As the broad implementation and use of wireless sensor nodes in Internet of Things (IOT) devices increase over the years, securing personal data becomes a growing issue. Physical unclonable functions (PUFs) and random number generators (RNGs) provide methods to generate security keys for data encryption. Transducers used in the energy harvesting systems of wireless sensor nodes, can generate the PUFs and RNGs. These transducers include piezoelectric devices (piezo), thermoelectric generators (TEG) and solar cells. This research studies the electrical properties of transducers at normal and low operating levels for electrical responses that can be used in PUF generation and random number generation respectively. The PUF generation discussed in this study analyzes the resonance frequency of 10 piezos, and the open-circuit voltages of 5 TEGs and 5 solar cells. The transducers are tested multiple times over a 10-day period to evaluate PUF reproducibility and reliability characteristics. The random number generation is accomplished by applying a low-level vibration, thermal or light excitation to each respective transducer. The generated electrical signals are amplified and digitally processed and analyzed using the National Institute of Standards and Technology (NIST) Statistical Test Suite. The experiment results for the PUF generation are promising and indicate that the piezos are the better choice due to their stable frequency output. Each transducer was able to produce random numbers and pass the NIST tests, but the TEGs passed the NIST tests more often than the other transducers. These results offer a preliminary basis for transducers to be used directly in security applications. / Master of Science

The thesis deals with issues of random numbers, their generating and use in cryptography. Introduction of work is aimed to resolution of random number generators and pseudo--random number generators. There is also included often used dividing generators on software and hardware. We mention advantages and disadvantages of each type and area of their use. Then we describe examples of random and pseudorandom numbers, mainly hardware based on physical phenomenon such as the decay of radioactive material or use atmospheric noise. The following part is devoted to suggestion own random number generator and a description of its functionality. In the second half of the work we devote to the field of cryptography. We know basic types of cryptographic systems, namely symmetric and asymmetric cryptosystems. We introduce a typical representant the various type and their properties. At the end of the work we again return to our random number generator and verify the randomness generated numbers and obtained cryptograms.

In the design of voltage-controlled oscillators (VCOs) for communication systems, timing jitter is of major concern since it is the largest contributor to the bit-error rate. The latest deep submicron processes provide the possibility of higher oscillator speed at the cost of increased device noise and a higher 1/f noise corner. Therefore it is crucial to characterize the upconverted 1/f noise for practical applications. This dissertation presents a simple model to relate the time domain jitter and frequency domain phase noise in the presence of non-negligible 1/f noise sources. It will simplify the design, simulation, and testing of the PLL, since with this technique only the open loop VCO needs to be considered. Design methodologies for white noise dominated ring oscillators and PLLs are also developed by analyzing the upconverted thermal noise in time domain using a LTI model. The trade-off and relationship between jitter, speed, power dissipation and VCO geometry are evaluated for different applications. This model is supported by the measured data from 24 ring oscillators with different geometry fabricated in TSMC 0.18um process. The theory developed in this dissertation is applied to the design of PLL- and DLL- based true random number generators (TRNG) for application in the area of“smart cards". New architectures of dual-oscillator sampling and delay-line sampling are proposed for random number generation, which has the advantage of lower power dissipation and lower cost over traditional approaches. Both structures are implemented in test chips fabricated in AMI 1.5um process. The PLL-based TRNG passed the NIST SP800-22 statistical test suite and the DLL-based TRNG passed both the NIST SP800-22 statistical test suite and the Diehard battery of tests.

This diploma thesis deals with creation of several random number generators. The data from these prototypes are then compared according to various aspects and statistical methods. The reader is familiar with the basic concepts, the existing random number generators and the technologies used.

Communication security is a very important part of modern life. A crucial aspect of security is the ability to identify with near 100% certainty who is on the other side of a connection. This problem can be overcome through the use of random number generators, which create unique identities for each person in a network. The effectiveness of an identity is directly proportional to how random a generator is. The speed at which a random number can be delivered is a critical factor in the design of a random number generator. This thesis covers the design and fabrication of three ring oscillator based truly random number generators, the first two of which were fabricated in 0.13µ m CMOS technology. The randomness from this type of random number generator originates from phase noise in a ring oscillator. The second and third ring oscillators were designed to have a low slew rate at the inverter switching threshold. The outputs of these designs showed vast increases in timing jitter compared to the first design. The third design exhibited improved randomness with respect to the second design.

Pulsars, as rotating magnetised neutron stars got much attention during the last 40 years since their discovery. Observations revealed them to be gamma-ray emitters with energies continuing up to the sub 100 GeV region. Better observation of this upper energy cut-off region will serve to enhance our theoretical understanding of pulsars and neutron stars. The H-test has been used the most extensively in the latest periodicity searches, whereas other tests have limited applications and are unsuited for pulsar searches. If the probability distribution of a test statistic is not accurately known, it is possible that, after searching through many trials, a probability for uniformity can be given, which is much smaller than the real value, possibly leading to false detections. The problem with the H-test is that one must obtain the distribution by simulation and cannot do so analytically. For such simulations, random numbers are needed and are usually obtained by utilising so-called pseudo-random number generators, which are not truly random. This immediately renders such generators as useless for the simulation of the distribution of the H-test. Alternatively there exists hardware random number generators, but such devices, apart from always being slow, are also expensive, large and most still don't exhibit the true random nature required. This was the motivation behind the development of a hardware random number generator which provides truly random U(0,l) numbers at very high speed and at low cost The development of and results obtained by such a generator are discussed. The device delivered statistically truly random numbers and was already used in a small simulation of the H-test distribution. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2005.

Communication security is a very important part of modern life. A crucial aspect of security is the ability to identify with near 100% certainty who is on the other side of a connection. This problem can be overcome through the use of random number generators, which create unique identities for each person in a network. The effectiveness of an identity is directly proportional to how random a generator is. The speed at which a random number can be delivered is a critical factor in the design of a random number generator. This thesis covers the design and fabrication of three ring oscillator based truly random number generators, the first two of which were fabricated in 0.13µ m CMOS technology. The randomness from this type of random number generator originates from phase noise in a ring oscillator. The second and third ring oscillators were designed to have a low slew rate at the inverter switching threshold. The outputs of these designs showed vast increases in timing jitter compared to the first design. The third design exhibited improved randomness with respect to the second design.

Cryptosystems are used to provide security in communications and data transmissions. Stream ciphers are private key systems that are often used to transform large volumn data. In order to have security, key streams used in stream ciphers must be fully analyzed so that they do not contain specific patterns, statistical infomation and structures with which attackers are able to quickly recover the entire key streams and then break down the systems. Based on different schemes to generate sequences and different ways to represent them, there are a variety of stream cipher analyses. The most important one is the linear analysis based on linear feedback shift registers (LFSRs) which have been extensively studied since the 1960's. Every sequence over a finite field has a well defined linear complexity. If a sequence has small linear complexity, it can be efficiently recoverd by Berlekamp-Messay algorithm. Therefore, key streams must have large linear complexities. A lot of work have been done to generate and analyze sequences that have large linear complexities. In the early 1990's, Klapper and Goresky discovered feedback with carry shift registers over Z/(p) (p-FCSRS), p is prime. Based on p-FCSRs, they developed a stream cipher analysis that has similar properties to linear analysis. For instance, every sequence over Z/(p) has a well defined p-adic complexity and key streams of small p-adic complexity are not secure for use in stream ciphers. This disstation focuses on stream cipher analysis based on feedback with carry shift registers. The first objective is to develop a stream cipher analysis based on feedback with carry shift registers over Z/(N) (N-FCSRs), N is any integer greater than 1, not necessary prime. The core of the analysis is a new rational approximation algorithm that can be used to efficiently compute rational representations of eventually periodic N-adic sequences. This algorithm is different from that used in $p$-adic sequence analysis which was given by Klapper and Goresky. Their algorithm is a modification of De Weger's rational approximation algorithm. The second objective is to generalize feedback with carry shift register architecture to more general algebraic settings which are called algebraic feedback shift registers (AFSRs). By using algebraic operations and structures on certain rings, we are able to not only construct feedback with carry shift registers, but also develop rational approximation algorithms which create new analyses of stream ciphers. The cryptographic implication of the current work is that any sequences used in stream ciphers must have large N-adic complexities and large AFSR-based complexities as well as large linear complexities.

Pulsars, as rotating magnetised neutron stars got much attention during the last 40 years since their discovery. Observations revealed them to be gamma-ray emitters with energies continuing up to the sub 100 GeV region. Better observation of this upper energy cut-off region will serve to enhance our theoretical understanding of pulsars and neutron stars. The H-test has been used the most extensively in the latest periodicity searches, whereas other tests have limited applications and are unsuited for pulsar searches. If the probability distribution of a test statistic is not accurately known, it is possible that, after searching through many trials, a probability for uniformity can be given, which is much smaller than the real value, possibly leading to false detections. The problem with the H-test is that one must obtain the distribution by simulation and cannot do so analytically. For such simulations, random numbers are needed and are usually obtained by utilising so-called pseudo-random number generators, which are not truly random. This immediately renders such generators as useless for the simulation of the distribution of the H-test. Alternatively there exists hardware random number generators, but such devices, apart from always being slow, are also expensive, large and most still don't exhibit the true random nature required. This was the motivation behind the development of a hardware random number generator which provides truly random U(0,l) numbers at very high speed and at low cost The development of and results obtained by such a generator are discussed. The device delivered statistically truly random numbers and was already used in a small simulation of the H-test distribution. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2005.

The class of generalized feedback shift register (GFSR) random number generators was a promising method for random number generation in the 1980's, but was abandoned because of some flaws such as poor performance on certain tests for randomness. The poor performance may be due to the choice of primitive polynomials used in the generators, rather than inherent flaws in the method. The original GFSR generators were all based on primitive trinomials. This project examines several alternative choices of primitive polynomials with more than one "interior" term to address this problem and hopefully provide access to good random number generators.