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Proof of Work (PoW) has been extensively utilized 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. In this work, we design a dual-functional blockchain framework that uses solving optimization problems to reach consensus as an alternative to PoW, channeling wasted resources into useful work. We model and analyze our framework by developing discrete Markov chains, and derive the security conditions to ensure that selfish miners behave honestly. Based on the security conditions, we derive a lower bound for the security overhead and analyze the trade-off between useful work efficiency and PoW safeguard. We further dive deep into the reward function design for the proposed dual-functional blockchain and provide practical design guidelines for reward functions assuming concavity and linearity respectively. Finally, simulation results are presented to validate and illustrate our analytical results.
Cao et al. (Wed,) studied this question.