International Association for Cryptologic Research

International Association
for Cryptologic Research


Song Tian


Translating the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves with $(\ell ,\ell ,\ell )$-Isogenies
Song Tian
We give an algorithm to compute $$(\ell ,\ell ,\ell )$$ ( ℓ , ℓ , ℓ ) -isogenies from the Jacobians of genus three hyperelliptic curves to the Jacobians of non-hyperelliptic curves over a finite field of characteristic different from 2 in time $$\tilde{O}(\ell ^3)$$ O ~ ( ℓ 3 ) , where $$\ell $$ ℓ is an odd prime which is coprime to the characteristic. An important application is to reduce the discrete logarithm problem in the Jacobian of a hyperelliptic curve to the corresponding problem in the Jacobian of a non-hyperelliptic curve.
Strongly Secure Authenticated Key Exchange from Supersingular Isogenies
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.


Man Ho Au (1)
Kunpeng Wang (1)
Xiu Xu (1)
Haiyang Xue (1)