Smoothness of Shortest Isogenies to Frobenius Conjugates

Name: Smoothness of Shortest Isogenies to Frobenius Conjugates
Uploaded: 2026-10-19T16:45:39.223666+00:00
Duration: 513 s
Description: The paper proves that $\delta_E$, the minimum degree of an isogeny from a supersingular elliptic curve $E$ to its Frobenius conjugate $E^{(p)}$, is smooth. This smoothness implies that Wesolowski's attack on the supersingular endomorphism ring problem, which has a complexity of $p^{1/3+o(1)}$, is unconditional and valid.

The paper proves that $\delta_E$, the minimum degree of an isogeny from a supersingular elliptic curve $E$ to its Frobenius conjugate $E^{(p)}$, is smooth. This smoothness implies that Wesolowski's attack on the supersingular endomorphism ring problem, which has a complexity of $p^{1/3+o(1)}$, is unconditional and valid.

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