Problem 1. A broken proof of work hash function. In class we discussed using a hash function H : X x Y - {0, 1, ...,2" -1} for a proof of work scheme. Once an r E X and a difficulty level D are published, it should take an expected D evaluations of the hash function to find a y ( Y such that H(x, y) {0, 1, . .., 2256 - 1} defined as H(x, y) := SHA256(x y). Here @ denotes a bit-wise xor. Show that this H is insecure as a proof of work hash. In particular, suppose D is fixed ahead of time. Show that a clever attacker can find a solution y EY with minimal effort once r E X is published. Hint: the attacker will do most of the work before x is published