A self-testing quantum random number generator

The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real-time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices.Comment: 12 pages, 4 figures, including supplementary materia

Stock Repurchase Agreements: Close Corporation Use of Designee Provision Permits Repurchase Despite Insufficient Earned Surplus

Statistical random number testing is a well studied field focusing on pseudo-random number generators, that is to say algorithms that produce random-looking sequences of numbers. These generators tend to have certain kinds of flaws, which have been exploited through rigorous testing. Such testing has led to advancements, and today pseudo random number generators are both very high-speed and produce seemingly random numbers. Recent advancements in quantum physics have opened up new doors, where products called quantum random number generators that produce acclaimed true randomness have emerged. Of course, scientists want to test such randomness, and turn to the old tests used for pseudo random number generators to do this. The main question this thesis seeks to answer is if publicly available such tests are good enough to evaluate a quantum random number generator. We also seek to compare sequences from such generators with those produced by state of the art pseudo random number generators, in an attempt to compare their quality. Another potential problem with quantum random number generators is the possibility of them breaking without the user knowing. Such a breakdown could have dire consequences. For example, if such a generator were to control the output of a slot machine, an malfunction could cause the machine to generate double earnings for a player compared to what was planned. Thus, we look at the possibilities to implement live tests to quantum random number generators, and propose such tests. Our study has covered six commonly available tools for random number testing, and we show that in particular one of these stands out in that it has a series of tests that fail our quantum random number generator as not random enough, despite passing an pseudo random number generator. This implies that the quantum random number generator behave differently from the pseudo random number ones, and that we need to think carefully about how we test, what we expect from an random sequence and what we want to use it for.Statistisk slumptalstestning är ett väl studerat ämne som fokuserar på så kallade pseudoslumpgeneatorer, det vill säga algorithmer som producerar slump-liknande sekvenser med tal. Sådana generatorer tenderar att ha vissa defekter, som har exploaterats genom rigorös tesning. Sådan testning har lett till framsteg och idag är pseudoslumpgeneratorer både otroligt snabba och producerar till synes slumpade tal. Framsteg inom kvantfysiken har lett till utvecklingen av kvantslumpgeneratorer, som producerar vad som hävdas vara äkta slump. Självklart vill forskare utvärdera sådan slump, och har då vänt sig till de gamla testerna som utvecklats för pseudoslumpgeneratorer. Den här uppsatsen söker utvärdera hurvida allmänt tillgängliga slumptester är nog bra för att utvärdera kvantslumpgeneratorer. Vi jämför även kvantslumpsekvenser med pseudoslumpsekvenser för att se om dessa väsentligen skiljer sig från varandra och på vilket sätt. Ett annat potentiellt problem med kvantslumpgeneratorer är möjligheten att dessa går sönder under drift. Om till exempel en kvantslumpgenerator används för att slumpgenerera resultatet hos en enarmad bandit kan ett fel göra så att maskinen ger dubbel vinst för en spelare jämfört med planerat. Därmed ser vi över möjligheten att implementera live-tester i kvantslumpgeneratorer, och föreslår några sådana tester. Vår studie har täckt sex allmänt tillgängliga verktyg för slumptalstestning, och vi visar att i synnerhet ett av dessa står ut på så sätt att det har en serie av tester som slumptalen från vår kvantslumpgenerator inte anser är nog slumpade. Trots det visar samma test att sekvensen från pseudoslumpgeneratorerna är bra nog. Detta antyder att kvantslumpgeneratorn beter sig annorlunda mot pseudoslumpgeneratorerna, och att vi behöver tänka över ordentligt kring hur vi testar slumpgeneratorer, vad vi förväntar oss att få ut och hurvida detta påverkar det vi skall använda slumpgeneratorn till

Testing a Random Number Generator: formal properties and automotive application

L'elaborato analizza un metodo di validazione dei generatori di numeri casuali (RNG), utilizzati per garantire la sicurezza dei moderni sistemi automotive. Il primo capitolo fornisce una panoramica della struttura di comunicazione dei moderni autoveicoli attraverso l'utilizzo di centraline (ECU): vengono riportati i principali punti di accesso ad un automobile, assieme a possibili tipologie di hacking; viene poi descritto l'utilizzo dei numeri casuali in crittografia, con particolare riferimento a quella utilizzata nei veicoli. Il secondo capitolo riporta le basi di probabilità necessarie all'approccio dei test statistici utilizzati per la validazione e riporta i principali approcci teorici al problema della casualità. Nei due capitoli centrali, viene proposta una descrizione dei metodi probabilistici ed entropici per l'analisi di dati reali utilizzati nei test. Vengono poi descritti e studiati i 15 test statistici proposti dal National Institute of Standards and Technology (NIST). Dopo i primi test, basati su proprietà molto semplici delle sequenze casuali, vengono proposti test più sofisticati, basati sull'uso della trasformata di Fourier (per testare eventuali comportamenti periodici), dell'entropia (strettamente connessi con la comprimibilità della sequenza), o sui random path. Due ulteriori test, permettono di valutare il buon funzionamento del generatore, e non solo delle singole sequenze generate. Infine, il quinto capitolo è dedicato all'implementazione dei test al fine di testare il TRNG delle centraline

Properties making a chaotic system a good Pseudo Random Number Generator

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction

Practical self-testing quantum random number generator based on an energy bound

We present a scheme for a self-testing quantum random number generator. Compared to the fully device-independent model, our scheme requires an extra natural assumption, namely that the mean energy per signal is bounded. The scheme is self-testing, as it allows the user to verify in real-time the correct functioning of the setup, hence guaranteeing the continuous generation of certified random bits. Based on a prepare-and-measure setup, our scheme is practical, and we implement it using only off-the-shelf optical components. The randomness generation rate is 1.25 Mbits/s, comparable to commercial solutions. Overall, we believe that this scheme achieves a promising trade-off between the required assumptions, ease-of-implementation and performance

Penerapan Algoritma Pembangkit Bilangan Acak Pada Aplikasi Game Ingatan Berdasarkan Perbandingan Antara Algoritma Linear Congruential Generator Dan Algoritma Lagged Fibonacci Generator

Linear Congruential Generator and Lagged Fibonacci Generator are some random number generator algorithms. These random number generator algorithms can be used to make a game to test memory (recall test). In recall test, these algorithms, LCG and LFG can generate random numbers and letters. Both of algorithms are necessary to be compared to get randomice. Thus, it needs to calculate mean, variance, and deviation standard of the two algorithms to determine the most appropriate algorithm to be used in memory game. Numbers and letters are scrambled in time to be remembered by player, then player must enter back the numbers and letters into the system. The system will check if the user answers same as numbers and letters shown previously. Based on the results of statistical testing, it is known that LFG is more appropriate to be used in memory game

Spectral analysis of random number generators

This paper is based on the theory developed by Dr. Evangelos Yfantis, professor of Computer Science at University of Nevada, Las Vegas. In this paper, we describe a method for testing the fairness of pseudorandom number generators using the Discrete Fourier Transform. We will show how the concept of a random process can be used in a representation for random discrete time signals. Using this concept, we have focused on the mathematical representations of the spectral analysis of a fair pseudorandom number generator. From this representation, a reasonable spectral expectation is determined. An algorithm which applies the developed method is described, and a modified shift register random number generator is used to produce sample data