# What is the best choice of the base g in El-Gamal PKC

I have just read in a book that in El-Gamal PKC, the best choice of a base g is a number whose order in the field ($$\mathbb{F}_p$$) is a large prime, and added: "approximately = $$\frac{p}{2}$$". but from my point of view choosing a primitive root as a base is more secure because then the key space will be at least twice as large as if you chose any other base of any other order.

Is there anything I am ignoring or what?

• In case anyone has the same question, choosing a big prime order is better because there are algorithms like Pohlig-HellMan algorithm which reduces the discrete logarithm problem with a base having order N to much easier problems whose bases have orders corresponding to the prime factors of the original order. So, choosing a Prime order will make this algorithm useless. Jul 12 at 1:03