Proofs of Useless Work -- Positive and Negative Results for Wasteless Mining Systems

Many blockchain systems today, including Bitcoin, rely on Proof of Work (PoW). Proof of work is crucial to the liveness and security of cryptocurrencies. The assumption when using PoW is that a lot of trial and error is required on average before a valid block is generated. One of the main concerns raised with regard to this kind of system is the inherent need to "waste" energy on "meaningless" problems. In fact, the Bitcoin system is believed to consume more electricity than several small countries. In this work we formally define three properties that are necessary for wasteless PoW systems: (1) solve "meaningful" problems (2) solve them efficiently and (3) be secure against double-spend attacks. These properties aim to create an open market for problem-solving, in which miners produce solutions to problems in the most efficient way (wasteless). The security of the system stems from the economical incentive created by the demand for solutions to these problems. We analyze these properties, and deduce constraints that must apply to such PoW systems. In our main result, we conclude that under realistic assumptions, the set of allowed problems must be preimage resistant functions in order to keep the system secure and efficient.