Improved Classical Cryptanalysis of the Computational Supersingular Isogeny Problem [article]

Craig Costello, Patrick Longa, Michael Naehrig, Joost Renes, Fernando Virdia
2019 IACR Cryptology ePrint Archive  
The main contribution of this work is an optimized implementation of the van Oorschot-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
more » ... 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.
dblp:journals/iacr/CostelloLNRV19 fatcat:wf73vqxatndfrjyuiwcb444iwi