True Random Number Generators

Quantum Random Number Generators(QRNGs), or True Random Number Generators, generate random numbers based on naturally unpredictable(or hard-to-predict) sources. Their unpredictability results in a broad application in cryptography and technology. Their sources range from nuclear decay gamma rays to cosmic rays, then to quantum optics. This thesis aims to explore various randomness sources and compare their efficiency by running a series of randomness tests. The specific setup for each random number generator will also be presented

Chaos-based true random number generators

Random number (bit) generators are crucial to secure communications, data transfer and storage, and electronic transactions, to carry out stochastic simulations and to many other applications. As software generated random sequences are not truly random, fast entropy sources such as quantum systems or classically chaotic systems can be viable alternatives provided they generate high-quality random sequences sufficiently fast. The discovery of spontaneous chaos in semiconductor superlattices at room temperature has produced a valuable nanotechnology option. Here we explain a mathematical model to describe spontaneous chaos in semiconductor superlattices at room temperature, solve it numerically to reveal the origin and characteristics of chaotic oscillations, and discuss the limitations of the model in view of known experiments. We also explain how to extract verified random bits from the analog chaotic signal produced by the superlattice.This work has been supported by the Spanish Ministerio de Economía y Competitividad grants FIS2011-28838-C02-01 and MTM2014-56948-C2-2-P

Extracting random numbers from quantum tunnelling through a single diode

Random number generation is crucial in many aspects of everyday life, as online security and privacy depend ultimately on the quality of random numbers. Many current implementations are based on pseudo-random number generators, but information security requires true random numbers for sensitive applications like key generation in banking, defence or even social media. True random number generators are systems whose outputs cannot be determined, even if their internal structure and response history are known. Sources of quantum noise are thus ideal for this application due to their intrinsic uncertainty. In this work, we propose using resonant tunnelling diodes as practical true random number generators based on a quantum mechanical effect. The output of the proposed devices can be directly used as a random stream of bits or can be further distilled using randomness extraction algorithms, depending on the application

On-chip jitter measurement for true random number generators

Applications of true random number generators (TRNGs) span from art to numerical computing and system security. In cryptographic applications, TRNGs are used for generating new keys, nonces and masks. For this reason, a TRNG is an essential building block and often a point of failure for embedded security systems. One type of primitives that are widely used as source of randomness are ring oscillators. For a ring-oscillator-based TRNG, the true randomness originates from its timing jitter. Therefore, determining the jitter strength is essential to estimate the quality of a TRNG. In this paper, we propose a method to measure the jitter strength of a ring oscillator implemented on an FPGA. The fast tapped delay chain is utilized to perform the on-chip measurement with a high resolution. The proposed method is implemented on both a Xilinx FPGA and an Intel FPGA. Fast carry logic components on different FPGAs are used to implement the fast delay line. This carry logic component is designed to be fast and has dedicated routing, which enables a precise measurement. The differential structure of the delay chain is used to thwart the influence of undesirable noise from the measurement. The proposed methodology can be applied to other FPGA families and ASIC designs

Enhanced Generic Architecture for Safety Increase of True Random Number Generators

Conventionally used generic architecture of true random number generators does not allow testing of random numbers during their generation. This paper introduces an extension of the conventionally used generic architecture and describes mechanisms that can be implemented in new blocks and ensures safety increase of true random number generators. Objective of new architecture extension is detection of deliberate malicious attacks that are directed against noise source and revelation of a significant decrease of the approximate entropy in the subsequences of generated random number sequences. The enhanced generic architecture has been implemented into known software model. Obtained results show that described mechanisms allow increasing quality of the generated random numbers sequences

Limitations of a True Random Number Generator in a Field Programmable Gate Array

Random number generators are used in many areas of engineering, computer science, most notably in simulations and cryptographic applications. There are true random number generators (TRNG) and pseudo random number generators (PRNG). Only a true random number generator is secure because the output bits are non-repeating and nonreproducible. As society has become more dependent on electronic technology the need for true random number generators has increased due to processes that require encryption in everyday use. A fast true random number generator on a field programmable gate array presents digital designers with the ability to have the generator on chip. Since random bits do not have to be brought into the processes from an outside source, they cannot be compromised. An oscillator sampling technique has proved to be an effective TRNG in a Xilinx FPGA. This research examines how the time of the differences in period of the two oscillators, the size of the jitter zone, and whether sampling on the rising and falling edge of the oscillator rather than just the rising edge affects the randomness of the TRNG. The proportion of the size of the jitter zone compared to the period difference between the two oscillators limits the performance of this technique. As the jitter zone gets larger, the proportion of the jitter zone to the difference in periods of the oscillators must increase for the output to remain random. Increasing the output rate by sampling on the rising and falling edge instead of only the rising was not effective. The output was random for only a jitter zone of 24 ps with a period difference of 50 ps and 100 ps

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