Optimization-based Proof of Useful Work: Framework, Modeling, and Security Analysis

TL;DR

This work formulates a generic optimization-based PoUW framework that redirects substantial mining power from meaningless hash puzzles to solving real optimization tasks, while preserving blockchain security via PoW overhead. It provides a rigorous security analysis for selfish and malicious behaviors, deriving the lower bound $\eta>\frac{1}{2}$ for the security overhead and establishing reward-design guidelines to deter deviation from honest mining. The authors develop a Markov-chain-based model of honest and selfish strategies, quantify incentive conditions with coefficients $\alpha_i,\beta_i,\gamma_i$, and prove that appropriate reward structures can guarantee Nash equilibrium in favor of honesty; they also derive necessary and probabilistic conditions against long-range attacks and malicious incursions. Simulations validate the theoretical results, demonstrate the impact of reward design on security regions, and illustrate practical trade-offs between useful-work efficiency and PoW safeguard, suggesting a viable path for sustainable, useful-computation blockchain systems.

Abstract

Proof of Work (PoW) has extensively served as the foundation of blockchain's security, consistency, and tamper-resistance. However, long has it been criticized for its tremendous and inefficient utilization of computational power and energy. Proof of useful work (PoUW) can effectively address the blockchain's sustainability issue by redirecting the computing power towards useful tasks instead of meaningless hash puzzles. Optimization problems, whose solutions are often hard to find but easy to verify, present a viable class of useful work for PoUW. However, most existing studies rely on either specific problems or particular algorithms, and there lacks comprehensive security analysis for optimization-based PoUW. Therefore, in this work, we build a generic PoUW framework that solves useful optimization problems for blockchain maintenance. Through modeling and analysis, we identify the security conditions against both selfish and malicious miners. Based on these conditions, we establish a lower bound for the security overhead and uncover the trade-off between useful work efficiency and PoW safeguard. We further offer the reward function design guidelines to guarantee miners' integrity. We also show that the optimization-based PoUW is secure in the presence of malicious miners and derive a necessary condition against long-range attacks. Finally, simulation results are presented to validate our analytical results.

Figures (11)

• Figure 1: A generic framework of optimization-based PoUW blockchain.
• Figure 2: Illustration of states for different strategy profiles.
• Figure 3: The state transition diagram for different strategy profiles. The numbers in circles represent the corresponding states shown in Fig. \ref{['fig:states']}. (a) (H, H). (b) (FS, H). (c) (H, IF).
• Figure 4: The example reward functions.
• Figure 5: $P\left(T_{2}^{o}+T_{2}^{p}<T_{1}^{p}\right)$ with respect to security overhead ratio $\eta$. Optimization-based PoUW is secure against malicious miners if $P\left(T_{2}^{o}+T_{2}^{p}<T_{1}^{p}\right)>\frac{1}{2}$.

Theorems & Definitions (18)

• Definition 1
• Definition 2: Security Conditions against Selfishness
• Theorem 1: Security Conditions against Selfishness
• proof
• Theorem 2: Security Overhead Bound
• proof
• Theorem 3
• Lemma 1
• proof
• proof