Supersingularity and Superspeciality Verification of Abelian Surfaces
Researchers give an O(log p) Monte Carlo test for supersingular abelian surfaces over finite fields.
The paper studies how to verify supersingular abelian surfaces, objects used in isogeny-based cryptography. It gives a Monte Carlo algorithm that tests an abelian surface over a prime field in O(log p) time with negligible failure probability, and a conclusive test when the order is smooth. It also provides algorithms for minimal or maximal abelian varieties and for superspecial Jacobians of any dimension.
- Monte Carlo supersingularity test runs in O(log p) with negligible error.
- A conclusive algorithm applies when the group order is smooth.
- Also verifies minimal or maximal abelian varieties of any dimension.
- Checks whether a Jacobian of any dimension is superspecial.
From the original article
1 min read at arxiv.orgSupersingular abelian surfaces are essential in isogeny-based cryptography. Despite this, we have no efficient algorithm to verify if a given abelian surface is supersingular.
By Maria Corte-Real Santos · arxiv.org
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