## CryptoDB

### Kunpeng Wang

#### Publications

Year
Venue
Title
2019
ASIACRYPT
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 strong OW-CPA secure PKE, $\mathsf {2PKE_{sidh}}$, based on SI-DDH assumption. By applying modified Fujisaki-Okamoto transformation, we obtain a [OW-CCA, OW-CPA] secure KEM, $\mathsf {2KEM_{sidh}}$. Secondly, we propose a two-pass AKE, $\mathsf {SIAKE}_2$, based on SI-DDH assumption, using $\mathsf {2KEM_{sidh}}$ as a building block. Thirdly, we present a modified version of $\mathsf {2KEM_{sidh}}$ that is secure against leakage under the 1-Oracle SI-DH assumption. Using the modified $\mathsf {2KEM_{sidh}}$ as a building block, we then propose a three-pass AKE, $\mathsf {SIAKE}_3$, based on 1-Oracle SI-DH assumption. Finally, we prove that both $\mathsf {SIAKE}_2$ and $\mathsf {SIAKE}_3$ 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.
2005
EPRINT
We compute Tate pairing over supersingular elliptic curves via the generic BGhES\cite{BGES} method for $p=5,7$. In those cases, the point multiplication by $p$ is efficiently computed by the Frobenius endomorphism. The function in a cycle can be efficiently computed by the method of continued fraction.

Man Ho Au (1)
Bao Li (1)
Song Tian (1)
Xiu Xu (1)
Haiyang Xue (1)