Class Of Random Number Generators Research Articles

SOURCES OF RANDOMNESS FOR USE IN RANDOM NUMBER GENERATION

Efficient generation of random numbers plays significant role in cryptographic applications. Such a generator has to produce unpredictable and un-correlated random bits. Random number generators are classified as pseudo-random number generators (PRNGs) and true random number generators (TRNGs). The first ones have the disadvantage that they can be proven predictable, while the latter ones can produce true random bits but it is not easy to re-produce specific sequences or implement them in constrained environments and there may exist correlations and biases of produced sequences. A third class of random number generators has been introduced, called hybrid-random number generators (h-RNGs), where there is a combination of a cryptographically strong PRNGs or TRNGs which are seeded, and possibly re-seeded, through a source of randomness with high entropy. In this paper, we present an overview of various sources of randomness that can be used either as direct random number generators or as seed sources in h-RNGs, for application in embedded systems.

TestU01

We introduce TestU01 , a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator's period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely used software. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01 , the article provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.

A class of random number generators based on Weyl sequence

The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution, of stochastic differential equations. In this paper, a class of random number generators (RNGs) based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.

Moly flow..er—the computer program for calculation of vacuum system conductance

The paper presents a new computer program for calculating a conductance with a high precision, based on the Monte-Carlo (MC) method. The high accuracy of the calculations has been obtained by using high-quality random number generators (RNG), specially selected for this purpose. This allows us to extend the application field of the MC simulations and to reduce the uncertainty of the results to below 10 −5. The paper describes the principles of the program conception, compares the results obtained for various classes of RNG and also gives the values of the Clausing-type factors for elementary shapes.

On the performance of birthday spacings tests with certain families of random number generators

We examine how a statistical test based on discrete spacings between points, in one or more dimensions, detects the regularities in certain popular classes of random number generators. We provide a rule of thumb giving the minimal sample size for the test to reject the generator systematically, as a function of the generator’s size (or period length), for generator families such as the linear congruential, Taus worthe, non linear inversive, etc. Full period linear congruential generators with a good behavior in the spectral test, for example, start to fail the two-dimensional test decisively at sample sizes approximately equal to the cubic root of their period length (or modulus).

Lattice computations for random numbers

We improve on a lattice algorithm of Tezuka for the computation of the k-distribution of a class of random number generators based on finite fields. We show how this is applied to the problem of constructing, for such generators, an output mapping yielding optimal k-distribution.

On the lattice structure of the add-with-carry and subtract-with-borrow random number generators

Marsaglia and Zaman recently proposed new classes of random number generators, called add-with-carry (AWC) and subtract-with-borrow (SWB), which are capable of quickly generating very long-period (pseudo)-random number sequences using very little memory. We show that these sequences are essentially equivalent to linear congruential sequences with very large prime moduli. So, the AWC/SWB generators can be viewed as efficient ways of implementing such large linear congruential generators. As a consequence, the theoretical properties of such generators can be studied in the same way as for linear congruential generators, namely, via the spectral and lattice tests. We also show how the equivalence can be exploited to implement efficient jumping-ahead facilities for the AWC and SWB sequences. Our numerical examples illustrate the fact that AWC/SWB generators have extremely bad lattice structure in high dimensions.

A New Class of Random Number Generators

We introduce a new class of generators of two types: add-with-carry and subtract-with-borrow. Related to lagged-Fibonacci generators, the new class has interesting underlying theory, astonishingly long periods and provable uniformity for full sequences. Among several that we mention, we recommend particularly promising ones that will generate a sequence of $2^{1751}$ bits, or a sequence of $2^{1376}$ 32-bit integers, or a sequence of $2^{931}$ reals with 24-bit fractions--all using simple computer arithmetic (subtraction) and a few memory locations.

A random-number generator

A new class of random-number generators is described, based on a combination of the logical exclusive-or operation and the McLaren-Marsaglia mechanism. It is suitable for any word length, requires no multiple-precision arithmetic, and contains no hard-to-determine constants. Though no theory is available, numerical tests have shown it to be very satisfactory. Execution time is less than twice that of standard congruential generators.