|Bill Allombert on Sun, 17 Nov 2013 23:11:05 +0100|
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|Re: Elliptic curve arithmetic in the Montgomery representation|
On Sun, Nov 17, 2013 at 09:50:55PM +0000, Richard Heylen wrote: > I have some calculations I would like to do with points on an elliptic > curve over a ring without having the benefit of knowing the y > coordinate. I believe the best way of dealing with this problem is > using the Montgomery representation which is probably implemented in > pari at some level due to the presence of ECM factoring routines. In GP your best bet is to use elliptic curve in short Weierstrass form and use a formal Y Somethink like Y;X; \\ Very important! We want Y to have higher priority than X. E=ellinit([0,0,0,a,b]); P=ellmul(E,[X,Mod(Y,Y^2-(X^3+a*X+b))],3); lift(P) (of course neither a,b and X need to be formal). Cheers, Bill.