**EC Cryptography Tutorials - Herong's Tutorial Examples** - Version 1.00, by Dr. Herong Yang

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

Last update: 2019.

Table of Contents

Geometric Introduction to Elliptic Curves

Algebraic Introduction to Elliptic Curves

Abelian Group and Elliptic Curves

Discrete Logarithm Problem (DLP)

Generators and Cyclic Subgroups

►tinyec - Python Library for ECC

►Perform Point Addition with tinyec

Find Subgroup with Point Addition

Set Subgroup Order to Higher Value

ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

ECDSA (Elliptic Curve Digital Signature Algorithm)