Alice and Bob use Diffie Hellman to agree on a key They chose p, a prime, and , a primitive element of Z p Alice sends x 1 a (mod p) to Bob Bob sends x 2 b (mod p) to Alice The agreed upon key is then ab mod p Eve learns x 2 and b and it turns out that gcd(b, p 1) 1 Explain how Eve can compute from the information she has

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Question: Alice and Bob use Diffie-Hellman to agree on a key. They chose p, a prime, and , a primitive element of Z p . Alice

Alice and Bob use Diffie-Hellman to agree on a key. They chose p, a prime, and , a primitive element of Z_p . Alice sends x₁ = ^a (mod p) to Bob. Bob sends x₂ = ^b (mod p) to Alice. The agreed upon key is then ^ab mod p. Eve learns x₂ and b and it turns out that gcd(b, p 1) = 1.

Explain how Eve can compute from the information she has.

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