Here is the problem Adam. You have a prime l which is about 2^165. You construct random curves over the field GF(l) and count the number of points n_1 on them. This is possible using Sage's use of an efficient SEA algorithm. When the number n_1 is prime, you then ask for all the points of order n_1 on the curve using the division_points () function. This is crazy! For a start, all the points on the curve will be returned; that is a list of points far too big to store. But you will never get there anyway since the division_points() function creates the division polynomial which has degree (n_1^2-1)/2, i.e. about 2^330.
It's hard to make a constructive suggestion without knowing what it is you are trying to do. If you write that down clearly, I'll try to help. I found that the abelian_group() function works fine for curves of this size (which makes me pleased, since I wrote it), whether or not the group is cyclic (which is usually is), so it may be that you should first find the generator(s) of the group and their orders, and work with that. John On Jun 23, 2:17 pm, adam mohamed <[email protected]> wrote: > Hi All, > > I solve the problem with the memory, thanks to William. But, now when I > impose some strict conditions so that I have to toss say 100 times in order > to hope for some curves to pop up, I am getting different kind of errors. I > have attached the code and the error message I got hereby. Maybe my code is > too naive that why I am having this problem. > > What I don't get is why the code seems to do well when the conditions are > less restrictive but once I change a little bit, them Sage is not happy! > Maybe one has to implement Reinier algorithms in order to avoid these kind > of problems. Is this doable in Sage now? > > Best wishes, > > Adam > > On Tue, Jun 23, 2009 at 1:14 PM, John Cremona <[email protected]>wrote: > > > > > On Jun 22, 7:59 pm, adam mohamed <[email protected]> wrote: > > > Hi, > > > > Thanks for the very quick response. I will try that tomorrow. Now I > > > understand the problem that we met when running the same code in a linux > > > machine. > > > I am doing this search for cryptographic applications, so I am dealing > > with > > > primes from the size of 170 bit Length. > > > I would like the 2-sylow of E( F_p) to be Z/4Z and #E( F_p) = 4*L with > > > L prime. > > > > Reinier Broker did his PhD about EC with prescribed order and we will > > would > > > like to find out if his algorithms have been implemented in Sage? > > > Hello Adam, > > > No, as far as I know Sage has nothing implemented for finding curves > > with prescribed order or structure. > > > John > > > > Regards, > > > > Adam > > > > On Mon, Jun 22, 2009 at 6:31 PM, William Stein <[email protected]> wrote: > > > > > On Mon, Jun 22, 2009 at 5:35 PM, harivola<[email protected] > > > > > wrote: > > > > > > Hi all, > > > > > > I am running a small script on a windows xp machine and some time I > > > > > am getting this error message: > > > > > /usr/local/sage/local/bin/sage-sage: line 348: 19954 Killed > > > > > python "$@" > > > > > You're probably running out of memory (=RAM). Try editing the file > > > > sage_vmx.vmx and increase the amount of RAM that is made available to > > > > the vmware machine running Sage. The default amount is very small. > > > > > > I don't get the meaning of that. By the way, does someone know an > > > > > efficient way in Sage to search for EC with prescribed order ( I need > > > > > curves over a big prime field with rational points of order 4 and > > > > > cofactor 4 ). Thanks. > > > > > Be way more precise. How big is "big prime field"? Do you want > > > > #E(F_p) = 4*n with n odd? Do you require that #E(E_p)[2] = 4 too? > > > > > William > > > > > > Best wishes > > > > > -- > > > > William Stein > > > > Associate Professor of Mathematics > > > > University of Washington > > > >http://wstein.org > > > > full_output.txt > 42KViewDownload > > test_ell.sage > 2KViewDownload --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
