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2 years ago
gh-36285: add Rémy Oudompheng's implementation of the BMSS algorithm The BMSS algorithm computes (the kernel polynomial of) a *normalized* isogeny from its degree $\ell$ and its domain and codomain in time $\widetilde O(\ell)$. Currently Sage uses Stark's algorithm for the same task, which takes time in $\Omega(\ell^2)$. An implementation in Sage of the BMSS algorithm is available thanks to @remyoudompheng, and in this patch we add it to the Sage library (following Rémy's suggestion). Benchmark results for isogenies over a ~280-bit prime field (red is Stark, blue is BMSS; axes are degree $\ell$ and seconds taken): ![Benchmark results for {Stark, BMSS} algorithms](https://github.com/sag emath/sage/assets/84067835/2a9f47d3-f1f9-4bb1-b3f1-6539de2a7562) URL: https://github.com/sagemath/sage/pull/36285 Reported by: Lorenz Panny Reviewer(s): github-actions[bot], Kwankyu Lee, Lorenz Panny
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