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I couldn't find any articles that addressed to how to decrypt c after it was encrypted using the Pohlig-Hellman cipher if $e$ and $n-1$ aren't relatively.

Can someone please tell me how to do it?

I couldn't find an questions about this on StackExchange.

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It is essentially the same as the answer I gave in How to compute $m$ value from RSA if $phi(n)$ is not relative prime with the $e$?, with the same restrictions ($e$ assumed prime, $e^2$ assumed not to be a divisor of $p-1$), with the sole change being that $\lambda = p - 1$.

It's easy enough to cover the composite $e$ case (factor $e$ into primes $e = r_1 r_2 … r_n$, and then find solutions for $c = m^{r_1 r_2 … r_n}$ by inverting each $r_i$ individually.

The other case $e^2$ is a divisor of $p-1$ is a lot tougher, and probably needs a different approach...

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