5.6.6 Hybrid Encryption And Key Exchange

Although public-key cryptography provides strong authentication and confidentiality, it is computationally expensive for bulk data. Consequently, most modern secure-communications systems adopt a hybrid encryption approach:

A short-term session key for a symmetric algorithm (such as AES) is generated.
This session key is encrypted with the recipient’s public key (e.g., via RSA or ECC).
The recipient decrypts the session key using their private key, after which both parties use the symmetric key for high-speed data encryption.

This process, known as a key-exchange protocol, ensures that a secure symmetric key can be established over an insecure channel without pre-shared secrets.

The best-known public-key key-exchange algorithm is the Diffie–Hellman (DH) protocol, introduced in 1976, which allows two parties to derive a shared secret key based on the discrete-logarithm problem rather than integer factorization. In its basic form:

Both parties agree on a large prime number p and a primitive root g (the base).
Each selects a private random integer ( $a$ and $b$ ) and exchanges corresponding public values: A = g^amod(p) and B = g^bmod(p).
Each then computes the shared secret:

K = B^{a} m o d (p) = A^{b} m o d (p)

(5.19)

Only the participants, who know a or b, can compute K; an eavesdropper knowing only g, p, A, B cannot feasibly derive the key without solving the discrete logarithm problem. The basic Diffie–Hellman protocol provides key agreement but does not by itself provide authentication; authenticated variants are required in practice.

Elliptic-curve variants such as elliptic-curve Diffie–Hellman (ECDH) now dominate secure-session establishment in TLS 1.3 and IKEv2 VPNs, offering stronger security per bit and faster negotiation than traditional RSA or DH.