mod – modular arithmetic in Python¶

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

Note

Mod is based on integer modulo operation %, not math.fmod
the result of an operation between a Mod and an int is a Mod
the result of an operation between a Mod and a float is a float

Package documentation: `mod.Mod`¶

class mod.Mod(value, modulus)¶

Integer number that automatically adds a modulus to arithmetic operations.

The floor division // implements the inverse of a multiplication with a modulus. Therefore, it should be used with care to avoid errors.

>>> number = Mod(2, 3)
>>> number
(2 % 3)
>>> quintuple = 5 * number
>>> quintuple // 5
(2 % 3)
>>>

Parameters:	value (int) – Mod number value modulus (int) – modulus associated with the value
Raises:	ValueError – one of the parameters is not a number or modulus == 0

copy(modulus=None)¶

Copy the Mod number

Parameters:	modulus (int) – modulus of the new Mod number
Return type:	Mod

inverse¶

Modular inverse of the number.

y is the inverse of x with the modulus n when:

\[y × x ≡ 1 (mod. n)\]

Return type:	Mod

modulus¶

Modulus value

Return type:	int

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