Frequency (Monobits) Test

Description:

The focus of the test is the proportion of zeroes and ones for the entire sequence. The purpose of this test is to determine whether that number of ones and zeros in a sequence are approximately the same as would be expected for a truly random sequence. The test assesses the closeness of the fraction of ones to ½, that is, the number of ones and zeroes in a sequence should be about the same.

Process

1. Program convert zeros to -1, and add them all into a single variable, which we will call Sn.


2. We perform the following statistics:

3. Calculate  P - value as follows:

 
Program:

	#!/usr/bin/python
	import random
	import math
	def createKeys():
	archivo = open('keys.txt', 'w')
	i = 0
	j = 0
	while i<100:
	while j<10:
	keys = random.randint(0,1)
	archivo.write(str(keys))
	j = j +1
	archivo.write('\n')
	j = 0
	i = i + 1
	archivo.close()
	TestMonobit()
	def TestMonobit():
	archivo = open('keys.txt', 'r')
	sn = 0
	x = 0
	n = 10
	for i in archivo.xreadlines():
	tamano = len(i)
	print i
	while x < tamano:
	if i[x] == "0":
	sn = sn + 1
	elif i[x] == "1":
	sn = sn - 1
	x = x + 1
	archivo.close()
	sobs = math.fabs(sn)/math.sqrt(n)
	p_value = math.erfc(sobs/math.sqrt(2))
	print p_value
	if(p_value >= 0.01):
	print "\nLos numeros son aleatorios\n"
	else:
	print "\nLos numeros no son aleatorios\n"
	def main():
	createKeys()
	main()

view raw evaluar.py hosted with ❤ by GitHub

Result

Bibliography:
http://www.random.org/statistics/frequency-monobit/
http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html