PAKEs: New Framework, New Techniques and More Efficient Lattice-Based Constructions in the Standard Model 📺
Password-based authenticated key exchange (PAKE) allows two parties with a shared password to agree on a session key. In the last decade, the design of PAKE protocols from lattice assumptions has attracted lots of attention. However, existing solutions in the standard model do not have appealing efficiency. In this work, we first introduce a new PAKE framework. We then provide two realizations in the standard model, under the Learning With Errors (LWE) and Ring-LWE assumptions, respectively. Our protocols are much more efficient than previous proposals, thanks to three novel technical ingredients that may be of independent interests. The first ingredient consists of two approximate smooth projective hash (ASPH) functions from LWE, as well as two ASPHs from Ring-LWE. The latter are the first ring-based constructions in the literature, one of which only has a quasi-linear runtime while its function value contains $$varTheta (n)$$ field elements (where n is the degree of the polynomial defining the ring). The second ingredient is a new key conciliation scheme that is approximately rate-optimal and that leads to a very efficient key derivation for PAKE protocols. The third one is a new authentication code that allows to verify a MAC with a noisy key.
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.