# How to decrypt Pohlig-Hellman cipher if e and (n-1) aren't relatively prime

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?

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...