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Troff
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Homework Statement
The original problem has to do with telling messages encrypted with a version of the ElGamal public key crypto system apart. It relies on exponentiation in an arbitrary cyclic group G of prime order p with generator g. The public key is [tex]y = g^x[/tex] where x is the private key.
Homework Equations
The Attempt at a Solution
Well - I don't actually want help finding a solution to the original problem, but the solution that I do have relies on the ability to calculate [tex]y^{-1}[/tex]. As far as I can tell [tex]\forall x \in G: x^{p} = 1[/tex], which would seem to imply that [tex]\forall x \in G: x^{p-1} = x^{-1}[/tex]. Either this is wrong in which case I'd like to understand what I'm missing or I am doing something wrong somewhere else, which I'd then correct or fail myself.