Forward Secure Offline Assisted Group Key Exchange From Isogeny-Based Blinded Key Encapsulation Mechanism
Surbhi Shaw, Ratna Dutta · IEEE Transactions on Information Theory · 2023
Group key exchangeis 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 anoffline assisted group key exchange($\textsf {OAGKE}$) protocol that offers forward secrecy. The core component of their$\textsf {OAGKE}$protocol is a variant ofkey encapsulation mechanism($\textsf {KEM}$) calledblinded$\textsf {KEM}$($\textsf {BKEM}$). However, their constructions of$\textsf {BKEM}$are susceptible to quantum attacks. This work proposes an isogeny-based$\textsf {BKEM}$and aforward secure$\textsf {OAGKE}$that is secure against adversaries equipped with quantum computers. Our construction of$\textsf {BKEM}$is based on theCommutative 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.