Arithm

A small arithmetic toolbox.
Built mostly for testing out various scalar multiplication algorithms (see ./ecc/mults.py) without having to use Sage.

Contains abstractions for Field (and binary field) arithmetic, with support for Weierstrass curves and ed25519.

Intended usage

This library is only intended for testing and performance measurement purposes. Some of the example scalar multiplications include side-channel countermeasures that might be patented, so are not fit for use in a commercial product without paying license fees to the rightful owner.

Usage examples

Binary Field

Creating a binary field requires providing an irreducible polynomial of degree matching the size of the given binary field.

from arithm.binary_field import BinaryField

BinaryField(8, 0x11b)

defines the AES GF(2^8) field, 0x11b being the binary representation of X^8 + X^4 + X^3 + X + 1

BinaryField(6, 0x7f)

defines GF(2^6) defined by X^6 + X^5 + X^4 + X^3 + X^2 + X + 1

Field

from arithm.field import Field

Field(10007)

a = F(57)