The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is presented here as a mathematical tool suitable for the analysis of time series and signals. To show the potential that the SWM has to analyze many different types of time series, the results of the analysis of a time series composed of a sequence of 10,000 numerical values are presented here. These va...

An urn contains balls of d ≥ 2 colors. At each time n ≥ 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag An,1, . . . , An,d be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT’s are available for such urns. In real problems, however, it is more reasonable to assume EAn,j = EAn,1 whenever n ≥ 1 and 1 ≤ j ≤ d0,...

This thesis begins with a general overview of pseudo-random number generators and some of their applications. This thesis then describes their applications to cryptography, and some additional requirements imposed by cryptography. This thesis then provides an introduction to the ring of quaternions, and discusses how they can be included in pseudo-random number generators. Finally, this thesis ...

Several widely used uniform random number generators have been extensively subjected to three commonly used statistical tests of uniformity and randomness. The object was 1) to examine the power of these statistical tests to discriminate between "good" and "bad" random number generators, 11) to correlate these results with recently proposed mathematical characterizations of random number genera...

We study a random number generation test where subjects are requested to write sequences of digits as random as possible. The results of our experiments are reported and a model-based approach is proposed for the analysis of the sequences from the test.

Fast and reliable pseudo-random number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with excellent statistical properties. We also discuss the problem of initialising random number generators, and con...

Microsoft attempted to implement theWichmann–Hill RNG in Excel 2003 and failed; it did not just produce numbers between zero andunity, itwould also produce negative numbers. Microsoft issued a patch that allegedly fixed the problem so that the patched Excel 2003 and Excel 2007 now implement the Wichmann–Hill RNG, as least according to Microsoft. We show thatwhatever RNG it is thatMicrosoft has ...

SUMMARY This paper presents an oscillator-based true random number generator (TRNG) that dynamically unbiases 0/1 probability. The proposed TRNG automatically adjusts the duty cycle of a fast oscillator to 50%, and generates unbiased random numbers tolerating process variation and dynamic temperature fluctuation. A prototype chip of the proposed TRNG was fabricated with a 65 nm CMOS process. Me...

Algorithmic post-processing is used to overcome statistical deficiencies of physical random number generators. We show that the quasigroup based approach for post-processing random numbers described in [MGK05] is ineffective and very easy to attack. We also suggest new algorithms which extract considerably more entropy from their input than the known algorithms with an upper bound for the numbe...

Conventional random number generators provide the speed but not necessarily the high quality output streams needed for large-scale stochastic simulations. Cryptographically-based generators, on the other hand, provide superior quality output but are often deemed too slow to be practical for use in large simulations. We combine these two approaches to construct a family of hybrid generators that...