Recent advances in the theory of nonlinear pseudorandom number generators

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Çeşmelioğlu, Ayça (2002) Recent advances in the theory of nonlinear pseudorandom number generators. [Thesis]

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Abstract

The classical linear congruential method for generating uniform pseudorandom numbers has some deficiencies that can render them useless for some simulation problems. This fact motivated the design and the analysis of nonlinear congruential methods for the generation of pseudorandom numbers. In this thesis, we aim to review the recent developments in the study of nonlinear congruential pseudorandom generators. Our exposition concentrates on inversive generators. We also describe the so-called power generator and the quadratic exponential generator which are particularly interesting for cryptographic applications. We give results on the period length and theoretical analysis of these generators. The emphasis is on the lattice structure, discrepancy and linear complexity of the generated sequences.
Item Type: Thesis
Uncontrolled Keywords: Discrepancy. -- inversive congruential generator. -- Lattice test. -- Linear complexity profile. -- Linear complexity, power generator. -- Period length. -- Pseudorandom number generator
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 18 Apr 2008 11:08
Last Modified: 26 Apr 2022 09:41
URI: https://research.sabanciuniv.edu/id/eprint/8146

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