Diffie-Hellman Key Exchange

The Diffie-Hellman key agreement protocol (1976) was the first practical method for establishing a shared secret over an unsecured communication channel.

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Diffie-Hellman Example

1. Alice and Bob agree on p = 23 and g = 5.

2. Alice chooses a = 6 and sends 5 6 mod 23 = 8.

3. Bob chooses b = 15 and sends 515 mod 23 = 19.

4. Alice computes 19 6 mod 23 = 2.

5. Bob computes 815 mod 23 = 2.

Then 2 is the shared secret.

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Suppose p is a prime of around 300 digits, and a and b at least 100 digits each. Discovering the shared secret given g, p, g a mod p and g b mod p would take longer than the lifetime of the universe, using the best known algorithm. This is called the discrete Algorithm problem.

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1. The Diffie Hellman protocol to have a Certificate Authority ensure that the public key is without a doubt originating from the source in which you believe. The reason for this accreditation is to prevent man-in-the middle (MITM) attacks.

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Calculate the shared secret key:

Given p=23 and g=5, The private key of A is 4 and the private key of B is 3. Then share a secret no. _____

• 18

• 81

• 7

• 20