Forward Secure Offline Assisted Group Key Exchange From Isogeny-Based Blinded Key Encapsulation Mechanism

Group key exchange
is a promising cryptographic protocol that has been studied extensively over the years. However, an overwhelming majority of them involve interaction among users. This makes them unsuitable in a cloud-based outsourced storage systems where users seek to store and share their files with their collaborators who stay offline until they want to access the file. To address this concern, Boyd et al. designed an
offline assisted group key exchange
(
$\textsf {OAGKE}$
) protocol that offers forward secrecy. The core component of their
$\textsf {OAGKE}$
protocol is a variant of
key encapsulation mechanism
(
$\textsf {KEM}$
) called
blinded

$\textsf {KEM}$
(
$\textsf {BKEM}$
). However, their constructions of
$\textsf {BKEM}$
are susceptible to quantum attacks. This work proposes an isogeny-based
$\textsf {BKEM}$
and a
forward secure

$\textsf {OAGKE}$
that is secure against adversaries equipped with quantum computers. Our construction of
$\textsf {BKEM}$
is based on the
Commutative Supersingular Isogeny Diffie-Hellman
(
$\textsf {CSIDH}$
) cryptosystem. We provide a formal security proof demonstrating the security of our scheme. Furthermore, we manifest an instantiation of our
$\textsf {BKEM}$
from
$\textsf {CSIDH-512}$
parameter set. Finally, we present our isogeny-based
$\textsf {OAGKE}$
protocol along with its rigorous security analysis.