Understanding and Constructing AKE via Double-key Key Encapsulation Mechanism.

Motivated by abstracting the common idea behind several implicitly authenticated key exchange (AKE) protocols, we introduce a primitive that we call double-key key encapsulation mechanism (2-key KEM). It is a special type of KEM involving two pairs of secret-public keys and satisfying some function and security property. Such 2-key KEM serves as the core building block and provides alternative approaches to simplify the constructions of AKE. To see the usefulness of 2-key KEM, we show how several existing constructions of AKE can be captured as 2-key KEM and understood in a unified framework, including widely used HMQV, NAXOS, Okamoto-AKE, and FSXY12-13 schemes. Then, we show (1) how to construct 2-key KEM from concrete assumptions, (2) how to adapt the classical Fujisaki-Okamoto transformation and KEM combiner to achieve the security requirement of 2-key KEM, (3) an elegant Kyber-AKE over lattice using the improved Fujisaki-Okamoto technique.