Timeline for An expression for the function $f_e$ that appears in the Weil Pairing

4 events

when toggle format	what		by	license	comment
Feb 18, 2013 at 8:05	answer	added	François Brunault		timeline score: 1
Feb 17, 2013 at 21:13	comment	added	user30035		Namely, any assertion of the form $P+Q=R$ is checked by drawing the line $L$ through $P$ and $Q$, which hits $E$ again at $S$, and then the line $M$ through $S$ and the origin hits the curve at $R$, and then $L/M$ has zeros at $P,Q$ and poles at $R$,origin. Now continue; at each stage you get a ratio of linear functions and you can multiply all of them together (the last one being the witness to $e_{N-1}+e=$origin) to get the function you want.
Feb 17, 2013 at 21:11	comment	added	user30035		If by "concrete" you mean the following: $p$ is an explicit given prime number $K$ is an explicit finite extension of $\mathbf{Q}_p$, $N$ is an explicit positive integer, and $E$ is an explicit elliptic curve in Weierstrass form whose coefficients I know explicitly, and I have an explicit point $e$ with explicit $x$ and $y$ coordinates -- if all this, then your proof that $e$ has order $N$ (which will perhaps be of the form "check $e+e=e_2$, $e_2+e=e_3$,...) can be translated into an explicit construction of $f$ [but the comment box is too small to explain the construction so hang on a second]
Feb 17, 2013 at 2:08	history	asked	George	CC BY-SA 3.0