[Resource Topic] 2020/244: On Adaptive Attacks against Jao-Urbanik’s Isogeny-Based Protocol

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

Authors: Andrea Basso, Péter Kutas, Simon-Philipp Merz, Christophe Petit, 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.

ePrint: https://eprint.iacr.org/2020/244

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