Redes de Telecomunicaciones y Laboratorio: Statistical test homework

Statistical test

Hi, in this homework i made a statistical test to my keys generated in the past homework, this is the link to my past homework (http://triana-integrador-cripto.blogspot.mx/2012/08/one-time-pad.html).

Ok, this is an example of 10 keys generated in mi program.

A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities.

Any method to generate random numbers must satisfy next conditions:

- Uniformly distributed
- Without constant repetition in a specified length (often not repeatable)

- Numbers must be independent of each other

- The series should be reproducible
- Numbers must be generated quickly

Well, there are many ways or methods to determine if a sequence of number are random.

I will use the method called: Media Test (Prueba de medias)

Media Test

Ok, media test method consists in verify that generated numbers have a statics media between upper and lower limits.

The 3 important elements to work with media test are the next:

* R = Is the summation of all numbers in the test, multiplied by (1/ total of numbers)
This number will be compared whit the lower and upper limits. If the R value is in the range of the limits, the numbers are random, if R is out of range with the limits, the numbers are not random.
R is calculated:

* Lower limit = Is the lowest limit to compare with the "r"

Lower limit is calculated:

Za = Z value of alfa (not acceptance level). You must use the normal distribution table
* Upper limit = Is the highest limit to compare with the "r"
Upper limit is calculated:

We are going to set an alfa, alfa value is the number of error probabilities. Assuming we want a 95 percent of acceptance level, alfa will be 5 percent of not acceptance, so alfa = 0.05.

I'll create the keys like in the one time pad homework, like this:

Then i created a code to count all 0 and 1 in the text file, and the total of numbers.
zAlfa = 0.5199, because alfa = 0.05, here is the table were i got "z" value: http://www.tuveras.com/estadistica/normal/tabla.htm

And finally with all the number added, i calculated the value of "r". And too calculated the values of lower and upper limits.

Like this:

This is the entire code (if you want to copy it):

	#!/usr/bin/python
	#Carlos Triana

	import random
	import math
	from numpy import *

	def createKeys():
	file1 = open('keys1.txt', 'w')#Creating file1
	i = 0
	j = 0
	while i<10:
	while j<7:
	number = random.randint(0,2)
	file1.write(str(number))#Filling file texts with random numbers
	j = j +1
	file1.write('\n') #To separate keys
	j = 0
	i = i + 1
	file1.close()
	mediaTest()

	def mediaTest():
	file1 = open('keys1.txt', 'r')#Reading key
	x = 0
	r = 0.0
	zero = 0.0 #To count the total of zero
	one = 1.0 #To count the total of one
	upperLimit = 0.0 #Upper limit value
	lowerLimit = 0.0 #Lower limit value
	zAlfa = 0.5199 #Value of Z whit alfa = 0.05
	for i in file1.xreadlines(): #To read each line of numbers
	size = len(i)
	while x < size:
	if i[x] == "0":
	zero = zero + 1.0 #If number = 0, increase counter(zero)
	elif i[x] == "1": #If number = 1, increase counter(one)
	one = one + 1.0
	x = x + 1
	x = 0
	file1.close()
	one = one - 1.0
	total = 0.0
	total = zero + one #Total of numbers
	r = (1/total)*(one) #'r' is the number to compare whit limits(upper,lower)
	lowerLimit = (0.5) - ((zAlfa/2)(1/math.sqrt(12(total)))) #Calculating lowerLimit
	upperLimit = (0.5) + ((zAlfa/2)(1/math.sqrt(12(total)))) #Calculating upperLimit
	if (r >= lowerLimit and r <= upperLimit):
	print "\nGenerated numbers are random :)\n"
	#If 'r' is between lowerLimit and upperLimim, numbers are random
	else:
	print "\nGenerated numbers are not random at all :(\n"
	#If 'r' is out of the limits, numbers are not random
	print "zero = " + str(zero) #Printing total of 0 in the txt
	print "one = " + str(one) #Printing total of 1 in the txt
	print "total = " + str(total) #Printing total of numbers
	print "r = " + str(r) #Printing R
	print "lowerLimit = " + str(lowerLimit) #Printing Lower and upper limits
	print "upperLimit = " + str(upperLimit)
	print
	def main():
	createKeys()
	main()