Embracing Hellman: A Simple Proof-of-Space Search consensus algorithm with stable block times using Logarithmic Embargo

Cryptocurrencies have become tremendously popular since the creation of Bitcoin. However, its central Proof-of-Work consensus mechanism is very power hungry. As an alternative, Proof-of-Space (PoS) was introduced that uses storage instead of computations to create a consensus. However, current PoS implementations are complex and sensitive to the Nothing-at-Stake problem, and use mitigations that affect their permissionless and decentralised nature. We introduce Proof-of-Space Search (PoSS) which embraces Hellman\u27s time-memory trade-off to create a much simpler algorithm that avoids the Nothing-at-Stake problem. Additionally, we greatly stabilise block-times using a novel dynamic Logarithmic Embargo (LE) rule. Combined, we show that PoSSLE is a simple and stable alternative to PoW with many of its properties, while being an estimated 10 times more energy efficient and sustaining consistent block times

Revisiting Simultaneous Consensus with Crash Failures

This paper addresses the “consensus with simultaneous decision” problem in a synchronous system prone to t process crashes. This problem requires that all the processes that do not crash decide on the same value (consensus) and that all decisions are made during the very same round (simultaneity). So, there is a double agreement, one on the decided value (data agreement) and one on the decision round (time agreement). This problem was first defined by Dwork and Moses who analyzed it and solved it using an analysis of the evolution of states of knowledge in a system with crash failures. The current paper presents a simple algorithm that optimally solves simultaneous consensus. Optimality means in this case that the simultaneous decision is taken in each and every run as soon as any protocol decides, given the same failure pattern and initial value. The design principle of this algorithm is simplicity, a first-class criterion. A new optimality proof is given that is stated in purely combinatorial terms

Broadcast Gossip Algorithms for Consensus on Strongly Connected Digraphs

We study a general framework for broadcast gossip algorithms which use companion variables to solve the average consensus problem. Each node maintains an initial state and a companion variable. Iterative updates are performed asynchronously whereby one random node broadcasts its current state and companion variable and all other nodes receiving the broadcast update their state and companion variable. We provide conditions under which this scheme is guaranteed to converge to a consensus solution, where all nodes have the same limiting values, on any strongly connected directed graph. Under stronger conditions, which are reasonable when the underlying communication graph is undirected, we guarantee that the consensus value is equal to the average, both in expectation and in the mean-squared sense. Our analysis uses tools from non-negative matrix theory and perturbation theory. The perturbation results rely on a parameter being sufficiently small. We characterize the allowable upper bound as well as the optimal setting for the perturbation parameter as a function of the network topology, and this allows us to characterize the worst-case rate of convergence. Simulations illustrate that, in comparison to existing broadcast gossip algorithms, the approaches proposed in this paper have the advantage that they simultaneously can be guaranteed to converge to the average consensus and they converge in a small number of broadcasts.Comment: 30 pages, submitte