Using Useful Tasks for Proof-of-Work for Blockchain Systems

This paper logically continues the paper about possible approaches to solving the "useful proof-of-work for blockchains" problem. We propose some alternative lines of searching for useful tasks for proof-of-work. These approaches are based on a fact that solving the hash puzzle is close to the multiple and independent repetition of the following experiment: assume that there is a fairly large set defined (for example, consisting of 2(n) elements for a fairly high n), and only a minor portion of the elements have a certain property. The experiment consists in uniformly choosing an element from this set and then checking whether this element has the indicated property. Thus the hash puzzle solution process can be replaced, for example, with searching for rare astronomical objects or positions in a game of Go that meet certain conditions. Moreover, we describe a possible attack against the blockchain system in which the task instance generation algorithm is replaced with the algorithm of choosing instances from the available database by unscrupulous task instance suppliers in case of their public collection. In addition, some ways of protecting against this attack are discussed.