CryptoDB

Paper: Cryptanalysis of an oblivious PRF from supersingular isogenies

Authors: Andrea Basso , University of Birmingham Péter Kutas , University of Birmingham and Eötvös Loránd University Simon-Philipp Merz , Royal Holloway, University of London Christophe Petit , Université Libre de Bruxelles Antonio Sanso , Ethereum Foundation and Ruhr Universität DOI: 10.1007/978-3-030-92062-3_6 Search ePrint Search Google ASIACRYPT 2021 We cryptanalyse the SIDH-based oblivious pseudorandom function from supersingular isogenies proposed at Asiacrypt'20 by Boneh, Kogan and Woo. To this end, we give an attack on an assumption, the auxiliary one-more assumption, that was introduced by Boneh et al. and we show that this leads to an attack on the oblivious PRF itself. The attack breaks the pseudorandomness as it allows adversaries to evaluate the OPRF without further interactions with the server after some initial OPRF evaluations and some offline computations. More specifically, we first propose a polynomial-time attack. Then, we argue it is easy to change the OPRF protocol to include some countermeasures, and present a second subexponential attack that succeeds in the presence of said countermeasures. Both attacks break the security parameters suggested by Boneh et al. Furthermore, we provide a proof of concept implementation as well as some timings of our attack. Finally, we examine the generation of one of the OPRF parameters and argue that a trusted third party is needed to guarantee provable security.
BibTeX
@inproceedings{asiacrypt-2021-31422,
title={Cryptanalysis of an oblivious PRF from supersingular isogenies},
publisher={Springer-Verlag},
doi={10.1007/978-3-030-92062-3_6},
author={Andrea Basso and Péter Kutas and Simon-Philipp Merz and Christophe Petit and Antonio Sanso},
year=2021
}