Key exchange

A key exchange (or key agreement) protocol allows two parties communicating over a public, authenticated channel to establish a shared secret key that is computationally indistinguishable from uniformly random to any eavesdropper. Unlike PKE, key exchange does not require a pre-established public key infrastructure.

Syntax

A two-party key exchange protocol is a pair of interactive algorithms $(KE_{A}, KE_{B})$ run between parties $A$ and $B$ over a shared transcript. Following execution, both parties output a key $k \in K$ . In the non-interactive setting:

$KE = (Gen, Combine)$ where $Gen (1^{λ}) \to (pk, sk)$ and each party publishes $pk_{A}, pk_{B}$ , then computes $k = Combine (sk_{A}, pk_{B}) = Combine (sk_{B}, pk_{A})$ .

Properties

Correctness

Both parties output the same key $k$ with probability 1 (over their randomness).

Security (indistinguishability from random)

A key exchange protocol is secure if for all efficient adversaries $A$ that observe the full transcript, the session key $k$ is computationally indistinguishable from a uniformly random key $k^{'} \leftarrow $ K$ .

Variations

Non-interactive key exchange (NIKE)

A NIKE allows any two parties to derive the same shared key from each other’s public keys alone, with no interaction at all. Diffie-Hellman over a cyclic group is the canonical example: $k = g^{ab}$ given public keys $g^{a}$ and $g^{b}$ .

Authenticated key exchange (AKE)

An AKE additionally guarantees that the parties authenticate each other’s identities during the protocol, preventing man-in-the-middle attacks.

Multi-party key exchange

Generalizes two-party KE to $n$ parties. Requires additional rounds or structure (e.g., Burmester-Desmedt, pairing-based constructions).

Other results

Participates in

Builds on Key exchange

Produces Key exchange

Barriers

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