How would I solve this question? Can you please make sure that the picture is clear to understand. This question focuses on discrete logarithm.

The aim of this question is to show that there are some groups in which the discrete logarithm problem (DLP) is easy. In this example, we will consider the multiplicative group G whose elements are exactly the set where p is a prime and the multiplication operation is multiplication modulo p. In particular, p = 2t + 1 for some positive integer t ≥ 2. The number of elements in , i.e., the order of the group, is 2t.

Recall that under DLP, we are given g and h such that gx ≡ h (mod p) for some unknown x, and we need to find x. We will assume that g is a generator of this group.

As an example, you may consider p = 28+1 = 257. Then g = 3 is a generator of this group. (Hint: It might be helpful to run parts (a) through (d) with these example values first to understand what they mean.)

Show that g1t ≡ 1 (mod p).