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

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