(2026-02) Tripling on Hessian curves via isogeny decomposition
2026-02-20
We provide a new interpretation of the arithmetic on Hessian Kummer lines using level-3 theta structures. This allows us to break the record for tripling on elliptic curves and their Kummer lines, requiring only 4 multiplications and 4 squarings per tripling for well-chosen curve parameters.