Find Subgroup with Point Addition

EC Cryptography Tutorials - Herong's Tutorial Examples

∟Find Subgroup with Point Addition

This section provides a tutorial example on how to find the subgroup of a given point on an elliptic curve using a loop of point additions with tinyec Python library.

Once you have elliptic curve created with tinyec Python library, you can find the subgroup of a given point on the curve with a loop of point additions:

>>> import tinyec.ec as ec

>>> s = ec.SubGroup(p=97,g=(0,0),n=1,h=1)

>>> c = ec.Curve(a=2,b=3,field=s,name='p97a2b3')

>>> p = ec.Point(curve=c,x=3,y=6)

>>> print(p)
(3, 6) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)

>>> z = ec.Inf(c)   # represents the infinite point on the curve

>>> r = p
>>> for i in range(0,97):
...     print(r)
...     if (r == z):
...        break
...     r = r + p   # point addition operation
... ^Z

(3, 6) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)
(80, 10) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)
(80, 87) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)
(3, 91) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)
Inf on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)