How would i find out Alices or Bobs private number from the details exchanged in public.  prime - g = 7  primitive root - n = 3  Alice - A = 3  Bob - B = 4  The details visible in public exchange are:  g = 7  n = 3  Ya == 27 mod 7  Yb == 81 mod 7  How would one go about finding Alices secret number A or Bobs secret number B from the exchange usings only the visible details exchanged in public space. Please provide an explanation to notation as well as a practice solution to the scenario I've provided.
I started to read about Diffie-Hellman exchange and I encountered a problem which I don't know how to solve.  Given $g=3$, $p=131$, $g^x\bmod p=112$, $g^y\bmod p=74$, compute $g^{xy}\bmod p$   $113$ $110$ $112$ $111$   How could I compute $g^{xy} \bmod p$? Or at least verify which one is correct. Any idea?
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