Strongly Secure Authenticated Key Exchange from Supersingular Isogeny [article]

Xiu Xu, Haiyang Xue, Kunpeng Wang, Song Tian, Bei Liang, Wei Yu
2018 IACR Cryptology ePrint Archive  
This paper aims to address the open problem, namely, to find new techniques to design and prove security of supersingular isogeny-based authenticated key exchange (AKE) protocols against the widest possible adversarial attacks, raised by Galbraith in 2018. Concretely, we present two AKEs based on a double-key PKE in the supersingular isogeny setting secure in the sense of CK + , one of the strongest security models for AKE. Our contributions are summarised as follows. Firstly, we propose a
more » ... g OW-CPA secure PKE, 2PKE sidh , based on SI-DDH assumption. By applying modified Fujisaki-Okamoto transformation, we obtain a [OW-CCA, OW-CPA] secure KEM, 2KEM sidh . Secondly, we propose a two-pass AKE, SIAKE2, based on SI-DDH assumption, using 2KEM sidh as a building block. Thirdly, we present a modified version of 2KEM sidh that is secure against leakage under the 1-Oracle SI-DH assumption. Using the modified 2KEM sidh as a building block, we then propose a three-pass AKE, SIAKE3, based on 1-Oracle SI-DH assumption. Finally, we prove that both SIAKE2 and SIAKE3 are CK + secure in the random oracle model and supports arbitrary registration. We also provide an implementation to illustrate the efficiency of our schemes. Our schemes compare favourably against existing isogeny-based AKEs. To the best of our knowledge, they are the first of its kind to offer security against arbitrary registration, wPFS, KCI and MEX simultaneously. Regarding efficiency, our schemes outperform existing schemes in terms of bandwidth as well as CPU cycle count.
dblp:journals/iacr/XuXWTLY18 fatcat:louxcoweqbdtzkq74jha35kb2a