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

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

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
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