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Basic arithmetic operations for points on elliptic curves.

Project description

PyECCArithmetic

This package provides basic arithmethic point operations on elliptic curves. The following operations for points are available:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Order of point (for fair points)
  • Inversion of a point
  • Is the point on the curve?

The following curves are already implemented:

  • secp224r1
  • secp256r1
  • secp384r1
  • secp521r1
  • brainpoolP160r1
  • brainpoolP192r1
  • brainpoolP224r1
  • brainpoolP256r1
  • brainpoolP320r1
  • brainpoolP384r1
  • brainpoolP512r1

It is also possible to define your own curve.

Installation

pip install PyECCArithmetic

Addition

from PyECCArithmetic import *

p = Point(x_1, y_1, curve=Curve.secp256r1())
q = Point(x_2, y_2, curve=Curve.secp256r1())

z = p + q # z is a new point

Subtraction

from PyECCArithmetic import *

p = Point(x_1, y_1) # curve defaults to Curve.secp256r1()
q = Point(x_2, y_2)

z = p - q # z = p + (-q), z is a new point

Multiplication

Multiplication is realised with the double and add algorithm.

from PyECCArithmetic import *

p = Point(x_1, y_1) # curve defaults to Curve.secp256r1()

z = p * 3 # z is a new point

Division

from PyECCArithmetic import *

p = Point(x_1, y_1) # curve defaults to Curve.secp256r1()
q = Point(x_2, y_2)

z = p / q # z is int, such that z * q == p

Order calculation

from PyECCArithmetic import *

p = Point(x_1, y_1) # curve defaults to Curve.secp256r1()
order = p.calcOrder(timeout=5) # tries to calculate the order for maximal timeout seconds 

Custom curve definition

from PyECCArithmetic import *

# Only curves defined as Weierstrass equation are supported
# y^2 = x^3 + a * x + b mod p
c = Curve(a, b, p, name='optional')

Is the point on the curve?

from PyECCArithmetic import *

onCurve = Point(1,1).isOnCurve # true or false 

Project details


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