Title:

The Design and Implementation of a Cryptographically Strong Pseudo-Random Number Generator

Objective:

For ages, poor algorithms for generating "random" numbers have plagued 
programmers and created gaping holes in security systems. There are a very 
amount of reasonably good prng's out there, and only a select few may be 
called "Cryptographically Strong." My intent is to make an algorithm for 
producing cryptographically strong pseudo-random sequences and implementing it 
in a computer program.

Justification:

Cryptography is a field which requires perfectly unpredictable numbers. While 
this is not possible, using a deterministic computer, it is of high importance 
to have algorithms to approximate perfection. The best algorithms, however, are 
pathetically slow in practical applications, my own implementation of one of 
the best, Blum Blum Shub, takes about 1/10th of a second to generate each new 
bit. Obviously, faster algorithms are needed for real programs.

Description:

A CSPRNG needs to have certain special qualities, above those of a simple prng.
Given a sequence of bits, a person should have no greater chance of predicting 
the next bit than 1/2, and must have a long period. Mine, in addition, must be 
fast (thus it cannot use multiplication, division, and therefore modulo 
operations) and cannot be based on hash functions except during the seeding 
stage.

For all practical purposes, my design should be able to spit out values 
indistinguishable from true random data.

Limitations:

"To infinity, and beyond!"