The aim of this question is to show that there are some groups in which the discrete logarithm problem (DLP) is easy. In

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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 Z ∗ p where p is a prime and the multiplication
operation is multiplication modulo p. In particular, p = (2^t) + 1
for some positive integer t ≥ 2. The number of elements in Z ∗ p ,
i.e., the order of the group, is 2^t
(a)Show that g^ (2^ t) ≡ 1 (mod p).( to do)
(b)Show that the square root of g^( 2 ^t) modulo p, i.e., g^( (2
^t)/ 2 )= g ^(2 ^(t−1)) ≡ −1 (mod p).(to do)