(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

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# Homework Help: Can I calculate the (multiplicative) inverse of any element in a cyclic group?

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