[Resource Topic] 2022/153: Faulty isogenies: a new kind of leakage

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Faulty isogenies: a new kind of leakage

Authors: Gora Adj, Jesús-Javier Chi-Domínguez, Víctor Mateu, Francisco Rodríguez-Henríquez


In SIDH and SIKE protocols, public keys are defined over quadratic extensions of prime fields. We present in this work a projective invariant property characterizing affine Montgomery curves defined over prime fields. We then force a secret 3-isogeny chain to repeatedly pass through a curve defined over a prime field in order to exploit the new property and inject zeros in the A-coefficient of an intermediate curve to successfully recover the isogeny chain one step at a time. Our results introduce a new kind of fault attacks applicable to SIDH and SIKE.

ePrint: https://eprint.iacr.org/2022/153

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