Given the prime p = 65497 and the generator g = 134 of ( Zp*, ⊗, 1). The number a = 17 is Alice’s secret El Gamal key.
a) Verify that p is prime and g is a generator of ( Zp*, ⊗, 1).
b) Calculate the public El Gamal key of Alice.
c) Alice has secretly chosen the following ephemeral key r = 45625. Verify the condition for r.
d) Calculate the signatur sig of m = 11123 with the above ephemeral key r.
e) Verify that (m, sig) is a valid signature of Alice.
f) Is (m, sig) = (221, 111, 333) a valid El Gamal signature of Alice?