Paper 2020/244

On Adaptive Attacks against Jao-Urbanik’s Isogeny-Based Protocol

Andrea Basso and Péter Kutas and Simon-Philipp Merz and Christophe Petit and Charlotte Weitkämper

Abstract

The $k$-SIDH protocol is a static-static isogeny-based key agreement protocol. At Mathcrypt 2018, Jao and Urbanik introduced a variant of this protocol which uses non-scalar automorphisms of special elliptic curves to improve its efficiency. In this paper, we provide a new adaptive attack on Jao-Urbanik's protocol. The attack is a non-trivial adaptation of Galbraith-Petit-Shani-Ti's attack on SIDH (Asiacrypt 2016) and its extension to $k$-SIDH by Dobson-Galbraith-LeGrow-Ti-Zobernig (IACR eprint 2019). Our attack provides a speedup compared to a naïve application of Dobson et al.'s attack to Jao-Urbanik's scheme, exploiting its inherent structure. Estimating the security of $k$-SIDH and Jao-Urbanik's variant with respect to these attacks, $k$-SIDH provides better efficiency.