Code demonstrating modulo bias

modulo_bias.py

# Code based on excellent article:
# https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
# by Yolan Romailler at Kudelski Security

import pandas
import os

# modulo bias
values = []
while len(values) <= 1000000:
    x = int.from_bytes(os.urandom(1), byteorder='little')
    values.append(x % 107)
s = pandas.DataFrame({'value':values})
pandas.DataFrame.plot(s).hist(bins=107).get_figure().savefig('modulo-bias.pdf')

# rejection sampling
values = []
while len(values) <= 1000000:
    x = int.from_bytes(os.urandom(1), byteorder='little')
    if x < 107: values.append(x % 107)
s = pandas.DataFrame({'value':values})
pandas.DataFrame.plot(s).hist(bins=107).get_figure().savefig('rejection-sampling.pdf')

# using large random number (32b)
values = []
while len(values) <= 1000000:
    x = int.from_bytes(os.urandom(32), byteorder='little')
    values.append(x % 107)
s = pandas.DataFrame({'value':values})
pandas.DataFrame.plot(s).hist(bins=107).get_figure().savefig('large-random.pdf')