Which of the following is considered a secure method of key exchange in cryptography?

The reason that Diffie-Hellman is recognized as a secure method of key exchange lies in its ability to allow two parties to generate a shared secret over an insecure channel without having to transmit the key itself. This method is based on the mathematical properties of modular arithmetic and discrete logarithms, which make it computationally difficult for an eavesdropper to derive the shared secret even if they can observe the exchanged data.

Diffie-Hellman effectively leverages the difficulty of the discrete logarithm problem, meaning that while the exchanged values may be intercepted, reconstructing the shared secret requires solving a problem that is currently infeasible with existing computational techniques. This ensures that communication remains private, as only the two parties involved can derive the shared key.

In contrast, other methods such as plaintext sharing or static key distribution expose the key directly to potential interception, making them vulnerable to attacks. Public key distribution is secure in its own right but relies heavily on the infrastructure and implementation of public key cryptography, which is more complex than the direct approach provided by Diffie-Hellman.

Thus, Diffie-Hellman stands out as a robust and widely used protocol for establishing a shared secret between parties in a secure and efficient manner.