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An introduction on random numbers, their history and applications is given, along with explanations of different methods currently used to generate them. Such generators can be of different kinds, and in particular they can be based on physical systems or algorithmic procedures. The latter type of procedures gives rise to pseudo-random number generators. Specifically, several such generators which are based on elliptic curves are examined. Therefore, in order to ease understanding, a basic primer on elliptic curves over fields and the operations arising from their group structure is also provided. Empirical tests to verify randomness of generated sequences are then considered. Afterwards, there are some statistical considerations and observations about theoretical properties of the generators at hand, useful in order to use them optimally. Finally, several randomly generated curves are created and used to produce pseudo-random sequences which are then tested by means of the previously described generators. In the end, an analysis of the results is attempted and some final considerations are made.

International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, California / In computer simulations of communication systems, linear congruential generators and shift registers are typically used to model noise and data sources. These generators are often assumed to be close to ideal (i.e. delta correlated), and an insignificant source of error in the simulation results. The samples generated by these algorithms have non-ideal autocorrelation functions, which may cause a non-uniform distribution in the data or noise signals. This error may cause the simulation bit-error-rate (BER) to be artificially high or low. In this paper, the problem is described through the use of confidence intervals. Tests are performed on several pseudo-random generators to access which ones are acceptable for computer simulation.

Noise radar systems have become more prevalent over the past couple of decades due to their superior performance over conventional continuous-wave and pulsed-wave radar systems in certain applications. However, one limiting factor of noise radar systems has been the generation of ultrabroadband waveforms. This thesis proposes a novel application of programmable pseudo-random bit generators (PRBGs) for use in noise radar applications. A long-sequence high-speed PRBG was designed using a low-cost and low-power complementary metal oxide semiconductor (CMOS) technology. The proposed circuit has a sequence length of approximately 4.3 Gbits and was designed to operate at 1 GHz providing a data rate of 1 Gbit/s. This new waveform generation technique would eliminate the requirement of a large variable delay-line (transmission-line) and reduce the power required by noise radar systems. It would allow such systems to become much more compact and create the opportunity for the move towards hand-held devices. It would further allow easier implementation of bistatic radar systems where the transmitting and receiving sites are physically far from one another. In addition, this programmable long-sequence PRBG could have applications in cryptology, communications, and other areas where the generation of high-speed random bit sequences is paramount. Unfortunately, an ASIC (application specific integrated circuit) design process documentation error rendered the fabricated IC's unusable. The error was caused by not enabling the input pads of the IC, which required an undocumented edit to the gate-level design file generated by Synopsys \textit{Design Vision}. Consequently, the circuit had to be realized on a field-programmable gate array (FPGA), which performed as expected, albeit at a lower frequency of 50 MHz. The PSD of the FPGA implementation created the expected output of a sinc-squared function with the first null at the clock frequency. This result proves that a LFSR PRBG is a viable noise source for use in noise radar systems. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2013-10-31 14:48:27.422

Vision-based positioning systems are founded primarily on a simple image processing technique of identifying various visually significant key-points in an image and relating them to a known coordinate system in a scene. Fiducial markers are used as a means of providing the scene with a number of specific key-points, or features, such that computer vision algorithms can quickly identify them within a captured image. This thesis proposes a reliable vision-based positioning system which utilizes a unique pseudo-random fiducial marker. The marker itself offers 49 distinct feature points to be used in position estimation. Detection of the designed marker occurs after an integrated process of adaptive thresholding, k-means clustering, color classification, and data verification. The ultimate goal behind such a system would be for indoor localization implementation in low cost autonomous mobile platforms.

In this thesis, we present constructions of leakage-resilient cryptographic primitives, and we give black-box impossibility results for certain classes of constructions of pseudo-random number generators. The traditional approach for preventing side-channel attacks has been primarily hardware-based. Recently, there has been significant progress in developing algorithmic approaches for preventing such attacks. These algorithmic approaches involve modeling side-channel attacks as {\em leakage} on the internal state of a device; constructions secure against such leakage are {\em leakage-resilient}. We first consider the problem of storing a key and computing on it repeatedly in a leakage-resilient manner. For this purpose, we define a new primitive called a {\em key proxy}. Using a fully-homomorphic public-key encryption scheme, we construct a leakage-resilient key proxy. We work in the ``only computation leaks'' leakage model, tolerating a logarithmic number of bits of polynomial-time computable leakage per computation and an unbounded total amount of leakage. We next consider the problem of verifying that a message sent over a public channel has not been modified, in a setting where the sender and the receiver have previously shared a key, and where the adversary controls the public channel and is simultaneously mounting side-channel attacks on both parties. Using only the assumption that pseudo-random generators exist, we construct a leakage-resilient shared-private-key authenticated session protocol. This construction tolerates a logarithmic number of bits of polynomial-time computable leakage per computation, and an unbounded total amount of leakage. This leakage occurs on the entire state, input, and randomness of the party performing the computation. Finally, we consider the problem of constructing a large-stretch pseudo-random generator given a one-way permutation or given a smaller-stretch pseudo-random generator. The standard approach for doing this involves repeatedly composing the given object with itself. We provide evidence that this approach is necessary. Specifically, we consider three classes of constructions of pseudo-random generators from pseudo-random generators of smaller stretch or from one-way permutations, and for each class, we give a black-box impossibility result that demonstrates a contrast between the stretch that can be achieved by adaptive and non-adaptive black-box constructions.

In this thesis, we present constructions of leakage-resilient cryptographic primitives, and we give black-box impossibility results for certain classes of constructions of pseudo-random number generators. The traditional approach for preventing side-channel attacks has been primarily hardware-based. Recently, there has been significant progress in developing algorithmic approaches for preventing such attacks. These algorithmic approaches involve modeling side-channel attacks as {\em leakage} on the internal state of a device; constructions secure against such leakage are {\em leakage-resilient}. We first consider the problem of storing a key and computing on it repeatedly in a leakage-resilient manner. For this purpose, we define a new primitive called a {\em key proxy}. Using a fully-homomorphic public-key encryption scheme, we construct a leakage-resilient key proxy. We work in the ``only computation leaks'' leakage model, tolerating a logarithmic number of bits of polynomial-time computable leakage per computation and an unbounded total amount of leakage. We next consider the problem of verifying that a message sent over a public channel has not been modified, in a setting where the sender and the receiver have previously shared a key, and where the adversary controls the public channel and is simultaneously mounting side-channel attacks on both parties. Using only the assumption that pseudo-random generators exist, we construct a leakage-resilient shared-private-key authenticated session protocol. This construction tolerates a logarithmic number of bits of polynomial-time computable leakage per computation, and an unbounded total amount of leakage. This leakage occurs on the entire state, input, and randomness of the party performing the computation. Finally, we consider the problem of constructing a large-stretch pseudo-random generator given a one-way permutation or given a smaller-stretch pseudo-random generator. The standard approach for doing this involves repeatedly composing the given object with itself. We provide evidence that this approach is necessary. Specifically, we consider three classes of constructions of pseudo-random generators from pseudo-random generators of smaller stretch or from one-way permutations, and for each class, we give a black-box impossibility result that demonstrates a contrast between the stretch that can be achieved by adaptive and non-adaptive black-box constructions.

Vision-based positioning systems are founded primarily on a simple image processing technique of identifying various visually significant key-points in an image and relating them to a known coordinate system in a scene. Fiducial markers are used as a means of providing the scene with a number of specific key-points, or features, such that computer vision algorithms can quickly identify them within a captured image. This thesis proposes a reliable vision-based positioning system which utilizes a unique pseudo-random fiducial marker. The marker itself offers 49 distinct feature points to be used in position estimation. Detection of the designed marker occurs after an integrated process of adaptive thresholding, k-means clustering, color classification, and data verification. The ultimate goal behind such a system would be for indoor localization implementation in low cost autonomous mobile platforms.

Vision-based positioning systems are founded primarily on a simple image processing technique of identifying various visually significant key-points in an image and relating them to a known coordinate system in a scene. Fiducial markers are used as a means of providing the scene with a number of specific key-points, or features, such that computer vision algorithms can quickly identify them within a captured image. This thesis proposes a reliable vision-based positioning system which utilizes a unique pseudo-random fiducial marker. The marker itself offers 49 distinct feature points to be used in position estimation. Detection of the designed marker occurs after an integrated process of adaptive thresholding, k-means clustering, color classification, and data verification. The ultimate goal behind such a system would be for indoor localization implementation in low cost autonomous mobile platforms.

Vision-based positioning systems are founded primarily on a simple image processing technique of identifying various visually significant key-points in an image and relating them to a known coordinate system in a scene. Fiducial markers are used as a means of providing the scene with a number of specific key-points, or features, such that computer vision algorithms can quickly identify them within a captured image. This thesis proposes a reliable vision-based positioning system which utilizes a unique pseudo-random fiducial marker. The marker itself offers 49 distinct feature points to be used in position estimation. Detection of the designed marker occurs after an integrated process of adaptive thresholding, k-means clustering, color classification, and data verification. The ultimate goal behind such a system would be for indoor localization implementation in low cost autonomous mobile platforms.