Problem
Question I: Suppose you were able to get control of 51% of mining resources of the bitcoin network. Could you forge a transaction between a bitcoin address of mine that I had posted publicly to an address of your choosing? If so, describe briefly what you could do to do this. If not, describe why this would not be possible.
Question II: You have two enemies (Abe and Earl) that hate modular arithmetic. They have decided to exchange keys by modifying Diffie-Hellman to remove the modulo operation after taking the values to powers. You overhear them agreeing to use 3 as the number they use as the base of their exponentiation (the alpha).
You then hear them exchange their public keys, with Abe's public key of 81 and Earl's public key of 2187