# 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
```