
What's so special about this pseudorandom number generator?
This carefully designed PRNG utilizes more than 1536 bits of internal “state” memory. The operating parameters of the generator's algorithm were carefully chosen (it uses a “safe prime” factor) to guarantee that every possible PRNG “state” is visited before the sequence begins to repeat. The result is that the “period” of this generator will be the “Germain prime” 1,768,863 x 2^{1535}  1, which is approximately 2.132 x 10^{468}. This is such a large number that it might as well be infinite. This generator effectively never repeats.
For our purposes, a “SeedKey” (such as the one above) is used to initialize the PRNG to a pseudorandomly chosen point in this incredibly large loop of unpredictable pseudorandom numbers, from which we then pull as many pseudorandom values as we need. The 256character “SeedKey” uses the 94 printable ASCII characters (spaces are ignored). Therefore, this yields 94^{256} possible seedkeys. This is 1.32 x 10^{505} possible strings, which is equivalent to 1,678 bits of entropy. Since this is greater than the total entropic state of the UHEPRNG, a SeedKey of this length and complexity is sufficient (and necessary) to fully initialize a PRNG of this complexity.
Anything else?
As a matter of fact, yes: Not only is it an extremely good pseudorandom number generator, it is also extremely fast. This makes its use with slow processors, or under interpreted languages (such as its implementation language, JavaScript) much more practical than many other much weaker PRNGs.
Where is it?
The JavaScript code is here, and you're welcome to it. This page is a simple demonstration of the proper use of this PRNG and may be used as a reference.
Why was this fancy PRNG developed?
Our “Off The Grid” (OTG) website password generation system is based upon Latin Squares. Latin Squares are ‘n’x‘n’ grids containing exactly one of each of ‘n’ symbols in every horizontal row and vertical column. Brute force guessing of the OTG system's grids is made effectively impossible by the large number of possible 26x26 Latin Squares. This remains true even when many pieces of a user's Latin Square have become known to an attacker due to the phenomenal number of Squares that are still possible containing what is known.
Although mathematicians have been unable to determine how many different 26x26 Squares can be created, they have been able to determine that the number is at least 9.337 x 10^{426}, or approximately 2^{1418}. This is an incredibly large number. But for our purposes it is only meaningful if any of those many possible Latin Squares could potentially be generated by our OTG grid generator. If we were to use any traditional PRNG, even something stateoftheart such as Fortuna, based upon a cryptographic symmetric cipher or a hash, we would be limited to generating Latin Squares from such a generator's much lower level of entropy . . . on the order of 256 or 384 bits. This would be more than sufficient for many cryptographic applications, but not for ours. Since 26x26 Latin Squares are known to have a potential entropy of at least 1418 bits, we needed a PRNG that could keep up. So an “ultrahigh entropy” PRNG, having an entropy of 1536 bits, was developed to allow access to all possible Latin Squares.
What's the “SeedKey” in the form above?
Not only do we want a system that is able to select one OTG grid from among the truly incredible number of possible Latin Squares, but every user needs to be able to regenerate their own personal one out of 10^{427} grids if their existing paper copy should ever need to be replaced, resized, recolored, refonted, or reprinted for any reason.
We achieve those two goals by generating and capturing a very long 1536bit pseudorandom number — the “SeedKey” — then using that number to set the ultrahigh entropy pseudorandom number generator's 1536bit “initial state” from which a single unique grid will be created.
Fortunately, the need to test the randomness of hopefullyrandom numbers is so well known that a great deal of effort has previously been expended in the creation of suites of randomnesstesting tools. Using the most well known, well used, and popular of these tools, multiple researchers have independently verified that the pseudorandom numbers generated by this algorithm passes the most stringent of tests for randomness. I breathed a sigh of relief after this, since the “diehard” and “dieharder” suites of tests are considered “difficult to pass” by researchers of randomness.
Everyone is invited to test it for themselves:
Pseudorandom numbers generated by this algorithm have handily passed the “Fourmilab.ch/random” tests as well as the tried and true “diehard” and “dieharder” test suites. For individuals wishing to verify the quality of this algorithm's pseudorandom numbers for themselves, a 256megabyte file of this algorithm's output may be downloaded from GRC, and a Microsoft Windows scripting host (WSH) version of this algorithm may be downloaded and run from the Windows command prompt to generate unique files of any size:
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