Many real-world applications use random numbers generated by pseudo-random number and true random number generators (TRNG). Unlike pseudo-random number generators which rely on an input seed to generate random numbers, a TRNG relies on a non-deterministic source to generate aperiodic random numbers. In this research, we develop a novel and generic software-based TRNG using a random source extracted from compute architectures of today. We show that the non-deterministic events such as race conditions between compute threads follow a near Gamma distribution, independent of the architecture, multi-cores or co-processors. Our design improves the distribution towards a uniform distribution ensuring the stationarity of the sequence of random variables.
We improve the random numbers statistical deficiencies by using a post-processing stage based on a heuristic evolutionary algorithm. Our post-processing algorithm is composed of two phases: (i) Histogram Specification and (ii) Stationarity Enforcement. We propose two techniques for histogram equalization, Exact Histogram Equalization (EHE) and Adaptive EHE (AEHE) that maps the random numbers distribution to a user-specified distribution. EHE is an offline algorithm with O(NlogN). AEHE is an online algorithm that improves performance using a sliding window and achieves O(N). Both algorithms ensure a normalized entropy of (0:95; 1:0].
The stationarity enforcement phase uses genetic algorithms to mitigate the statistical deficiencies from the output of histogram equalization by permuting the random numbers until wide-sense stationarity is achieved. By measuring the power spectral density standard deviation, we ensure that the quality of the numbers generated from the genetic algorithms are within the specified level of error defined by the user. We develop two algorithms, a naive algorithm with an expected exponential complexity of E[O(eN)], and an accelerated FFT-based algorithm with an expected quadratic complexity of E[O(N2)]. The accelerated FFT-based algorithm exploits the parallelism found in genetic algorithms on a homogeneous multi-core cluster. We evaluate the effects of its scalability and data size on a standardized battery of tests, TestU01, finding the tuning parameters to ensure wide-sense stationarity on long runs. / October 2016
| Identifer | oai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/31619 |
| Date | 01 September 2016 |
| Creators | MIJARES CHAN, JOSE JUAN |
| Contributors | Thomas, Gabriel (Elec. & Comp. Eng) Thulasiraman, Parimala (Computer Science), Yahampath, Pradeepa (Elec. & Comp. Eng) Pistorius, Stephen (Physics & Astronomy) Nayak, Amiya (University of Ottawa) |
| Source Sets | University of Manitoba Canada |
| Detected Language | English |
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