Order of randomly generated elliptic curve
I was computing order of random elliptic curves over prime field with out any problem. But when it comes to computing order of elliptic curves over binary field(characteristic 2 field), it computes well for small values of a and b of the elliptic curve. The problem comes when a and b parameters are large, specifically for 163 bit elliptic curve parameters. I can generate random point of the elliptic curve of 163 bits. However, when I compute its order, it displays exhaust memory and then it exits and some times Jim dead message is displayed.
I could not understand the problem. Could you say something for me regarding this problem? Thank you in advance.
Can you post a sequence of commands that exhibits the problem?
Example: b = 0x423d0900aeb5645491fee539c297946cbc6a4f1f5 Z.<x>=GF(2)[] K.=GF(2^163, 'a', modulus = x^163 + x^7 + x^6 + x^3 + 1) bb = Z(b.digits(2)) E = EllipticCurve(K,[1, 1, 0, 0, bb]) print E.order() this is sample problem that I could not compute its order Volker Braun