Random number generator with eXtra Entropy.

This little module is a simple and reliable way to improve randomness of any random or pseudo-random number generator.

We never being 100% sure in real randomness and cryptographic quality of any externally-provided RNG, and this is a good idea to be able to add some addition entropy to by own hands. This module provides following features:

1. Easy way to combine unrestricted number of randomness sources (CompoundRandom class).
2. Tool to transform several additional bytes of extra entropy into complete random-like mess (HashRandom class).

Why we can be sure that combining independent random sources can only improve quality of RNG

Imagine the situation. We have two independent streams of bits, x and y, and can predict upcoming bits with probabilities respectively px and py. Each probability lay in [0 .. 1] interval, but really if we have prediction tool that does not confuse us deliberately, probabilities lay in [0.5 .. 1] interval. After x XOR y operation we have r stream. Prediction probability pr is a sum of probabilities of two right and two wrong predictions:

pr = px*py + (1-px)*(1-py) = 2*px*py - px - py + 1

Let`s find the condition for situation when pr exceeds px.

2*px*py - px - py + 1 > px

2*px*py - 2*px > py - 1

2*px*(py - 1) > py - 1

py is less than 1, so we convert (py - 1) into (1 - py).

2*px*(1 - py) < 1 - py

After cutting (1 - py) we have:

2*px < 1

px < 0.5

Therefore, pr can exceed px only if pr predictor deliberately makes wrong predictions, so uncertainity about x XOR y cannot be less than maximal uncertainity about the x and y.

How to embed

There are two ways to embed this functionality into your project:

1. Get this module by pip install random_xe and then import into your module by import random_xe.
2. Directly download random_xe.py file and adopt it into your project.

How to use

Import this module:

>>> import random_xe

Create and try HashRandom PRNG initialized with 'Hello world':

>>> import random_xe
>>> myrandom1 = random_xe.HashRandom('Hello world')
>>> myrandom1.randint(100, 200)
156
>>> myrandom1.gauss(20, 10)
8.243867125227318

myrandom1 uses SHA-256 hashing function (option by default).

Let`s try to combine this PRNG with another HashRandom based on SHA3-512 and initialized from user input:

>>> from hashlib import sha3_512
>>> myrandom2 = random_xe.CompoundRandom(myrandom1, random_xe.HashRandom(input('Type somethig: '), sha3_512))
Type somethig: ldjggndjKfuT830
>>> myrandom2.getrandbits(128)
171962833922528548054430533031273437533

ALWAYS combine additional entropy with SystemRandom source:

>>> from getpass import getpass
>>> from time import perf_counter
>>> # Three sources:
>>> # - SystemRandom;
>>> # - user input;
>>> # - timing.
>>> def super_myrandom():
    t_start = perf_counter()
    return random_xe.CompoundRandom(random_xe.SystemRandom(),
        random_xe.HashRandom(
            getpass('Type somethig:'), sha3_512),
        random_xe.HashRandom(perf_counter() - t_start))

>>> myrandom3 = super_myrandom()
>>> myrandom3.getrandbits(128)
214560115455406687033892278367232976155

Detailed description and discussion (in Russian): https://habr.com/post/423093/