If $p$ is an odd prime and $n$ natural,it is known that the group $Z^*_{p^n}$ is cyclic.Explain why the selection-choice of the group $Z^*_{{3^{1000}}}$ for the construction of a cryptosystem ElGamal it's not good.
This is a question that has been asked in a mathematical lecture of my university and i would like to share it here and help me to find a solution