You have two enemies (Abe and Earl) that hate modular arithm…
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. What are Abe and Earl’s private keys? Show how these numbers were obtained.
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