Suppose Alice is a U.S. spy on a 7-day trip to a faraway land and wants to prove for each day she is gone that she not been captured. She has chosen a secret random number, x, which she is keeping secret. But she did tell her CIA handler the value y = H(H(H(H(H(H(H(x))))))), where H is a one-way cryptographic hash function. Unfortunately, her enemy, Eve, was able to listen in on this message; hence, Eve also knows the value of y. Explain how Alice can send a single message every day that proves she has not been captured.