Alice and Bob want to set up a symmetric cryptographic channel using the Diffie-Hellman key exchange protocol. Alice chooses p = 457 and needs to find a generator of Zp. How would you test if g is a generator of Zp? How many exponents a ≥ 1 do you need to test at most to prove that a given g is a generator of Z∗457?Hint: The order ordG(g) of any element g ∈ G must divide the order of the finite group G.
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