Smoothness of Shortest Isogenies to Frobenius Conjugates
Proof makes Wesolowski's subexponential attack on the supersingular endomorphism ring problem unconditional.
The paper studies a uniformly random supersingular elliptic curve and the minimum degree of an isogeny from that curve to its Frobenius conjugate. It proves that this degree is smooth. The result removes a condition from Wesolowski's p^(1/3+o(1)) attack, making the attack on the supersingular endomorphism ring problem unconditional.
- Proves smoothness of the shortest isogeny degree to the Frobenius conjugate.
- Applies to a uniform supersingular curve over the algebraic closure of F_p.
- Makes Wesolowski's p^(1/3+o(1)) endomorphism-ring attack unconditional.
From the original article
1 min read at arxiv.orgLet $E$ be chosen uniformly from the geometric isomorphism classes of supersingular elliptic curves over $\overline{\mathbb{F}}_p$ and $δ_E$ be the minimum degree of isogenies from $E$ to its Frobenius conjugate $E^{(p)}$. We prove the smoothness of $δ_E$ and hence affirm Wesolowski's $p^{1/3+o(1)}$ attack on the supersingular endomorphism ring problem is unconditional.
By Yi Ouyang · arxiv.org
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