Improved Classical Cryptanalysis of SIKE in Practice

Craig Costello; Patrick Longa; Michael Naehrig; Joost Renes; Fernando Virdia

Paper 2019/298 Original: eprint.iacr.org/2019/298 ↗

Improved Classical Cryptanalysis of SIKE in Practice

Craig Costello

Patrick Longa

Michael Naehrig

Joost Renes

Fernando Virdia

Abstract

The main contribution of this work is an optimized implementation of the vanOorschot-Wiener (vOW) parallel collision finding algorithm. As is typical for cryptanalysis against conjectured hard problems (e. g. factoring or discrete logarithms), challenges can arise in the implementation that are not captured in the theory, making the performance of the algorithm in practice a crucial element of estimating security. We present a number of novel improvements, both to generic instantiations of the vOW algorithm finding collisions in arbitrary functions, and to its instantiation in the context of the supersingular isogeny key encapsulation (SIKE) protocol, that culminate in an improved classical cryptanalysis of the computational supersingular isogeny (CSSI) problem. In particular, we present a scalable implementation that can be applied to the Round-2 parameter sets of SIKE that can be used to give confidence in their security levels.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2020-06-03: last updated; 2019-03-20: published
Short URL: https://ia.cr/2019/298
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2019/298,
      author = {Craig Costello and Patrick Longa and Michael Naehrig and Joost Renes and Fernando Virdia},
      title = {Improved Classical Cryptanalysis of SIKE in Practice},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/298},
      year = {2019},
      url = {https://eprint.iacr.org/2019/298}
}