PANGRANDOMONIUM : Rhizome Function Anagram Random Generator

Herein are described principles and a scheme of random number generation styled as, pangrandomonium, or ‘pangrand’. Pangrand is a anagrammatic random number generator that uses rhizome functions as chaotic indexing and shuffling instructions to reorder and sum perfect pangrams. Brief descriptions are given for the principles of pangram summing and rhizome indexing functions, Source code of the random number generator is included herewith. The source code is attached to the PDF file.

Sections:

1. Pangrams (Holoalphabetic arrays) ;

2. Rhizome Functions ; 

3. Rhizome Hardness Problems ;

4. Random Generator Methods ;

5. Errata ;

6. Source Code.

About the included demonstration software:

This random number generator mixes unpredictable timestamp entropy into a pool by using the timestamp bytes as generators for shuffling three arrays of pangram bytes. Each pangram contains the bytes 0 to 255 shuffled randomly. After much shuffling two arrays are added together for output. One array is used as the seed for the next output.

512 clock bytes are converted into 256 bytes of output in each round. The generator values are derived from an accumulator pair of 128 bits total.

This method is useful because the shuffled bytes never change value. They just change their positions in the arrays. Using the shuffled data as instructions for transforming the input data guarantees a very good distribution of random instruction values. Then we use the transformed input as instructions to repeat the process on the shuffled data arrays. Moreover, if we add the bytes across the two pangram alphabets, the output can't be correlated to the secret values. A huge number of random array states yield same output of one block yet will not match on the following block of output.
    
Since output values are dependent on pangram positions, and changing two value positions affects all forward transformations, it is mathematically hard for an attacker to manipulate internal state to a desired ordering. One change is likely to form a algebraic road block to further calculated changes of the pangram orderings.