A Fair and Resilient Decentralized Clock Network for Transaction Ordering

Traditional blockchain design gives miners or validators full control over transaction ordering, i.e., they can freely choose which transactions to include or exclude, as well as in which order. While not an issue initially, the emergence of decentralized finance has introduced new transaction order dependencies allowing parties in control of the ordering to make a profit by front-running others' transactions. In this work, we present the Decentralized Clock Network, a new approach for achieving fair transaction ordering. Users submit their transactions to the network's clocks, which run an agreement protocol that provides each transaction with a timestamp of receipt which is then used to define the transactions' order. By separating agreement from ordering, our protocol is efficient and has a simpler design compared to other available solutions. Moreover, our protocol brings to the blockchain world the paradigm of asynchronous fallback, where the algorithm operates with stronger fairness guarantees during periods of synchronous use, switching to an asynchronous mode only during times of increased network delay.Comment: In Proceedings of 27th International Conference on Principles of Distributed Systems (OPODIS

Improved Solutions for Multidimensional Approximate Agreement via Centroid Computation

In this paper, we present distributed fault-tolerant algorithms that approximate the centroid of a set of n data points in $\mathbb{R}^d$. Our work falls into the broader area of approximate multidimensional Byzantine agreement. The standard approach used in existing algorithms is to agree on a vector inside the convex hull of all correct vectors. This strategy dismisses many possibly correct data points. As a result, the algorithm does not necessarily agree on a representative value. In fact, this does not allow us to compute a better approximation than $2d$ of the centroid in the synchronous case. To find better approximation algorithms for the centroid, we investigate the trade-off between the quality of the approximation, the resilience of the algorithm, and the validity of the solution. For the synchronous case, we show that it is possible to achieve a $1$-approximation of the centroid with up to $t<n/(d+1)$ Byzantine data points. This approach however does not give any guarantee on the validity of the solution. Therefore, we develop a second approach that reaches a $2\sqrt{d}$-approximation of the centroid, while satisfying the standard validity condition for agreement protocols. We are even able to restrict the validity condition to agreement inside the box of correct data points, while achieving optimal resilience of $t< n/3$. For the asynchronous case, we can adapt all three algorithms to reach the same approximation results (up to a constant factor). Our results suggest that it is reasonable to study the trade-off between validity conditions and the quality of the solution

Communication-Optimal Convex Agreement

Byzantine Agreement (BA) allows a set of $n$ parties to agree on a value even when up to $t$ of the parties involved are corrupted. While previous works have shown that, for $\ell$-bit inputs, BA can be achieved with the optimal communication complexity $\mathcal{O}(\ell n)$ for sufficiently large $\ell$, BA only ensures that honest parties agree on a meaningful output when they hold the same input, rendering the primitive inadequate for many real-world applications. This gave rise to the notion of Convex Agreement (CA), introduced by Vaidya and Garg [PODC\u2713], which requires the honest parties\u27 outputs to be in the convex hull of the honest inputs. Unfortunately, all existing CA protocols incur a communication complexity of at least $\Omega(\ell n^2)$. In this work, we introduce the first CA protocol with the optimal communication of $\mathcal{O}(\ell n)$ bits for inputs in $\mathbb{Z}$ of size $\ell = \Omega(\kappa \cdot n^2 \log n)$, where $\kappa$ is the security parameter

Byzantine Agreement with Median Validity

We introduce a stronger validity property for the byzantine agreement problem with orderable initial values: The median validity property. In particular, the decision value is required to be close to the median of the initial values of the non-byzantine nodes. The proximity to the median scales with the desired level of fault-tolerance: If no fault-tolerance is required, algorithms have to decide for the true median. If the number of failures is maximal, algorithms must still decide on a value within the range of the input values of the non-byzantine nodes. We present a deterministic algorithm satisfying this property for n >= 3t+1 within t+1 phases, where t is the maximum number of byzantine nodes and n is the total number of nodes