The continuous improvement in the speed of digital components in conjunction with reduction of size has brought about a revolutionary age of microprocessors. Mathematical functions, which at one time could only be implemented by complex analog circuitry, can now be easily implemented via microprocessors and high density digital components. Principles of random number generation must be understood in order to implement pseudo-random algorithms in a digital random frequency generator (DRFG) design. Chapter 1 is a discussion of several types of random number algorithms which have been used in the past and outlines the deficiencies and advantages associated with each individual algorithm. In particular, problems such a cycling and maximum period deficiency are discussed. The discussions in Chapter 1 lead to the selection of a random number algorithm which can be used in a DRFG design. There are other characteristics which should be observed in the evaluation of acceptable random number algorithms. In Chapter 2 three tests are described which can be applied in order to test the algorithm for the well-known uniformity and independence criteria. These tests are implemented in a Fortran program which is used to evaluated the algorithm selected in Chapter 1. The random number generator evaluation program (RNGEP) listing is presented in Appendix B. The results of the tests applied to the DRFG random number algorithm are presented in Appendix C.

Thesis (M.S.)--Florida State University, 2003. / Advisor: Michael Mascagni, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed Mar. 2, 2004). Includes bibliographical references.

This thesis contains a brief review of some of the work that has been done concerning the generation and testing of pseudo-random numbers. Computer subroutine programs written in FORTRAN IV are given for the generation of pseudo-random numbers from Pearson distributions as well as from any combination of mixtures of two Pearson distributions, a normal distribution with arbitrary mean and variance and a uniform distribution on any finite interval. The Pearson distribution may be specified either by the first four moments or from sample data, then the parameters of the fitted distribution are printed and, if desired, a graph of the distribution. A graph of the mixture of distributions may be obtained from 10,000 pseudo-random numbers from the mixture. The speed of generation varies from about 10,000 random numbers per minute (on the IBM 7040), for a Pearson distribution with moments calculated from the generated numbers, to more than 100,000 numbers per minute if mixtures are used. The subroutines are applied to a Monte Carlo investigation of the robustness of several methods of confidence interval estimation. / M.S.

Οι γεννήτριες τυχαίων αριθμών (ΓΤΑ) βρίσκονται στη ζωή του ανθρώπου εδώ και χιλιάδες χρόνια. Η πιο συχνή εφαρμογή τους είναι σε παιχνίδια που εμπεριέχουν τύχη, θεωρείστε για παράδειγμα το ζάρι που αποτελεί μια από τις πιο παλιές και πιο γνωστές γεννήτριες τυχαίων αριθμών. Ωστόσο με την πρόοδο της τεχνολογίας βρήκαν εφαρμογή και σε άλλους τομείς και κυρίως στην κρυπτογραφία, όπως για παράδειγμα στην ασφαλή μεταφορά δεδομένων στο διαδίκτυο ή στη διατήρηση της ασφάλειας ενός τοπικού δικτύου. Στα πλαίσια αυτής τη διπλωματικής θα δούμε τις κατηγορίες στις οποίες χωρίζονται οι ΓΤΑ καθώς επίσης και διάφορες πηγές τυχαιότητας γι’ αυτές. Στη συνέχεια θα επικεντρωθούμε στις Γεννήτριες Πραγματικά Τυχαίων Αριθμών και την εφαρμογή τους σε ολοκληρωμένα κυκλώματα όπως τα FPGA και θα δούμε κατάλληλες τεχνικές για την υλοποίηση τους. Έπειτα παρουσιάζουμε τη δομή και τη λειτουργία δύο γεννητριών που βασίζονται στην τεχνική που αξιοποιεί το jitter των ταλαντωτών. Η βασική τους διαφορά, η οποία κατ’ επέκταση επηρεάζει και το συνολικό σχεδιασμό, είναι ότι η μία έχει έναν αργό και ένα γρήγορο ταλαντωτή, ενώ η άλλη δύο γρήγορους ταλαντωτές. Στο στάδιο της υλοποίησης θα χρησιμοποιήσουμε τη γλώσσα περιγραφής υλικού VHDL και θα δούμε τη συμπεριφορά των σχεδιασμών μας όσον αφορά την επιφάνεια που καταλαμβάνουν και την ισχύ που καταναλώνουν για συγκεκριμένες τεχνολογίες FPGA. Επίσης θα ελέγξουμε τη στατιστική ποιότητα των ακολουθιών bit που παράγουν οι γεννήτριες μας για να επαληθεύσουμε την αποτελεσματική λειτουργία των σχεδιασμών μας. Τέλος θα συγκρίνουμε τις δύο ΓΠΤΑ που σχεδιάσαμε στους τομείς που μόλις αναφέραμε. / -

Randomness is an important part of computer science. A large group of work, both in theoretical and practical computer science, is dedicated to the study of whether true 'randomness' is necessary for a variety of applications and protocols to work. One of the main uses for randomness is in the generation of keys, used as a security measure for many cryptographic protocols. The main measure of randomness is achieved by looking at entropy, a measure of the disorder of a system. Nature is able to provide us with many sources that are high in entropy. However, many cryptographic protocols need sources of randomness that are stronger (higher in entropy) than what is present naturally to ensure security. Therefore, a gap exists between what is available in Nature, and what is necessary for provable security. This paper looks to bridge this gap. Research in pseudorandom number generation has gone on for decades. However, many of the past constructions were lacking in either documentation or provable security of their methods. The need for a pseudorandom number generator (PRG) with provable security and strong documentation is evident. A new construction of a PRG is introduced. The new construction, labeled XRNG, looks to encompass recent research in the field of extractors along with previously known research in the field of pseudorandom number generation. Extractors, as the name suggests, looks to extract close to random information from high entropy sources.

Mon travail porte sur la construction de générateurs aléatoires de conditions de vent en Bretagne. Ces modèles permettent de simuler artificiellement des conditions météorologiques réalistes et sont couramment utilisés pour la gestion des risques liés aux aléas climatiques. Ils sont construits sur la base de données historiques dans le but de produire des simulations cohérentes avec le climat actuel mais peuvent intégrer des scénarios de changement climatique. Les séquences simulées permettent de pallier le manque de données réelles et sont utilisées en entrée de modèles économiques ou écologiques. / This work is aimed at constructing stochastic weather generators. These models enable to simulate artificially weather data that have statistical properties consistent with observed meteorology and climate. Outputs of these models are generally used in impact studies in agriculture or in ecology.

Random Numbers form the heart and soul of a discrete-event simulation system. There are few situations where the actions of the entities in the process being simulated can be completely predicted in advance. The real world processes are more probabilistic than deterministic. Hence, such chances are represented in the system by using various statistical models, like random number generators. These random number generators can be used to represent a various number of factors, such as length of the queue. However, simulations have grown in size and are sometimes required to run on multiple machines, which share the various methods or events in the simulation among themselves. These Machines can be distributed across a LAN or even the internet. In such cases, to keep the validity of the simulation model, we need rollback-able random number generators. This thesis is an effort to develop such rollback able random number generators for the Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES) environment developed by NASA. These rollback-able random number generators will also add several statistical distribution models to the already rich SPEEDES library.

Proliferation of computers with varying word sizes has led to increases in software use where random number generation is required. Several techniques have been developed. Criteria of randomness, portability, period, reproducibility, variety, speed, and storage are used to evaluate developed generation methods. The Tausworthe method is the only method to meet the portability requirement, and is chosen to be implemented. A C language implementation is proposed as a possible implementation and test results are presented to confirm the acceptability of the proposed code. / Master of Science

No description available.

Les nombres aléatoires ont été de tous temps utilisés pour des jeux de hasard, plus récemment pour créer des codes secrets et ils sont aujourd'hui nécessaire à l'exécution de programmes informatiques. Les générateurs de nombres aléatoires sont maintenant bien éloignés de simples dés à lancer et sont constitués de circuits électroniques ou d'algorithmes. Ceci pose des problèmes quant à la reconnaissance du caractère aléatoire des nombres générés. De plus, de la même manière ou autrefois les dés étaient pipés pour augmenter les chances de gagner, il est aujourd'hui possible d'influencer la sortie des générateurs de nombres aléatoires.Ce sujet est donc toujours d'actualité avec des exemples récents très médiatisés. Ceci concernait en effet la console de jeu PS3 qui génère un nombre aléatoire constant où la distribution de clefs secrètes redondantes sur internet.Ce mémoire présente l'étude de plusieurs générateurs ainsi que diverses manières de les perturber. Il montre ainsi des faiblesses inhérentes à leurs conceptions et des conséquences possibles de leur défaillance sur des composants de sécurité. Ces travaux ont de plus permis de mettre en évidence l'importance des problématiques concernant le test des nombres aléatoires ainsi que des retraitements corrigeant des biais dans ces nombres. / Random numbers have been used through the ages for games of chance, more recently for secret codes and today they are necessary to the execution of computer programs. Random number générators have now evolved from simple dices to electronic circuits and algorithms. Accordingly, the ability to distinguish between random and non-random numbers has become more difficult. Furthemore, whereas in the past dices were loaded in order to increase winning chances, it is now possible to influence the outcome of random number generators.In consequence, this subject is still very much an issue and has recently made the headlines. Indeed, there was talks about the PS3 game console which generates constant random numbers and redundant distribution of secret keys on the internet.This thesis presents a study of several generators as well as different means to perturb them. It shows the inherent defects of their conceptions and possible consequences of their failure when they are embedded inside security components. Moreover, this work highlights problems yet to be solved concerning the testing of random numbers and the post-processing eliminating bias in these numbers distribution.