A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies

In today's world, several applications demand numbers which appear random but are generated by a background algorithm; that is, pseudo-random numbers. Since late $19^{th}$ century, researchers have been working on pseudo-random number generators (PRNGs). Several PRNGs continue to develop, each one demanding to be better than the previous ones. In this scenario, this paper targets to verify the claim of so-called good generators and rank the existing generators based on strong empirical tests in same platforms. To do this, the genre of PRNGs developed so far has been explored and classified into three groups -- linear congruential generator based, linear feedback shift register based and cellular automata based. From each group, well-known generators have been chosen for empirical testing. Two types of empirical testing has been done on each PRNG -- blind statistical tests with Diehard battery of tests, TestU01 library and NIST statistical test-suite and graphical tests (lattice test and space-time diagram test). Finally, the selected $29$ PRNGs are divided into $24$ groups and are ranked according to their overall performance in all empirical tests

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Large Scale Stochastic Dynamics

The goal of this workshop was to explore the recent advances in the mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. There were 53 participants, including 4 postdocs and graduate students, working in diverse intertwining areas of probability and statistical mechanics. During the meeting, 24 talks of 50 minutes were scheduled and an evening session was organised with 10 more short talks of 10 minutes, mostly by younger participants. These talks addressed the following topics: hydrodynamic limits and hydrodynamic fluctuations with a special emphasis on KPZ fluctuations, scaling limits in percolation and random walks, approach to equilibrium in reversible systems with a strong focus on kinetically constrained dynamics

Pseudorandom number generator by cellular automata and its application to cryptography.

by Siu Chi Sang Obadiah.Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.Includes bibliographical references (leaves 66-68).Abstracts in English and Chinese.Chapter 1 --- Pseudorandom Number Generator --- p.5Chapter 1.1 --- Introduction --- p.5Chapter 1.2 --- Statistical Indistingushible and Entropy --- p.7Chapter 1.3 --- Example of PNG --- p.9Chapter 2 --- Basic Knowledge of Cellular Automata --- p.12Chapter 2.1 --- Introduction --- p.12Chapter 2.2 --- Elementary and Totalistic Cellular Automata --- p.14Chapter 2.3 --- Four classes of Cellular Automata --- p.17Chapter 2.4 --- Entropy --- p.20Chapter 3 --- Theoretical analysis of the CA PNG --- p.26Chapter 3.1 --- The Generator --- p.26Chapter 3.2 --- Global Properties --- p.27Chapter 3.3 --- Stability Properties --- p.31Chapter 3.4 --- Particular Initial States --- p.33Chapter 3.5 --- Functional Properties --- p.38Chapter 3.6 --- Computational Theoretical Properties --- p.42Chapter 3.7 --- Finite Size Behaviour --- p.44Chapter 3.8 --- Statistical Properties --- p.51Chapter 3.8.1 --- statistical test used --- p.54Chapter 4 --- Practical Implementation of the CA PNG --- p.56Chapter 4.1 --- The implementation of the CA PNG --- p.56Chapter 4.2 --- Applied to the set of integers --- p.58Chapter 5 --- Application to Cryptography --- p.61Chapter 5.1 --- Stream Cipher --- p.61Chapter 5.2 --- One Time Pad --- p.62Chapter 5.3 --- Probabilistic Encryption --- p.63Chapter 5.4 --- Probabilistic Encryption with RSA --- p.64Chapter 5.5 --- Prove yourself --- p.65Bibliograph

Techniques for the realization of ultra- reliable spaceborne computer Final report

Bibliography and new techniques for use of error correction and redundancy to improve reliability of spaceborne computer

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

Spatial Synthesis: Centrality and Hierarchy

There is a file containing the full book in pdf format. Animated figures are attached within the pdf. To access them, download the pdf and open it will a full pdf reader, such as Adobe Acrobat. There are three zipped files with interactive maps (Imaps) that support material in Chapter 6. Download these, unzip them, and then launch the map by opening the file, index.html. There are single chapter/section files, presented as pdfs. Again, animated images are attached within the files. Download them and open using a full pdf reader to see the attachments. Finally, there is an older, partial, zipped file of much of the book, which is only of limited utility.First in a set of volumes on spatial synthesis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58264/2/Spatial Synthesis.ziphttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/3/SpatialSynthesisVol1Book1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/4/06_SSFig6.5a_imap6.1.ziphttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/5/06_SSFig6.5b_imap6.2.ziphttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/6/06_SSFig6.5c_imap6.3.ziphttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/7/00_SS_CoverFull.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/8/0_SSIntroductionFull.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/9/01_SSChapter 1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/10/02_SSChapter 2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/11/03_SSChapter 3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/12/04_SSChapter 4.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/13/05_SSChapter 5.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/14/06_SSChapter 6.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/15/07_SSBibliography.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/16/08_SSAppendicesFull.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/17/09_SSImaps.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/58264/18/10_SSvirtualreality.pdfDescription of SpatialSynthesisVol1Book1.pdf : Book with animated attachmentsDescription of 06_SSFig6.5a_imap6.1.zip : Imap 6.1Description of 06_SSFig6.5b_imap6.2.zip : Imap 6.2Description of 06_SSFig6.5c_imap6.3.zip : Imap 6.3Description of 00_SS_CoverFull.pdf : Cover/frontmatterDescription of 0_SSIntroductionFull.pdf : Introduction and associated linksDescription of 01_SSChapter 1.pdf : Chapter 1Description of 02_SSChapter 2.pdf : Chapter 2Description of 03_SSChapter 3.pdf : Chapter 3Description of 04_SSChapter 4.pdf : Chapter 4Description of 05_SSChapter 5.pdf : Chapter 5Description of 06_SSChapter 6.pdf : Chapter 6Description of 07_SSBibliography.pdf : BibliographyDescription of 08_SSAppendicesFull.pdf : Appendices overviewDescription of 09_SSImaps.pdf : Appendix ImapsDescription of 10_SSvirtualreality.pdf : Appendix virtual realit