Alice wishes to transfer a short message K to Bob secretly. She chooses a large prime...

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Alice wishes to transfer a short message K to Bob secretly. She chooses a large prime number p, and selects a random number a with gcd(a,p-1) = 1. Bob selects a random number b with gcd (b, p - 1) = 1. 1) Alice sends K₁ = Ka (mod p) to Bob. 2) Bob sends K₂ = K (mod p) to Alice. 3) Alice sends K3 = K₂¹ (mod p) to Bob. Show that at the end of this protocol, both Alice and Bob have the secret message K. Alice wishes to transfer a short message K to Bob secretly. She chooses a large prime number p, and selects a random number a with gcd(a,p-1) = 1. Bob selects a random number b with gcd (b, p - 1) = 1. 1) Alice sends K₁ = Ka (mod p) to Bob. 2) Bob sends K₂ = K (mod p) to Alice. 3) Alice sends K3 = K₂¹ (mod p) to Bob. Show that at the end of this protocol, both Alice and Bob have the secret message K.