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)
- 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
- 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):
* 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):
These are some screen shots of my program running:
TEST:
Generated keys Results
Bibliography:
If you have any doubt you can leave it in comments.
Sorry for my bad english. Thank you!
