In DL (discrete logarithm) based algorithms the private (secret) key is uniformly selected from the group Zq*. The public key is then computed from this private key. Is it feasible to do the opposite,...

In DL (discrete logarithm) based algorithms the private (secret) key is uniformly selected from the group Zq*. The public key is then computed from this private key. Is it feasible to do the opposite, i.e., select the public key uniformly from Zq* and compute the private key? Discuss.