Therefore both Alice and Bob know a shared secret g ab mod p. She can however calculate (g b) a mod p = g ab mod p.īob knows b and g a, so he can calculate (g a) b mod p = g ab mod p. She is not able to calculate the value b from Bob's public key as this is a hard mathematical problem (known as the discrete logarithm problem). Alice now knows a and Bob's public key g b mod p. If Alice and Bob wish to communicate with each other, they first agree between them a large prime number p, and a generator (or base) g (where 0 < g < p).Īlice chooses a secret integer a (her private key) and then calculates g a mod p (which is her public key).īob chooses his private key b, and calculates his public key in the same way.Īlice and Bob then send each other their public keys. The shared secret can then be used as the basis for some encryption key to be used for further communication. Its an agreement scheme because both parties add material used to derive the key (as opposed to transport, where one party selects the key). The Diffie-Hellman algorithm provides the capability for two communicating parties to agree upon a shared secret between them.
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