I'm working in the context of ElGamal encryption problem as describe in the second image of this post. In my problem, I work on $\mathbb{Z}_p^*$ with p prime. I'm told that I should look for subgroups of index two so that the discrete logarithm problem becomes easier. I'm working with sage.
- How can I look for the subgroup of index 2 in $\mathbb{Z}_p^*$ with sage?
- Once I find the subgroup of index 2 how would I solve the discrete logarithm problem on it? How would I use this result for solve the discrete logarithm problem in the whole group?