Basic arithmetic operations for points on elliptic curves.

# PyECCArithmetic

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

• 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
``````

```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

This version 1.1.0 1.0.2 1.0.1 1.0.0