Bit commitment:-
Alice claims that she is able to predict what the stock market average will be one month from now. To prove she can do it without revealing the value ahead of time, she offers to give Bob now an encrypted version of the future average (say x) and in one month give Bob the inverse of the key she used so that he can verify the result.
Bob is suspicious and wants better assurance that Alice does not have a number of different inversion keys that she could choose from to match the actual stock market value when it is known. Can he ask her to encrypt something else as well that will guarantee the security of her commitment?