Based on the fact that we don't have a P algorithm for the discrete logarithm of the cyclic group as of 2020, but we do have an efficient algorithm for modular exponentiation. But nor do we have proof that one does not exist! Living on the edge as usual for public-key cryptography.
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Alice publishes and Bob publishes in a public cyclic group; each can then compute the shared secret . Its security relies on the difficulty of recovering the exponents or otherwise solving the computational Diffie--Hellman problem.
Diffie–Hellman key exchange is a method that allows two parties to securely establish a shared secret key over an insecure communication channel. This shared key can then be used for symmetric encryption of messages. The key exchange process, developed by Whitfield Diffie and Martin Hellman in 1976, enables the parties to agree on a secret key without the need to exchange the key itself.