eprint.iacr.orgpaperSmoothness of Shortest Isogenies to Frobenius Conjugatess
Paper by Yi Ouyang, Wei Wei and Zheng Xu on the minimum degree of an isogeny from a supersingular elliptic curve E to its Frobenius conjugate E^(p). It bounds the probability that this degree is smooth, which makes Wesolowski's p^(1/3+o(1)) attack on the supersingular endomorphism ring problem unconditional. It also gives a uniform asymptotic formula, with Dirichlet L-values in the main term, for the probability that a connection isogeny of degree n exists.
TL;DR Proves Wesolowski's p^(1/3) attack on the supersingular endomorphism ring problem works unconditionally by bounding smoothness of shortest Frobenius-conjugate isogenies.
Organisations named here
- Wei Wei
- Yi Ouyang
- Zheng Xu
Concepts named here
- Connection isogeny existence probability
- Isogeny to Frobenius conjugate
- Smoothness of isogeny degree
- Supersingular endomorphism ring problem
- Wesolowski
Related in other
eprint.iacr.orgpaperRerandomizable Garbling for Arithmetic Circuits
aseemshrey.inarticle