Final answer:
The security of the Diffie-Hellman-Merkle Key Agreement protocol relies on the hard-to-solve discrete logarithm problem, which underpins the secure exchange of cryptographic keys between parties.
Step-by-step explanation:
The security of the Diffie-Hellman-Merkle Key Agreement protocol is based on the computational difficulty of the discrete logarithm problem in finite fields or modulo a prime. Specifically, it is a challenge to reverse the exponentiation process without the knowledge of the private key, which is the basis for the protocol's ability to securely exchange cryptographic keys over an insecure channel. The protocol allows two or more parties to establish a shared secret that can be used for subsequent encryption of messages.