Perform Point Addition with tinyec

EC Cryptography Tutorials - Herong's Tutorial Examples

∟Perform Point Addition with tinyec

This section provides a tutorial example on how to perform the point addition operation on a given elliptic curve with tinyec Python library.

If you want to perform point addition operation on an elliptic curve with tinyec Python library, you must do it in three steps.

1. Create the elliptic curve. For example:

>>> 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')

2. Create ec.Point objects with their x and y coordinates an ec.Curve object. For example:

>>> p = ec.Point(curve=c,x=3,y=6)
>>> q = ec.Point(curve=c,x=80,y=10)

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

>>> print(q)
(80, 10) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)

3. Perform the point addition with the "+" operator. For example:

>>> r = p + q

>>> print(r)
(80, 87) on "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)

Ok. The point addition is performed correctly, you can verify it manually.

If you create an ec.Point object with an invalid curve point, tinyec will tell you the point is off the curve:

>>> t = ec.Point(curve=c,x=1,y=1)

>>> print(t)
(1, 1) off "p97a2b3" => y^2 = x^3 + 2x + 3 (mod 97)

Or you can verify if a given point is on or off the curve with the ec.curve.on_curve() method:

>>> c.on_curve(1,1)
False

>>> c.on_curve(3,6)
True

Table of Contents

About This Book

Geometric Introduction to Elliptic Curves

Algebraic Introduction to Elliptic Curves

Abelian Group and Elliptic Curves

Discrete Logarithm Problem (DLP)

Finite Fields

Generators and Cyclic Subgroups

Reduced Elliptic Curve Groups

Elliptic Curve Subgroups

►tinyec - Python Library for ECC

What Is tinyec

Download and Install tinyec

Build New Curves with tinyec

►Perform Point Addition with tinyec

Find Subgroup with Point Addition

Set Subgroup Order to Higher Value

EC (Elliptic Curve) Key Pair

ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

ECDSA (Elliptic Curve Digital Signature Algorithm)

ECES (Elliptic Curve Encryption Scheme)

EC Cryptography in Java

Standard Elliptic Curves

Terminology

References

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