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TestU01: A C library for empirical testing of random number generators
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2007
"... 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 ot ..."
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Cited by 85 (3 self)
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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 widelyused software. The tests can be applied to instances of the generators predefined in the library, or to userdefined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the paper 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.
High Quality Uniform Random Number Generation Through LUT Optimised Linear Recurrences
"... This paper describes a class of FPGAspecific uniform random number generators with a 2 k − 1 length period, which can provide k random bits percycle for the cost of k Lookup Tables (LUTs) and k flipflops. The generator is based on a binary linear recurrence, but with a recurrence matrix optimised ..."
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Cited by 32 (18 self)
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This paper describes a class of FPGAspecific uniform random number generators with a 2 k − 1 length period, which can provide k random bits percycle for the cost of k Lookup Tables (LUTs) and k flipflops. The generator is based on a binary linear recurrence, but with a recurrence matrix optimised for LUT based architectures. It avoids many of the problems and inefficiencies associated with LFSRs and Tausworthe generators, while retaining the ability to efficiently skip ahead in the sequence. In particular we show that this class of generators produce the highest sample rate for a given area compared to LFSR and Tausworthe generators. The statistical quality of this type of generators is very good, and can be used to create small and fast generators with long periods which pass all common empirical tests, such as Diehard, Crush, BigCrush and the NIST cryptographic tests. 1.
TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators
, 2007
"... This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many spec ..."
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Cited by 27 (2 self)
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This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many specific generators proposed in the literature or found in widelyused software. It provides general implementations of the classical statistical tests for random number generators, as well as several others proposed in the literature, and some original ones. These tests can be applied to the generators predefined in the library and to userdefined generators. Specific tests suites for either sequences of uniform random numbers in [0, 1] or bit sequences are also available. Basic tools for plotting vectors of points produced by generators are provided as well. Additional software permits one 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.
An application of finite field: Design and implementation of 128bit instructionbased fast pseudorandom number generator
, 2007
"... (1) SIMDoriented Mersenne Twister (SFMT) is a new pseudorandom number generator (PRNG) which uses 128bit Single Instruction Multiple Data (SIMD) operations. SFMT is designed and implemented on C language with SIMD extensions and also implemented on standard C without SIMD. (2) Properties of SFMT a ..."
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Cited by 10 (0 self)
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(1) SIMDoriented Mersenne Twister (SFMT) is a new pseudorandom number generator (PRNG) which uses 128bit Single Instruction Multiple Data (SIMD) operations. SFMT is designed and implemented on C language with SIMD extensions and also implemented on standard C without SIMD. (2) Properties of SFMT are studied by using finite field theories, and they are shown to be equal or better than Mersenne Twister (MT), which is a widely used PRNG. (3) Generation speed of SFMT is measured on Intel Pentium M, Pentium IV, AMD Athlon 64 and PowerPC G4. It is shown to be about two times faster than MT implemented using SIMD. 1
Pseudorandom number generators for Monte Carlo simulations on ATI Graphics Processing Units
 Comput. Phys. Commun
, 2011
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The MD6 hash function A proposal to NIST for SHA3
, 2008
"... This report describes and analyzes the MD6 hash function and is part of our submission package for MD6 as an entry in the NIST SHA3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desir ..."
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Cited by 3 (1 self)
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This report describes and analyzes the MD6 hash function and is part of our submission package for MD6 as an entry in the NIST SHA3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desired size from 1 to 512 bits, inclusive, including
Comparison of Point Sets and Sequences for QuasiMonte Carlo and for Random Number Generation
"... Algorithmic random number generators require recurring sequences with very long periods and good multivariate uniformity properties. Point sets and sequences for quasiMonte Carlo numerical integration need similar multivariate uniformity properties as well. It then comes as no surprise that both ty ..."
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Cited by 3 (0 self)
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Algorithmic random number generators require recurring sequences with very long periods and good multivariate uniformity properties. Point sets and sequences for quasiMonte Carlo numerical integration need similar multivariate uniformity properties as well. It then comes as no surprise that both types of applications share common (or similar) construction methods. However, there are some differences in both the measures of uniformity and the construction methods used in practice. We briefly survey these methods and explain some of the reasons for the differences.
The MD6 Hash Function
 Advances in Cryptology  Crypto 2008
"... This report describes and analyzes the MD6 hash function, an entry in the NIST SHA3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desired size from 1 to 512 bits, inclusive, including ..."
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Cited by 2 (0 self)
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This report describes and analyzes the MD6 hash function, an entry in the NIST SHA3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desired size from 1 to 512 bits, inclusive, including
Random Numbers for Parallel Computers: Requirements and Methods
, 2014
"... We examine the requirements and the available methods and software to provide (or imitate) uniform random numbers in parallel computing environments. In some settings, the goal is to use parallel processors to fill up rapidly a large array of random numbers. In other settings, thousands or millions ..."
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Cited by 2 (2 self)
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We examine the requirements and the available methods and software to provide (or imitate) uniform random numbers in parallel computing environments. In some settings, the goal is to use parallel processors to fill up rapidly a large array of random numbers. In other settings, thousands or millions of independent streams of random numbers are required, each one computed on a single processing element.