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I encountered a question that I can't seem to get around it. Lets say user A and B uses the DHKE defined over $GF(2^8)$ induced by the irreducible polynomial $x^8 + x^4 + x^3 + x^2 + 1$ and the primitive root $10$ (base $2$).

  1. What will be the corresponding public key if user A chooses a private key $X_a=3$?

  2. What will be the public key of user B if B chooses a private key $X_b=9$?

  3. What would be the shared secret key between A and B under normal conditions?

My answers says that for 1), its $10^3=1000$. Would that be correct? Because if I understand correctly, it's 10(base 2) but $10^3=1000$ will be base 10, right? For 2) (ans=3A(base 16)) and 3) (0C (base 16)), I am totally clueless... thanks for any help rendered!

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