We give a number of approaches which, to a newcomer, may seem like natural ways to attack the SIDH/SIKE protocol, and explain why each of these approaches seems to fail, at least with the specific setup and parameters of SIKE. Our aim is to save some time for others who are looking to assess the security of SIDH/SIKE. We include methods that fail to attack the pure isogeny problem, namely: looking at the Fp-subgraph, lifting to characteristic zero, and using Weil restrictions. We also include methods that fail to make use of the public 2-power and 3-power torsion points, namely: interpolation techniques, any purely group-theoretic approaches, and constructing an endomorphism à la Petit to exploit the auxiliary points, but with balanced parameters.
|Publication status||Published - 2019|
|Event||CFAIL 2019 - Columbia University, New York, United States|
Duration: 31 May 2019 → 2 Jun 2019
|Period||31/05/19 → 2/06/19|