Final answer:
The Diffie-Hellman algorithm is specifically designed for the establishment and exchange of symmetric keys over an insecure medium.
Step-by-step explanation:
The asymmetric algorithm used to establish and exchange symmetric keys over an insecure medium is Diffie-Hellman. Although RSA (Rivest-Shamir-Adleman) can also be used to exchange keys, Diffie-Hellman is specifically designed for this purpose, and it allows two parties to securely share a symmetric key even if they have no previous knowledge of each other. This key can then be used for symmetric encryption for a secure communication session. ElGamal and Elliptic Curve Cryptography (ECC) also provide asymmetric cryptographic solutions, but the core use of Diffie-Hellman is key exchange.