2022.08.18 16:49:27 (1560277701054779398) from Daniel J. Bernstein, replying to "Damien Robert (@GondoPloum)" (1560189178591285248):
Can you lift this to a computation on ideal classes, so as to be able to quickly handle (e.g.) any given supersingular curve over F_p after curve-independent precomputation?
2022.08.17 22:58:35 (1560008210970460162) from "Damien Robert (@GondoPloum)", replying to "Damien Robert (@GondoPloum)" (1560008142439817216):
As I explain in this paper, this representation is mostly theoretical because to compute a decomposition of F I need to evaluate f on log N points (using a standard evaluation algorithm), living in extensions of degree O(log N). [11/13]
2022.08.17 22:59:02 (1560008323604385801) from "Damien Robert (@GondoPloum)", replying to "Damien Robert (@GondoPloum)" (1560008210970460162):
So unless I need to evaluate f on *lots* of points, this won't be useful. But notice that the decomposition of F only needs to be computed once, once computed it can be sent in polylog space so its a lot more compact than representing f by its kernel. [12/13]
2022.08.17 22:59:20 (1560008397776379905) from "Damien Robert (@GondoPloum)", replying to "Damien Robert (@GondoPloum)" (1560008323604385801):
So we could imagine some isogeny protocols making use of it. But my main goal was to give more applications of the theory of higher dimensional isogenies to algorithms on elliptic curves. [13/13]
2022.08.18 10:57:41 (1560189178591285248) from "Damien Robert (@GondoPloum)", replying to "Damien Robert (@GondoPloum)" (1560008397776379905):
Since it is not yet on eprint, here is a local link: http://www.normalesup.org/~robert/pro/publications/articles/polylog_isogenies.pdf