An Alternative to Pseudo-random Number Generators

Two methods for generating sets of vectors which approximate normal distributio

On Quaternionic Pseudo-Random Number Generators

There is no dearth of published literature on the design, implementation, analysis, or use of pseudo-random number generators or PRNGs. For example, [6] [7] [14] and the references therein, provide a broad overview and firm grounding for the subject. This report complements and elaborates upon the work of McKeever [9], who investigated PRNGs constructed in a non-commutative setting with the target application being so-called cryptographically secure PRNGs as discussed in [12] or [13]. Novel solutions to the problem of designing cryptographically secure PRNGS continue to be proposed [1] [2] [10] [15], so despite the caution and skepticism required, the area remains active. The concept elaborated upon here is computation in a finite non-commutative object which is more than a matrix ring over a finite field. Specifically, we consider computation in a homomorphic image of a maximal order of an ordinary quaternion algebra. In Section Two we develop the necessary algebraic machinery. In Section Three we consider PRNG design in this computational setting. In Section Four we attempt some preliminary analysis of the PRNGs described. In Section Five we offer some final remarks and conclusions

Pseudo-random number generators.

by Lee Kim-hung.Thesis (M.Phil.)--Chinese University of Hong Kong.Bibliography: leaf 60

Pseudo-random number generators for Monte Carlo simulations on Graphics Processing Units

Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX generator is found to be the most appropriate for using on GPU in Monte Carlo simulations. The brief review of the pseudo-random number generators used in modern software packages for Monte Carlo simulations in high-energy physics is present.Comment: 31 pages, 9 figures, 3 table

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70This paper is a review of some applications of probabilistic models in cryptography, coding theory and tests for pseudo-random number generators (PRNG). Using quasigroup transformations, we design streams ciphers and error-correcting codes with suitable properties. Some tests for pseudo random number generators are designed, too. They are based on random walk on discrete coordinate plane

Random walk tests for pseudo-random number generators

It is well known that there are no perfectly good generators of random number sequences, implying the need of testing the randomness of the sequences produced by such generators. There are many tests for measuring the uniformity of random sequences, and here we propose a few new ones, designed by random walks. The experiments we have made show that our tests discover some discrepancies of random sequences passing many other tests

A Repetition Test for Pseudo-Random Number Generators

A new statistical test for uniform pseudo-random number generators (PRNGs) is presented. The idea is that a sequence of pseudo-random numbers should have numbers reappear with a certain probability. The expectation time that a repetition occurs provides the metric for the test. For linear congruential generators (LCGs) failure can be shown theoretically. Empirical test results for a number of commonly used PRNGs are reported, showing that some PRNGs considered to have good statistical properties fail. A sample implementation of the test is provided over the Interne