Reposted by Maria Corte-Real Santos
New paper! Given a Jacobian over Fp, can you easily check supersingularity?
If you've worked with these objects in magma, you know how annoying this question can be. Turns out it's very easy: we give efficient probabilistic tests, and conclusive if you need to be absolutely sure.
ia.cr/2026/2259
eprint.iacr.org
Supersingularity and Superspeciality Verification of Abelian Surfaces
Supersingular abelian surfaces are essential in isogeny-based cryptography. Despite this, we have no efficient algorithm to verify if a given abelian surface is supersingular. In this work, we initiat...
![Abstract. We introduce WayFinder, a framework for generalizing the Delfs-Galbraith and SuperSolver algorithms for the supersingular isogeny problem. Our framework extends the search for elliptic curves with an orientation by an order containing $\mathbb{Z}[\ell \sqrt{-p}]$ to more general orders, and we derive a cost model for such generalisations. Our cost model not only works in a more general context, but also provides more accurate predictions when applied to SuperSolver. We instantiate WayFinder for orders containing $\mathbb{Z}[\ell_1\sqrt{-\ell_2p}]$ where ℓ_(i) are 1 or primes such that the modular curve X₀(ℓ₂) has genus 0. We then introduce a low-storage algorithm for computing an isogeny between two oriented supersingular elliptic curves, even when the curves are oriented by distinct orders. Together, these provide an algorithm that improves on the state of the art for solving the isogeny problem, and a cost model with potential applications to parameter selection in isogeny-based cryptography.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fwa55bujvdrwlwlwgqmmxmuf/bafkreidps3jwwz33rxdmp6w7ok6w462ioosoazxxabir2thhplfnfytz6m)
