Diffie-Hellman key exchange.

Alice and Bob use Diffie-Hellman key exchange to share secrets. They start with prime numbers, pick private keys, generate and share public keys, and then generate a shared secret key.

Step 0

The test program supplies prime numbers p and g.

Step 1

Alice picks a private key, a, greater than 1 and less than p. Bob does the same to pick a private key b.

Step 2

Alice calculates a public key A.

A = gᵃ mod p

Using the same p and g, Bob similarly calculates a public key B from his private key b.

Step 3

Alice and Bob exchange public keys. Alice calculates secret key s.

s = Bᵃ mod p

Bob calculates

s = Aᵇ mod p

The calculations produce the same result! Alice and Bob now share secret s.

This exercise requires you to perform calculations on large numbers. To correctly represent large numbers, the [BigInteger](

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