I have been reading various articles about random numbers and their generators. There are usually 3 important conclusions that I draw from them:
So, with the latter-most of these observations in mind, how would we be able to
I'm tempted to say that so long as you generate a sufficiently large enough sample set 1,000,000+, you should see more or less a uniform dispersion of (pseudo)random numbers occur. However, I'm sure some Maths genius has a way of discrediting this, because surely the by laws of probability you could get a run of one number just as likely as any other sequence.
From what I have read, if you really need random numbers its best to try and reuse what cryptographic libraries use. The field of Cryptography is obviously complex and relies on random numbers for key generation. From the section in OWASP's guide titled "Reversible Authentication Tokens" it says this...
The only way to generate secure authentication tokens is to ensure there is no way to predict their sequence. In other words: true random numbers.
It could be argued that computers can not generate true random numbers, but using new techniques such as reading mouse movements and key strokes to improve entropy has significantly increased the randomness of random number generators. It is critical that you do not try to implement this on your own; use of existing, proven implementations is highly desirable.
Most operating systems include functions to generate random numbers that can be called from almost any programming language.
My take is that unless you're coding Cryptographic libraries yourself, put trust in those that are (e.g. use Java Cryptography Extension) so you don't have to proove it yourself.