Iftikhar Burhanuddin on Tue, 18 Jun 2002 12:14:22 -0700 (PDT)

 Re: Point multiplication on elliptic curves over Q_{p} (fwd)

```> Which version of GP, on which architecture ?  I cannot reproduce your problem
> with any of pari-2.2.3, 2.1.2, or 2.1.3 on either Solaris or Linux.

gp/pari calculator version 2.2.2 (alpha)
cygwin
windows 2000 professional
pentium III

Regards.

On Tue, 18 Jun 2002, Karim BELABAS wrote:

> On Fri, 14 Jun 2002, Iftikhar Burhanuddin wrote:
> > Say f is an elliptic curve over Q_{p} and P is a point on the curve,
> > e is the reduced elliptic curve,
> > nump are the number of points on e [nump = p+1-ellap(f,p)],
> > randno1 and randno2 are randomly generated integers.
> >
> > P1 = ellpow(f,P,nump);
> > P2 = ellpow(f,P1,nump);
> > P3 = ellpow(f,P,nump*nump);
> >
> > I would expect P2 and P3 to be equal but they are not. I can't figure out
> > why. Also...
>
> Which version of GP, on which architecture ?  I cannot reproduce your problem
> with any of pari-2.2.3, 2.1.2, or 2.1.3 on either Solaris or Linux.
>
>     Karim.
>
> P.S: The trimmed down version of your problem which I checked [ I always get
> the expected '1' in the end ]:
> {
>   f = [0, 0, 0, 127, 84, 0, 254, 336, -16129, -6096, -72576, -134144704,
> 3539605824/2096011, [-0.6591621847848914369629989104,
> 0.3295810923924457184814994552 - 11.28387659846507686555138306*I,
> 0.3295810923924457184814994552 + 11.28387659846507686555138306*I]~,
> 1.124876961763701162003259070, -0.5624384808818505810016295354 +
> 0.5404019960642208768091252385*I, -2.941144737565557494801181503 - 5.97757508
> E-29*I, 1.470572368782778747400590751 - 4.205787211666463317926236011*I,
> 0.6078857554637603730809302940];
>   P =  [27 + O(131^40), 3 + 95*131 + 111*131^2 + 97*131^3 + 109*131^4 +
> 15*131^5 + 114*131^6 + 123*131^7 + 82*131^8 + 2*131^9 + 12*131^10 + 22*131^11
> + 89*131^12 + 26*131^13 + 44*131^14 + 14*131^15 + 25*131^16 + 89*131^17 +
> 96*131^18 + 55*131^19 + 59*131^20 + 106*131^21 + 26*131^22 + 94*131^23 +
> 75*131^24 + 39*131^25 + 115*131^26 + 71*131^27 + 70*131^28 + 112*131^29 +
> 121*131^30 + 29*131^31 + 34*131^32 + 101*131^33 + 76*131^34 + 110*131^35 +
> 77*131^36 + 52*131^37 + 17*131^38 + 30*131^39 + O(131^40)];
> }
> P1 = ellpow(f, P , 150);
> P2 = ellpow(f, P1, 150);
> P2 == ellpow(f, P, 150*150)
>
> --
> Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
> Dép. de Mathematiques, Bat. 425  Fax: (+33) (0)1 69 15 60 19
> Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
> F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas
> --