(a) Solve for x: 931x = 4 mod 12345. (b) Using Fermat's theorem, solve for x: x = 5300001 mod 11. (C) Suppose that someone suggests the following way to confirm that the two of you are in possession of the same secret key. You create a random bit string the length of the key, XOR it with the key, and send the result over the channel. Your partner XORs the incoming block with the key (which should be the same as your key) and sends it back. You check, and if what you receive is your original random string, you have verified that your partner has the same secret key, yet neither have you ever transmitted the key. Is there a flaw in this scheme? Comment