Modular arithmetic in Python
Project description
Description
Modular arithmetic is arithmetic for integers, where numbers wrap around when reaching a given value called modulus. For example 6 ≡ 1 (mod 5). Modular arithmetic has several practical applications including: music, banking, book publishing, cryptography… and of course math.
The purpose of this package is to simplify the use of modular arithmetic in Python3.
Usage
This package provides Mod integers that compute arithmetic operations like + - * // ** with a modulus:
from mod import Mod
# Funny math here
x = Mod(5, 7) # x ≡ 5 (mod 7)
(x + 2) == 0 # True: 5 + 2 ≡ 7 ≡ 0 (mod 7)
(x + 7) == x # True: 5 + 7 ≡ 12 ≡ 5 (mod 7)
(x**3) == (x + 1) # True: 5³ ≡ 125 ≡ 6 (mod 7)
(1 // x) == 3 # True: 5 × 3 ≡ 15 ≡ 1 (mod 7) ⇒ 5⁻¹ ≡ 3 (mod 7)
A naive implementation of RSA encryption algorithm using mod package:
from mod import Mod
# My RSA keys
public_key = Mod(3, 61423)
private_key = Mod(40619, 61423)
# My very secret message
top_secret_message = 666
# RSA encryption
encrypted = top_secret_message**public_key
# RSA decryption
decrypted = encrypted**private_key
# My secret message have been correctly encrypted and decrypted :-)
assert decrypted == top_secret_message
Package documentation: mod.Mod
Install
Run the following command to install mod package
pip3 install mod
Links
Package documentation located at http://mod.readthedocs.io/en/latest/
Python package available at https://pypi.python.org/pypi/mod
Source code repository: https://github.com/yoeo/mod
Indices
mod — Copyright (c) 2020 Y. SOMDA, MIT License
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