The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel.
Let the users be named User1 and User2. First, they agree on two prime numbers g and p. The numbers g and p need not be kept secret from other users.
Now User1 chooses a large random number a as his private key and User2 similarly chooses a large number b.
User1 then computes A = (ga mod p), which he sends to User2, and User2 computes B = (gb mod p), which he sends to User1.
Now User1 computes Key = (Ba mod p) = ((gb mod p)a mod p)
and User2 computes Key = (Ab mod p) = ((ga mod p)b mod p)
user1 and User2 agree on p = 13 and g = 5.
User1 chooses a = 4 and sends A = (ga mod p) = (54 mod 13) = 1.
User2 chooses b = 3 and sends B = (gb mod p) = (53 mod 13) = 8.
User1 computes (Ba mod p) = 84 mod 13 = 1
User2 computes (Ab mod p) = 13 mod 13 = 1
Then 1 is the shared secret.
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