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Communication Dans Un Congrès Année : 2022

An Effective Lower Bound on the Number of Orientable Supersingular Elliptic Curves

Résumé

In this article, we prove a generic lower bound on the number of O-orientable supersingular curves over F p 2 , i.e curves that admit an embedding of the quadratic order O inside their endomorphism ring. Prior to this work, the only known effective lower-bound is restricted to small discriminants. Our main result targets the case of fundamental discriminants and we derive a generic bound using the expansion properties of the supersingular isogeny graphs. Our work is motivated by isogeny-based cryptography and the increasing number of protocols based on O-oriented curves. In particular, our lower bound provides a complexity estimate for the brute-force attack against the new O-uber isogeny problem introduced by De Feo, Delpech de Saint Guilhem, Fouotsa, Kutas, Leroux, Petit, Silva and Wesolowski in their recent article on the SETA encryption scheme.
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Dates et versions

hal-03886746 , version 1 (06-12-2022)

Identifiants

  • HAL Id : hal-03886746 , version 1

Citer

Antonin Leroux. An Effective Lower Bound on the Number of Orientable Supersingular Elliptic Curves. SAC 2022 - Selected Areas in Cryptography, Aug 2022, Windsor, Canada. ⟨hal-03886746⟩
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