Efficient supersingularity testing over $\mathbb{F}_p$ and CSIDH key validation

We introduce an efficient deterministic algorithm for testing supersingularity of elliptic curves over $\mathbb{F}_p$, optimized for small-characteristic fields relevant to CSIDH.

• Our method improves the runtime and reliability of public-key validation in CSIDH.
• We compare our approach with classical $j$-invariant and point-counting techniques.
• The resulting implementation offers significant speedups with provable correctness.