Jan-13-2024, 02:13 AM
Understanding the Formula to Qualify Random Numbers
“Best Possible Mean” minus Standard Deviation:
- Define “Best Possible Mean: Is the same as Mean, add all numbers in list and divide by number of items. I write it this way so it is understood that the best it can be is “Best Possible Mean”. Working with binary the “Best Possible Mean” is: 0 + 1 = (1 / 2) = 0.5.
- Define Standard Deviation: A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.
The closer to “Best Possible Mean” and RANDOM is what the goal is. Therefore “Best Possible Mean” minus Standard Deviation is a concrete base for random. It gives a definitive way of working with random numbers.
Now to deal with RANDOM with mathematics:
- It looks random. This means that it passes all the statistical tests of randomness that we can find.
- It is unpredictable. It must be computationally infeasible to predict what the next random bit will be, given complete knowledge of the algorithm or hardware generating the sequence and all of the previous bits in the stream.
- It cannot be reliably reproduced. If you run the sequence generator twice with the exact same input (at least as exact as humanly possible), you will get two completely unrelated random sequences.
The output of a generator satisfying these three properties will be good enough for a one-time pad, key generation, and any other cryptographic applications that require a truly random sequence generator.
I hope this makes things clearer.