When we talk about "random" numbers, we generally talk about two fundamental properties: Predictability and Bias. Both are closely related, but are subtly different. Predictability in reference to random numbers is the statistical problem of predicting the next value when knowing any number of previous values. Bias on the other hand is the statistical problem of predicting the next value when knowing the distribution of previous values.

He looks at how predictability can effect true random number generation and a common mistake in generation related to bias in the calculation method. He talks about some of the functions PHP includes to work with randomness, but notes that they all have their flaws. He points to the PHP-CryptLib package as a solution (adhering to the guidelines in RFC 4086 for randomness). He includes some sample code of how to use it to generate random numbers, tokens and sets of bytes. You can find the full source over on github.

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