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Aldossari, H. (2022). Scrambling Additive Lagged-Fibonacci Generators. Retrieved from https://purl.lib.fsu.edu/diginole/2022_Summer_Aldossari_fsu_0071E_17365
Random numbers are used in a variety of applications including simulation, sampling, and cryptography. Fortunately, there exist many well-established methods of random number generation. An example of a well-known pseudorandom number generator is the Lagged-Fibonacci Generator (LFG). Marsaglia showed that lagged-Fibonacci generator using addition failed some of his DIEHARD statistical tests while it passed all when longer lags were used. This paper presents a scrambler that takes bits from a pseudorandom number generator and outputs (hopefully) improved pseudorandom numbers. The scrambler is based on a modified Feistel function, a method used in the generation of cryptographic random numbers, and multiplication by a chosen multiplier. We show that this scrambler improves the quality of pseudorandom number by applying it to the additive LFG with small lags. The scrambler performs well based on its performance with the Testu01 suite of randomness tests. The scrambling of the LFG is so successful that scrambled LFGs with small lags perform as well as unscrambled LFGs with long lags. This comes at the cost of a doubling of execution time, and provides users with generators with small memory footprints that can provide parallel generators like the LFGs in the SPRNG parallel random number generation package.
A Dissertation submitted to the Department of Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Bibliography Note
Includes bibliographical references.
Advisory Committee
Michael Mascagni, Professor Directing Dissertation; Giray Okten, University Representative; Sudhir Aggarwal, Committee Member; Piyush Kumar, Committee Member.
Publisher
Florida State University
Identifier
2022_Summer_Aldossari_fsu_0071E_17365
Aldossari, H. (2022). Scrambling Additive Lagged-Fibonacci Generators. Retrieved from https://purl.lib.fsu.edu/diginole/2022_Summer_Aldossari_fsu_0071E_17365