Whitepapers

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Quai Network: Reignite The Crypto Revolution (Litepaper)

Published 10 October 2024 A highlevel overview of the first decentralized energy dollar on the only scalable and programmable Proof-of-Work blockchain. Read the full litepaper on qu.ai

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Optimal Reward Allocation via Proportional Splitting

Published 13 March 2025 Following the publication of Bitcoin’s arguably most famous attack, selfish mining, various works have introduced mechanisms to enhance blockchain systems’ game theoretic resilience. Some reward mechanisms, like FruitChains, have been shown to be equilibria in theory. However, their guarantees assume non-realistic parameters and their performance degrades significantly in a practical deployment setting. In this work we introduce a reward allocation mechanism, called Proportional Splitting (PRS), which outperforms existing state of the art. We show that, for large enough parameters, PRS is an equilibrium, offering the same theoretical guarantees as the state of the art. In addition, for practical, realistically small, parameters, PRS outperforms all existing reward mechanisms across an array of metrics. We implement PRS on top of a variant of PoEM, a Proof-of-Work (PoW) protocol that enables a more accurate estimation of each party’s mining power compared to e.g., Bitcoin. We then evaluate PRS both theoretically and in practice. On the theoretical side, we show that our protocol combined with PRS is an equilibrium and guarantees fairness, similar to FruitChains. In practice, we compare PRS with an array of existing reward mechanisms and show that, assuming an accurate estimation of the mining power distribution, it outperforms them across various well-established metrics. Finally, we realize this assumption by approximating the power distribution via low-work objects called “workshares” and quantify the tradeoff between the approximation’s accuracy and storage overhead. Read the full paper on arxiv.org.

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A Better Proof-of-Work Fork Choice Rule

Published 9 February 2024 We propose a modification to the fork choice rule of proof-of-work blockchains. Instead of choosing the heaviest chain, we choose the chain with the most intrinsic work. The intrinsic work of a block is roughly the number of zeroes at the front of its hash. This modification allows us to safely decrease the confirmations required, yielding a 28.5% improvement in confirmation delay or, dually, safely increase the block production rate, yielding a 16.3% improvement in throughput, as compared to the vanilla Bitcoin proof-of-work fork choice rule. Our modification is at the level of the proof-of-work inequality, and thus can be composed with any other methods to improve latency or throughput that have been proposed in the literature. We report the experimental findings by measuring them on a production-grade implementation of our system, whose testnet is already deployed in the wild. Lastly, we formally prove the security of our new protocol in the Bitcoin Backbone model. Read the full paper on iacr.org.

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PoEM: Proof-of-Entropy-Minima

Published 8 March 2023 Nakamoto consensus has been incredibly influential in enabling robust blockchain systems, and one of its components is the so-called heaviest chain rule (HCR). Within this rule, the calculation of the weight of the chain tip is performed by adding the difficulty threshold value to the previous total difficulty. Current difficulty based weighting systems do not take the intrinsic block weight into account. This paper proposes a new mechanism based on entropy differences, named proof of entropy minima (POEM), which incorporates the intrinsic block weight in a manner that significantly reduces the orphan rate of the blockchain while simultaneously accelerating finalization. Finally, POEM helps to understand blockchain as a static time-independent sequence of committed events. Read the full paper on arxiv.org.

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Scalable Multi-Chain Coordination via the Hierarchical Longest Chain Rule

Published in 2022 IEEE International Conference on Blockchain (Blockchain) This paper introduces BlockReduce, a Proof-of-Work based blockchain system which achieves high transaction throughput by means of a hierarchy of merged mined blockchains, each operating in parallel on a partition of the overall application state. Most notably, the full PoW available within the network is applied to all blockchains in BlockReduce, and cross-blockchain state transitions are enabled seamlessly within the core protocol. This paper shows that, given a hierarchy of blockchains and its associated security model, BlockReduce scales super-linearly in transaction throughput with the number of blockchains operated by the protocol. BlockReduce utilizes a novel consensus rule to select the canonical chain—i.e., the chain of blocks referencing state updates to be applied—for each blockchain. In Bitcoin and other more traditional systems, the Longest Chain Rule (LCR) stipulates that the canonical chain is the sequence of valid blocks with the most work (often referred to as the longest chain or, more accurately, the heaviest chain). BlockReduce follows a similar rule but must also account for the existence of coincident blocks within the hierarchy. Read the full paper on ieee.org.

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Hashcore: Proof-of-Work Functions for General Purpose Processors

Published in 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS) Over the past five years, the rewards associated with mining Proof-of-Work blockchains have increased substantially. As a result, miners are heavily incentivized to design and utilize Application Specific Integrated Circuits (ASICs) that can compute hashes far more efficiently than existing general purpose hardware. Currently, it is difficult for most users to purchase and operate ASICs due to pricing and availability constraints, resulting in a relatively small number of miners with respect to total user base for most popular cryptocurrencies. In this work, we aim to invert the problem of ASIC development by constructing a Proof-of-Work function for which an existing general purpose processor (GPP, such as an x86 IC) is already an optimized ASIC. In doing so, we will ensure that any would-be miner either already owns an ASIC for the Proof-of-Work system they wish to participate in or can attain one at a competitive price with relative ease. In order to achieve this, we present HashCore, a Proof-of-Work function composed of “widgets” generated pseudo-randomly at runtime that each execute a sequence of general purpose processor instructions designed to stress the computational resources of such a GPP. The widgets will be modeled after workloads that GPPs have been optimized for, for example, the SPEC CPU 2017 benchmark suite for x86 ICs, in a technique we refer to as inverted benchmarking. We provide a proof that HashCore is collision-resistant regardless of how the widgets are implemented. We observe that GPP designers/developers essentially create an ASIC for benchmarks such as SPEC CPU 2017. By modeling HashCore after such benchmarks, we create a Proof-of-Work function that can be run most efficiently on a GPP, resulting in a more accessible, competitive, and balanced mining market. Read the full paper on ieee.org.

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BlockReduce: Scaling Blockchain to Human Commerce

Published 31 October 2018 This paper introduces BlockReduce, a Proof-of-Work (PoW) based blockchain system which achieves high transaction throughput through a hierarchy of merged mined blockchains, each operating in parallel on a partition the overall application state. Most notably, the full PoW available within the network is applied to all blockchains in BlockReduce, and cross-blockchain state transitions are enabled seamlessly within the core protocol. This paper shows that, given a hierarchy of blockchains and its associated security model, the protocol scales super-linearly in transaction throughput with the number of blockchains operated by the protocol. Read the full paper on arxiv.org.