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currently working on generation elliptic curve for ECDSA and met some problems:
An elliptic curve: y**2 = x**3 + ax + b (mod p)
Point on elliptic curve: G = (Gx, Gy)

  1. How to find a cardinality of Elliptic curve?
  2. How to find the order of point G on that elliptic curve?

-- As for 1.: the cardinality may be found with SEA (which fit nicely for large modules p). Is there any implementation for SEA within Python?
-- As for 2: any solution within Python?

P.S.
Sorry for my English and thank you.

Janne Karila
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ted
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1 Answers1

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This is related to this topic.

Sage is a powerful math package with a Python front-end. With Sage you will be able to use PARI/GP package

You have also some information in their FAQ about elliptic curves

Community
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Zeugma
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  • can it be used like `import sage` `EC.cardinality()` in python? – ted Apr 30 '12 at 08:27
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    You will be able to do so as per this [example](http://www.sagemath.org/doc/faq/faq-usage.html#how-do-i-import-sage-into-a-python-script) and [ec doc](http://www.sagemath.org/doc/reference/sage/schemes/elliptic_curves/ell_finite_field.html). Yet you need to run your script through the sage special version of Python interpreter as mentioned in the FAQ – Zeugma Apr 30 '12 at 08:56