosely connected networks that does not require such global knowledge dependent initialization. In more details, we give a methodology to determine whether a set of nodes will always deliver the authentic message, in any execution. Then, we give conditions for perfect reliable broadcast in a torus network. Finally, we provide experimental evaluation for our solution, and determine the number of randomly distributed Byzantine failures than can be tolerated, for a given correct broadcast probability.Comment: 1

Lessons from HotStuff

This article will take you on a journey to the core of blockchains, their Byzantine consensus engine, where HotStuff emerged as a new algorithmic foundation for the classical Byzantine generals consensus problem. The first part of the article underscores the theoretical advances HotStuff enabled, including several models in which HotStuff-based solutions closed problems which were opened for decades. The second part focuses on HotStuff performance in real life setting, where its simplicity drove adoption of HotStuff as the golden standard for blockchain design, and many variants and improvements built on top of it. Both parts of this document are meant to describe lessons drawn from HotStuff as well as dispel certain myths