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

Proof of Work (PoW) has extensively served as the foundation of blockchain's security, consistency, and tamper-resistance, but 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 consensus. Through modeling and analysis, we identify the security conditions against both selfishness and maliciousness. 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.