The RandomTools[BlumBlumShub] subpackage contains functions for creating pseudo-random number generators using the Blum, Blum, and Shub algorithm.  The integers x[1], x[2], ... are generated using the quadratic recurrence

where  is a product of two primes and , the seed, may be specified by the user.  They use the least significant bits of the x's to form the random numbers.

The Blum, Blum, and Shub generator is intended to be used for cryptographic applications.  For this purpose it uses very large primes, primes of length 308, 462 or 616 digits so that n cannot be factored.  It extracts the log[2](log[2](n)) least significant bits of the x's which are known to be cryptographically secure.  The primes used have certain properties so that  can be chosen so that the sequence of bits generated will have a provably very long period.

Each command in the RandomTools[BlumBlumShub] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.

As the underlying implementation of the RandomTools[BlumBlumShub] subpackage is a module, it is also possible to use the form BlumBlumShub:-command to access a command from the package. For more information, see Module Members.

To display the help page for a particular BlumBlumShub command, see Getting Help with a Command in a Package.