NAVAL POSTGRADUATE SCHOOL MONTEREY CA MONTEREY United States
Cryptography is essential for secure online communications. Many different types of ciphers are implemented in modern-day cryptography, but they all have one common factor. All ciphers require a source of randomness, which makes them unpredictable. One such source of this randomness is a random number generator. This thesis focuses on Pseudorandom Number Generators PRNG, specifically, a PRNG called Blum-Blum-Shub BBS. In this thesis, we make two modifications to BBS, and test our modified generators for randomness using the National Institute of Standards and Technology NIST tests. The original BBS is a quadratic generator that generates bits based on the output of squaring terms in a sequence. The first modification replaces the quadratic generator with a cubic generator. The second modification generates bits faster by using more bits per iteration. Data collected in this thesis suggests that the cubic modification performs just as well as the original generator. In addition, data from this thesis suggests that taking more bits per iteration can speed up this process while retaining randomness. In addition, we propose a new cryptosystem based upon the modification of the BBS PRNG introduced in this thesis.