Random number generators (RNGs) are widely used in conducting Monte Carlo simulation studies, which are important in the field of statistics for comparing power, mean differences, or distribution shapes between statistical approaches. Statistical results, however, may differ when different random number generators are used. Often older methods have been blindly used with no understanding of their limitations. Many random functions supplied with computers today have been found to be comparatively unsatisfactory. In this study, five multiplicative linear congruential generators (MLCGs) were chosen which are provided in the following statistical packages: RANDU (IBM), RNUN (IMSL), RANUNI (SAS), UNIFORM(SPSS), and RANDOM (BMDP). Using a personal computer (PC), an empirical investigation was performed using five criteria: period length before repeating random numbers, distribution shape, correlation between adjacent numbers, density of distributions and normal approach of random number generator (RNG) in a normal function. All RNG FORTRAN programs were rewritten into Pascal which is more efficient language for the PC. Sets of random numbers were generated using different starting values. A good RNG should have the following properties: a long enough period; a well-structured pattern in distribution; independence between random number sequences; random and uniform distribution; and a good normal approach in the normal distribution. Findings in this study suggested that the above five criteria need to be examined when conducting a simulation study with large enough sample sizes and various starting values because the RNG selected can affect the statistical results. Furthermore, a study for purposes of indicating reproducibility and validity should indicate the source of the RNG, the type of RNG used, evaluation results of the RNG, and any pertinent information related to the computer used in the study. Recommendations for future research are suggested in the area of other RNGs and methods not used in this study, such as additive, combined, mixed and shifted RNGs.

Random numbers are important for gaming, simulation and cryptography. Random numbers have been generated using analog circuitry. Two problems exist with using analog circuits in a digital design: (1) analog components require an analog circuit designer to insure proper structure and functionality and (2) analog components are not easily transmigrated into a different fabrication technology. This paper proposes a class of random number generators that are constructed using only digital components and typical digital design methodology. The proposed classification is called divergent path since the path of generated numbers through the range of possible values diverges at every sampling. One integrated circuit was fabricated and several models were synthesized into a FPGA. Test results are given.

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International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / A significant problem in the processing chain of a low resolution quantization system is the Analog to Digital converter quantization error. The classical model of quantization treats the error generated as a random additive process that is independent of the input and uniformly distributed. This model is valid for complex or random input signals that are large relative to a least significant bit. But the model fails catastrophically for small, simple signals applied to high resolution quantization systems, and in addition, the model fails for simple signals applied to low resolution quantization systems, i.e. one to 6 bits resolution. This paper will discuss a means of correcting this problem by the application of dither. Two methods of dither will be discussed as well as a real-life implementation of the techniques.

Random number generator is a key component for strengthening and securing the confidentiality of electronic communications. Random number generators can be divided as either pseudo random number generators or true random number generators. A pseudo random number generator produces a stream of numbers that appears to be random but actually follow predefined sequence. A true random number generator produces a stream of unpredictable numbers that have no defined pattern. There has been growing interest to design true random number generator in past few years. Several Field Programmable Gate Array (FPGA) and Application Specific Integrated Circuit (ASIC) based approaches have been used to generate random data that requires analog circuit. RNGs having analog circuits demand for more power and area. These factors weaken hardware analog circuit-based RNG systems relative to hardware completely digital-based RNGs systems. This thesis is focused on the design of completely digital true random number generator ASIC.

by Siu Chi Sang Obadiah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 66-68). / Abstracts in English and Chinese. / Chapter 1 --- Pseudorandom Number Generator --- p.5 / Chapter 1.1 --- Introduction --- p.5 / Chapter 1.2 --- Statistical Indistingushible and Entropy --- p.7 / Chapter 1.3 --- Example of PNG --- p.9 / Chapter 2 --- Basic Knowledge of Cellular Automata --- p.12 / Chapter 2.1 --- Introduction --- p.12 / Chapter 2.2 --- Elementary and Totalistic Cellular Automata --- p.14 / Chapter 2.3 --- Four classes of Cellular Automata --- p.17 / Chapter 2.4 --- Entropy --- p.20 / Chapter 3 --- Theoretical analysis of the CA PNG --- p.26 / Chapter 3.1 --- The Generator --- p.26 / Chapter 3.2 --- Global Properties --- p.27 / Chapter 3.3 --- Stability Properties --- p.31 / Chapter 3.4 --- Particular Initial States --- p.33 / Chapter 3.5 --- Functional Properties --- p.38 / Chapter 3.6 --- Computational Theoretical Properties --- p.42 / Chapter 3.7 --- Finite Size Behaviour --- p.44 / Chapter 3.8 --- Statistical Properties --- p.51 / Chapter 3.8.1 --- statistical test used --- p.54 / Chapter 4 --- Practical Implementation of the CA PNG --- p.56 / Chapter 4.1 --- The implementation of the CA PNG --- p.56 / Chapter 4.2 --- Applied to the set of integers --- p.58 / Chapter 5 --- Application to Cryptography --- p.61 / Chapter 5.1 --- Stream Cipher --- p.61 / Chapter 5.2 --- One Time Pad --- p.62 / Chapter 5.3 --- Probabilistic Encryption --- p.63 / Chapter 5.4 --- Probabilistic Encryption with RSA --- p.64 / Chapter 5.5 --- Prove yourself --- p.65 / Bibliography

by Yuen Ching Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 61-[63]). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Why use cryptography? --- p.1 / Chapter 1.2 --- Why is authentication important ？ --- p.2 / Chapter 1.3 --- What is the relationship between authentication and digital sig- nature? --- p.3 / Chapter 1.4 --- Why is random number important? --- p.3 / Chapter 2 --- Background --- p.5 / Chapter 2.1 --- Cryptography --- p.5 / Chapter 2.1.1 --- Symmetric key cryptography --- p.5 / Chapter 2.1.2 --- Asymmetric key cryptography --- p.7 / Chapter 2.1.3 --- Authentication --- p.8 / Chapter 2.2 --- Elliptic curve cryptography --- p.9 / Chapter 2.2.1 --- Mathematical background for Elliptic curve cryptography --- p.10 / Chapter 2.3 --- Pseudorandom number generator --- p.12 / Chapter 2.3.1 --- Linear Congruential Generator --- p.13 / Chapter 2.3.2 --- Inversive Congruential Generator --- p.13 / Chapter 2.3.3 --- PN-sequence generator --- p.14 / Chapter 2.4 --- Digital Signature Scheme --- p.14 / Chapter 2.5 --- Babai's lattice vector algorithm --- p.16 / Chapter 2.5.1 --- First Algorithm: Rounding Off --- p.17 / Chapter 2.5.2 --- Second Algorithm: Nearest Plane --- p.17 / Chapter 3 --- Several Digital Signature Schemes --- p.18 / Chapter 3.1 --- DSA --- p.19 / Chapter 3.2 --- Nyberg-Rueppel Digital Signature --- p.21 / Chapter 3.3 --- EC.DSA --- p.23 / Chapter 3.4 --- EC-Nyberg-Rueppel Digital Signature Scheme --- p.26 / Chapter 4 --- Miscellaneous Digital Signature Schemes and their PRNG --- p.29 / Chapter 4.1 --- DSA with LCG --- p.30 / Chapter 4.2 --- DSA with PN-sequence --- p.33 / Chapter 4.2.1 --- Solution --- p.35 / Chapter 4.3 --- DSA with ICG --- p.39 / Chapter 4.3.1 --- Solution --- p.40 / Chapter 4.4 --- EC_DSA with PN-sequence --- p.43 / Chapter 4.4.1 --- Solution --- p.44 / Chapter 4.5 --- EC一DSA with LCG --- p.45 / Chapter 4.5.1 --- Solution --- p.46 / Chapter 4.6 --- EC-DSA with ICG --- p.46 / Chapter 4.6.1 --- Solution --- p.47 / Chapter 4.7 --- Nyberg-Rueppel Digital Signature with PN-sequence --- p.48 / Chapter 4.7.1 --- Solution --- p.49 / Chapter 4.8 --- Nyberg-Rueppel Digital Signature with LCG --- p.50 / Chapter 4.8.1 --- Solution --- p.50 / Chapter 4.9 --- Nyberg-Rueppel Digital Signature with ICG --- p.51 / Chapter 4.9.1 --- Solution --- p.52 / Chapter 4.10 --- EC- Nyberg-Rueppel Digital Signature with LCG --- p.53 / Chapter 4.10.1 --- Solution --- p.54 / Chapter 4.11 --- EC- Nyberg-Rueppel Digital Signature with PN-sequence --- p.55 / Chapter 4.11.1 --- Solution --- p.56 / Chapter 4.12 --- EC-Nyberg-Rueppel Digital Signature with ICG --- p.56 / Chapter 4.12.1 --- Solution --- p.57 / Chapter 5 --- Conclusion --- p.59 / Bibliography --- p.61