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Elliptic curves

asked 2013-04-02 11:30:13 -0600

updated 2015-01-13 14:01:07 -0600

FrédéricC gravatar image
F.<x> = GF(2)[]

K.<a> = GF(2**163, name='a', modulus=x^163 + x^7 + x^6 + x^3 +1 )

b = 0x000000020A601907B8C953CA1481EB10512F78744A3205FD

b1 = F(b.digits(2))

xx1 = 0x00000003F0EBA16286A2D57EA0991168D4994637E8343E36

yy1 = 0x00000000D51FBC6C71A0094FA2CDD545B11C5C0C797324F1

xx2 = F(xx1.digits(2))

yy2 = F(yy1.digits(2))

E = EllipticCurve(K,[1,1,0,0,b1])

punto = E([xx2,yy2])

punto.order()

When i try to find the order I got this error!

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_17.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cHVudG8ub3JkZXIoKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>

  File "/tmp/tmpLBskY6/___code___.py", line 2, in <module>
    exec compile(u'punto.order()
  File "", line 1, in <module>

  File "/sagenb/sage_install/sage-5.4-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_point.py", line 3295, in order
    N = generic.order_from_bounds(self,bounds,operation='+')
  File "/sagenb/sage_install/sage-5.4-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/groups/generic.py", line 1405, in order_from_bounds
m = d * bsgs(Q, identity, bounds, operation=operation)
File "/sagenb/sage_install/sage-5.4-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/groups/generic.py", line 475, in bsgs
for i0 in misc.srange(m):
  File "/sagenb/sage_install/sage-5.4-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/misc.py", line 1185, in srange
return ZZ.range(start, end, step)
  File "integer_ring.pyx", line 456, in sage.rings.integer_ring.IntegerRing_class.range (sage/rings/integer_ring.c:6534)
RuntimeError: Segmentation fault
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Comments

1

Running this code consumed all the RAM in my computer. Perhaps this has something to do with the error. What is your question?

fidbc gravatar imagefidbc ( 2013-04-02 14:36:59 -0600 )edit

2 answers

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answered 2013-12-15 00:50:54 -0600

John Cremona gravatar image

Elliptic curves over very large binary fields are not well supported in Sage, so the code is here reverting to generic algorithms, which cannot cope with such large examples.

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answered 2013-04-02 19:46:02 -0600

How to fix this error or how to make I Get the order!

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Asked: 2013-04-02 11:30:13 -0600

Seen: 130 times

Last updated: Dec 15 '13