Post-Quantum Constant-Round Group Key Exchange from Static Assumptions
Katsuyuki Takashima · Mathematics for industry · 2020
Abstract We revisit a generic compiler from a two-party key exchange (KE) protocol to a group KE (GKE) one by Just and Vaudenay. We then give two families of GKE protocols fromstaticassumptions, which are obtained from the general compiler. The first family of the GKE protocols is a constant-round GKE by using secure key derivation functions (KDFs). As special cases, we have such GKE fromstaticRing-LWE (R-LWE), where “static” means that the parameter size in the R-LWE does not depend on the number of group members,n, and also from the standard SI-DDH and CSI-DDH assumptions. The second family consists of two-round GKE protocols from isogenies, which are proven secure fromnewisogeny assumptions, the first (resp. second) of which is based on the SIDH (resp. CSIDH) two-party KE. The underlying newstaticassumptions are based on indistinguishability betweena product value of supersingular invariantsand a random value.