Approved for public release; distribution is unlimited / Includes supplementary material / Reissued 30 May 2017 with correction to degree on title page. / Randomness is at the heart of today's computing. There are two categorical methods to generate random numbers: pseudorandom number generation (PRNG) methods and true random number generation (TRNG) methods. While PRNGs operate orders of magnitude faster than TRNGs, the strength of PRNGs lies in their initial seed. TRNGs can function to generate such a seed. This thesis will focus on studying the feasibility of using the next generation Naval Postgraduate School Femto Satellite (NPSFS) as a TRNG. The hardware for the next generation will come from the Intel Quark D2000 along with its onboard BMC150 6-axis eCompass. We simulated 3-dimensional motion to see if any raw data from the BMC150 could be used as an entropy source for random number generation.We studied various "schemes" on how to select and output specific data bits to determine if more entropy and increased bitrate could be reached. Data collected in this thesis suggests that the BMC150 contains certain bits that could be considered good sources of entropy. Various schemes further utilized these bits to yield a strong entropy source with higher bitrate. We propose the NPSFS be studied further to find other sources of entropy. We also propose a prototype be sent into space for experimental verification of these results. / Lieutenant, United States Navy

A numerical investigation of the performance of two candidate designs for injection into supersonic flow, including a comparison of two renormalized group theory (RNG) based k-epsilon turbulence models with a more conventional k-epsilon model. The chosen designs were an unswept ramp injector with four injection ports and a novel nine-hole injector array. The objectives of the investigation were to provide reliable computational solutions to the flowfields in question using both RNG and standard k-epsilon turbulence models and to compare the solutions to experiment, thereby to judge the relative performance of the turbulence models. A second objective of the investigation was to use the computed data to provide design insights for the nine-hole injector array. This investigation made use of GASP(tm) version 2.2, a commercial computational fluid dynamics code that was augmented by the addition of one RNG-based k-epsilon turbulence model derived by Zhou, et. al. and one variant of Zhou's model, which was derived by the author. Mesh sequencing studies were performed to measure solution quality, with the fine mesh for the injector array containing roughly one million grid nodes and the fine mesh for the ramp injector containing more than six million grid nodes. Results of these studies indicated that the injector-array solution was significantly under-resolved in the farfield, though the quality was better in the vicinity of the injector itself. The ramp-injector solution, while not perfectly grid-resolved, showed much better grid convergence in both the nearfield and farfield. Accordingly, comparison with experiment was better for the ramp injector than for the injector array. For both injectors, the differences between solutions generated with RNG-based k-epsilon and standard k-epsilon turbulence models were negligibly small." Despite inadequate grid resolution in the farfield, the computational investigation of the nine-hole injector array did yield several important design insights. Particularly, the significance to mixing and losses of the placement of the outer injectors of the second and third rows was determined. / Ph. D.

L’objet de cette thèse porte sur la modélisation mathématique des générateurs physiques de nombres aléatoires, tout particulièrement dans le contexte des systèmes embarqués. Les axes principaux sont les modèles stochastiques des sources d'entropie, l’établissement de tests statistiques adaptés et l’exploitation des défauts détectés / The purpose of this thesis focuses on the mathematical modeling of physical random number generators, especially in the context of embedded systems. The main axes are the stochastic modeling of entropy sources, the establishment of appropriate statistical tests and the exploitation of detected weaknesses.

Background. Being able to trust cryptographic algorithms is a crucial part of society today, because of all the information that is gathered by companies all over the world. With this thesis, we want to help both Promestra AB and potential future customers to evaluate if you can trust their random number generator. Objectives. The main objective for the study is to compare the random number generator in Promestra security with the help of the test suite made by the NationalInstitute of Standards and Technology. The comparison will be made with other random number generators such as Mersenne Twister, Blum-Blum-Schub and more. Methods. The selected method in this study was to gather a total of 100 million bits of each random number generator and use these in the National Institute ofStandards and Technology test suite for 100 tests to get a fair evaluation of the algorithms. The test suite provides a statistical summary which was then analyzed. Results. The results show how many iterations out of 100 that have passed and also the distribution between the results. The obtained results show that there are some random number generators that have been tested that clearly struggles in many of the tests. It also shows that half of the tested generators passed all of the tests. Conclusions. Promestra security and Blum-Blum-Schub is close to passing all the tests, but in the end, they cannot be considered to be the preferable random number generator. The five that passed and seem to have no clear limitations are:Random.org, Micali-Schnorr, Linear-Congruential, CryptGenRandom, and MersenneTwister.

Zufallszahlen werden für die unterschiedlichsten Anwendungsfälle benötigt. Einen besonderen Stellenwert hat dabei die Kryptographie. Im Rahmen dieser Arbeit werden verschiedene klassische und quantenmechanische Zufallszahlengeneratoren auf ihre Eignung zur Verwendung für kryptographische Zwecke geprüft. Dazu werden zunächst einige notwendige Grundlagen gelegt, um verschiedene Verfahren für die Evaluierung der generierten Zufallszahlen zu beleuchten. Einen besonderen Stellenwert nimmt dabei die Qualität der Zufallszahlen ein. Wie diese gemessen werden kann und wodurch sich qualitativ hochwertige Zufallszahlen auszeichnen, sind Fragen, die im Rahmen dieser Arbeit beantwortet werden. Zur Beurteilung der Qualität der Zufallszahlen werden eine Reihe statistischer Tests herangezogen, die auf eine Auswahl von klassischen und quantenmechanischen Zufallszahlengeneratoren angewendet werden. Die Ergebnisse entsprechen dabei teilweise nicht den Erwartungen. Berücksichtigt man nur die Qualität der erzeugten Zufallszahlen, so stellt sich heraus, dass einige klassische Generatoren mit den quantenmechanischen Alternativen mithalten können. Allerdings werden auch einige Limitationen bei der Anwendung der Tests sichtbar.:1. Einführung 1.1. Motivation 1.2. Zielstellung 1.3. Vorgehensweise 2. Theoretische Grundlagen 2.1. Zufall, Zufallszahlen und Zufallszahlengeneratoren im mathematischen Kontext 2.2. Exkurs in die Quantenmechanik 2.3. Stand der Technik 3. Praktische Verwendung von Zufallszahlen 3.1. Verwendung von Zufallszahlen für Kryptographie 3.2. Qualität von Zufallszahlen im kryptographischen Kontext 3.3. Praktische Umsetzung und Einordnung von Zufallszahlengeneratoren 4. Ausgewählte Implementierungen von Zufallszahlengeneratoren 4.1. Klassische Zufallszahlengeneratoren 4.1.1. Linearer Kongruenzgenerator 4.1.2. Linux /dev/(u)random 4.2. Quantenmechanische Zufallszahlengeneratoren 4.2.1. ID Quantique Quantis 4.2.2. QuintessenceLabs qStream 4.2.3. IBM Quantencomputer 5. Statistisches Testen von Zufallszahlengeneratoren 5.1. Allgemeine Tests 5.2. Tests nach NIST SP 800-22 - Rev. 1a 5.3. Dieharder-Tests 6. Anwendung statistischer Tests auf ausgewählte Zufallszahlengeneratoren 6.1. Erwartungen 6.2. Linearer Kongruenzgenerator 6.3. Linux /dev/urandom 6.4. ID Quantique Quantis 6.5. QuintessenceLabs qStream 6.6. IBM Quantencomputer 7. Evaluation 8. Fazit 8.1. Zusammenfassung 8.2. Kritische Würdigung 8.3. Ausblick

Dois dos principais objetivos no estudo da aerodinâmica de veículos comerciais são a redução no consumo de combustível e o aumento na eficiência da refrigeração do motor. Esses objetivos podem ser alcançados através do desenvolvimento de dispositivos que modifiquem o escoamento do ar ao redor do veículo e também através da alteração da forma das superfícies externas. A inclinação das superfícies da parte traseira de um ônibus, por exemplo, tem grande influência sobre a esteira turbulenta que se forma atrás do veículo. O uso de ferramentas computacionais permite uma redução de custo e maior flexibilidade na análise aerodinâmica de autoveículos. Ainda é preciso, no entanto, que o resultado dessas ferramentas computacionais seja verificado com o maior número possível de casos para que se possa escolher e ajustar o modelo matemático de forma adequada. O objetivo do presente trabalho é a verificação dos resultados computacionais e experimentais no desenvolvimento de metodologias que visem à redução no consumo de combustível e aumento na eficiência da refrigeração do motor. Foram comparados resultados experimentais e computacionais do escoamento sobre um modelo de um ônibus comercial em escala 1:17,5. Para a realização do experimento foi utilizado um túnel de vento de seção aberta, onde foram analisadas as distribuições de pressão nas superfícies da carroceria e o arrasto aerodinâmico. Para o teste computacional, foi utilizado um software de dinâmica dos fluidos computacional em que as equações de Navier-Stokes com média de Reynolds são resolvidas pelo método dos volumes finitos usando um modelo de turbulência RNG 'capa' - 'épsilon' / Two main objectives in the study of commercial vehicle aerodynamics are the reduction in fuel consumption and the improvement in engine refrigeration efficiency. These objectives can be achieved through development of devices which vary the flow characteristics around the vehicle and also through modification of the shape of external surfaces. The slope of rear surfaces, for instance, has large influence over the wake turbulence which forms behind the vehicle. The use of computational tools yields cost reduction and greater flexibility in automotive aerodynamic analysis. There is still a need, however, for verification of results, generated by these computational tools, with the largest possible number of test cases so that the mathematical model is adequately chosen and adjusted. The objective of the present work is the verification of experimental and computational results in the development of methodologies aiming at reduction of fuel consumption and improvement in engine refrigeration efficiency. Experimental and computational aerodynamic results were compared for a commercial bus model with a 1:17.5 scale. The experiments were conducted in an open section wind tunnel where pressure distribution and aerodynamic drag were analyzed. The numerical analysis was conducted using computational fluid dynamics software which solves the Reynolds Averaged Navier-Stokes equations using the finite volume method with a RNG 'capa' - 'épsilon' turbulence model

Dois dos principais objetivos no estudo da aerodinâmica de veículos comerciais são a redução no consumo de combustível e o aumento na eficiência da refrigeração do motor. Esses objetivos podem ser alcançados através do desenvolvimento de dispositivos que modifiquem o escoamento do ar ao redor do veículo e também através da alteração da forma das superfícies externas. A inclinação das superfícies da parte traseira de um ônibus, por exemplo, tem grande influência sobre a esteira turbulenta que se forma atrás do veículo. O uso de ferramentas computacionais permite uma redução de custo e maior flexibilidade na análise aerodinâmica de autoveículos. Ainda é preciso, no entanto, que o resultado dessas ferramentas computacionais seja verificado com o maior número possível de casos para que se possa escolher e ajustar o modelo matemático de forma adequada. O objetivo do presente trabalho é a verificação dos resultados computacionais e experimentais no desenvolvimento de metodologias que visem à redução no consumo de combustível e aumento na eficiência da refrigeração do motor. Foram comparados resultados experimentais e computacionais do escoamento sobre um modelo de um ônibus comercial em escala 1:17,5. Para a realização do experimento foi utilizado um túnel de vento de seção aberta, onde foram analisadas as distribuições de pressão nas superfícies da carroceria e o arrasto aerodinâmico. Para o teste computacional, foi utilizado um software de dinâmica dos fluidos computacional em que as equações de Navier-Stokes com média de Reynolds são resolvidas pelo método dos volumes finitos usando um modelo de turbulência RNG 'capa' - 'épsilon' / Two main objectives in the study of commercial vehicle aerodynamics are the reduction in fuel consumption and the improvement in engine refrigeration efficiency. These objectives can be achieved through development of devices which vary the flow characteristics around the vehicle and also through modification of the shape of external surfaces. The slope of rear surfaces, for instance, has large influence over the wake turbulence which forms behind the vehicle. The use of computational tools yields cost reduction and greater flexibility in automotive aerodynamic analysis. There is still a need, however, for verification of results, generated by these computational tools, with the largest possible number of test cases so that the mathematical model is adequately chosen and adjusted. The objective of the present work is the verification of experimental and computational results in the development of methodologies aiming at reduction of fuel consumption and improvement in engine refrigeration efficiency. Experimental and computational aerodynamic results were compared for a commercial bus model with a 1:17.5 scale. The experiments were conducted in an open section wind tunnel where pressure distribution and aerodynamic drag were analyzed. The numerical analysis was conducted using computational fluid dynamics software which solves the Reynolds Averaged Navier-Stokes equations using the finite volume method with a RNG 'capa' - 'épsilon' turbulence model

clRNG et clProbdist sont deux interfaces de programmation (APIs) que nous avons développées pour la génération de nombres aléatoires uniformes et non uniformes sur des dispositifs de calculs parallèles en utilisant l’environnement OpenCL. La première interface permet de créer au niveau d’un ordinateur central (hôte) des objets de type stream considérés comme des générateurs virtuels parallèles qui peuvent être utilisés aussi bien sur l’hôte que sur les dispositifs parallèles (unités de traitement graphique, CPU multinoyaux, etc.) pour la génération de séquences de nombres aléatoires. La seconde interface permet aussi de générer au niveau de ces unités des variables aléatoires selon différentes lois de probabilité continues et discrètes. Dans ce mémoire, nous allons rappeler des notions de base sur les générateurs de nombres aléatoires, décrire les systèmes hétérogènes ainsi que les techniques de génération parallèle de nombres aléatoires. Nous présenterons aussi les différents modèles composant l’architecture de l’environnement OpenCL et détaillerons les structures des APIs développées. Nous distinguons pour clRNG les fonctions qui permettent la création des streams, les fonctions qui génèrent les variables aléatoires uniformes ainsi que celles qui manipulent les états des streams. clProbDist contient les fonctions de génération de variables aléatoires non uniformes selon la technique d’inversion ainsi que les fonctions qui permettent de retourner différentes statistiques des lois de distribution implémentées. Nous évaluerons ces interfaces de programmation avec deux simulations qui implémentent un exemple simplifié d’un modèle d’inventaire et un exemple d’une option financière. Enfin, nous fournirons les résultats d’expérimentation sur les performances des générateurs implémentés. / clRNG and clProbdist are two application programming interfaces (APIs) that we have developed respectively for the generation of uniform and non-uniform random numbers on parallel computing devices in the OpenCL environment. The first interface is used to create at a central computer level (host) objects of type stream considered as parallel virtual generators that can be used both on the host and on parallel devices (graphics processing units, multi-core CPU, etc.) for generating sequences of random numbers. The second interface can be used also on the host or devices to generate random variables according to different continuous and discrete probability distributions. In this thesis, we will recall the basic concepts of random numbers generators, describe the heterogeneous systems and the generation techniques of parallel random number, then present the different models composing the OpenCL environment. We will detail the structures of the developed APIs, distinguish in clRNG the functions that allow creating streams from the functions that generate uniform random variables and the functions that manipulate the states of the streams.We will describe also clProbDist that allow the generation of non-uniform random variables based on the inversion technique as well as returning different statistical values related to the distributions implemented. We will evaluate these APIs with two simulations, the first one implements a simplified example of inventory model and the second one estimate the value of an Asian call option. Finally, we will provide results of experimentations on the performance of the implemented generators.

<p>Slumptalsgeneratorer är bland de viktigaste byggblocken inom dagens säkerhetssystem och infrastruktur. Det finns dock en uppsjö av varierande implementeringsmodeller i såväl mjukvara som hårdvara. Att konstruera en slumptalsgenerator som har tillträckligt bra egenskaper för att användas i säkerhetssystem är inte någon trivial uppgift. </p><p>I denna rapport diskuteras de två huvud metoderna att generera slumptal, dels i mjukvara (PRNG), dels i hårdvara (TRNG). Olika synvinklar och angreppssätt att generera och testa slumptal diskuteras och utvärderas. Dessutom diskuteras för- och nackdelarna med de olika generatorerna och hur dessa kan vara sårbara om inte försiktighetsåtgärder vidtas. </p><p>Resultatet antyder på att valet av en slumptalsgenerator är högst beroende på den applikation dessa slumptal ska användas i. Det rekommenderas dock att man använder en TRNG (hårdvaru-generatorer) för att seeda en PRNG (Pseudo-Random Number Generator) eller att använda sig av en TRNG och då kompensera för den skeva sannolikhetsfördelningen som uppstår.</p>

Slumptalsgeneratorer är bland de viktigaste byggblocken inom dagens säkerhetssystem och infrastruktur. Det finns dock en uppsjö av varierande implementeringsmodeller i såväl mjukvara som hårdvara. Att konstruera en slumptalsgenerator som har tillträckligt bra egenskaper för att användas i säkerhetssystem är inte någon trivial uppgift. I denna rapport diskuteras de två huvud metoderna att generera slumptal, dels i mjukvara (PRNG), dels i hårdvara (TRNG). Olika synvinklar och angreppssätt att generera och testa slumptal diskuteras och utvärderas. Dessutom diskuteras för- och nackdelarna med de olika generatorerna och hur dessa kan vara sårbara om inte försiktighetsåtgärder vidtas. Resultatet antyder på att valet av en slumptalsgenerator är högst beroende på den applikation dessa slumptal ska användas i. Det rekommenderas dock att man använder en TRNG (hårdvaru-generatorer) för att seeda en PRNG (Pseudo-Random Number Generator) eller att använda sig av en TRNG och då kompensera för den skeva sannolikhetsfördelningen som uppstår.