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Fast and reliable random number generators for scientific computing, Lecture
 Proc. PARA'04 Workshop on the StateoftheArt inScientific Computing
"... Abstract. Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with exce ..."
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Abstract. Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with excellent statistical properties. We also discuss the problem of initialising random number generators, and consider how to combine two or more generators to give a better (though usually slower) generator. 1
PRNGlib: A Parallel Random Number Generator Library
, 1996
"... PRNGlib provides several pseudorandom number generators through a common interface on any Shared or Distributed Memory Parallel architecture. Common routines are specified to initialize the generators with appropriate seeds on each processor and to generate uniform or (normal, Poisson, exponential ..."
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PRNGlib provides several pseudorandom number generators through a common interface on any Shared or Distributed Memory Parallel architecture. Common routines are specified to initialize the generators with appropriate seeds on each processor and to generate uniform or (normal, Poisson, exponential) distributed random vectors. We concentrate on those generators which assure high quality (i.e., passing most of the empirical and theoretical tests), have a long period, and can be calculated quickly, also in parallel, i.e., it must be possible to generate the same random sequence independent of the number of processors. This splitting facility implies a method to skip over n pseudorandom numbers without calculating all intermediate values, i.e., an O(log n) algorithm is required. Taking into account these criteria Lagged Fibonacci, Generalized Shift Register, and Multiplicative Linear Congruential generators are implemented with (almost) arbitrary specifications for lags, multipliers, m...
Almost Irreducible and Almost Primitive Trinomials
 in Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams, Fields Institute
, 2003
"... Consider polynomials over GF(2). We de ne almost irreducible and almost primitive polynomials, explain why they are useful, and give some examples and conjectures relating to them. 2 ..."
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Consider polynomials over GF(2). We de ne almost irreducible and almost primitive polynomials, explain why they are useful, and give some examples and conjectures relating to them. 2
This is a Chapter from the Handbook of Applied Cryptography
, 1996
"... s), p.146, 1985. [790] J.L. MASSEY AND X. LAI, "Device for converting a digital block and the use thereof", European Patent # 482,154, 29 Apr 1992. [791] , "Device for the conversion of a digital block and use of same", U.S. Patent # 5,214,703, 25 May 1993. [792] J.L. MASSEY AND J.K. OMURA, "Meth ..."
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s), p.146, 1985. [790] J.L. MASSEY AND X. LAI, "Device for converting a digital block and the use thereof", European Patent # 482,154, 29 Apr 1992. [791] , "Device for the conversion of a digital block and use of same", U.S. Patent # 5,214,703, 25 May 1993. [792] J.L. MASSEY AND J.K. OMURA, "Method and apparatus for maintaining the privacy of digital messages conveyed by public transmission ", U.S. Patent # 4,567,600, 28 Jan 1986. [793] J.L. MASSEY AND R.A. RUEPPEL, "Linear ciphers and random sequence generators with multiple clocks", Advances in Cryptology Proceedings of EUROCRYPT 84 (LNCS 209), 7487, 1985. [794] J.L. MASSEY AND S. SERCONEK, "A Fourier transform approach to the linear complexity of nonlinearly filtered sequences", Advances in CryptologyCRYPTO '94 (LNCS 839), 332340, 1994. [795] M. MATSUI, "The first experimental cryptanalysis of the Data Encryption Standard", Advances in CryptologyCRYPTO '94 (LNCS 839), 111, 1994. [796] , "Linear cryptanalysis metho...
RANEXP: Experimental Random Number Generator Package
, 1994
"... this article, the general design of RANEXP is outlined and the generators included are briefly described. The theoretical background for these generators is not discussed here, since various textbooks and review articles cover this field. For details on the algorithms, chapter 3 of Knuth[5], chapter ..."
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this article, the general design of RANEXP is outlined and the generators included are briefly described. The theoretical background for these generators is not discussed here, since various textbooks and review articles cover this field. For details on the algorithms, chapter 3 of Knuth[5], chapter 6 of Bratley/Fox/Schrage[2], chapter 7 of Press et.al[11, 12] and the review articles by James[4] and Marsaglia[7] may be referenced. The bibliography of the separate RANEXP manual contains further references. The generators are implemented in ANSI C[1], which is wellsuited to efficiently implement those algorithms in a way fully conforming to the language standard, thus enhancing portability. A separate Fortran interface is provided which enables Fortran application programs to use the generators.
Primitive and Almost Primitive Trinomials
, 2002
"... We consider the problem of testing trinomials over GF(2) for irreducibility or primitivity. In particular, we consider trinomials whose degree r is a Mersenne exponent. We describe a new algorithm for testing primitivity of such trinomials. The algorithm has been used to find primitive trinomials of ..."
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We consider the problem of testing trinomials over GF(2) for irreducibility or primitivity. In particular, we consider trinomials whose degree r is a Mersenne exponent. We describe a new algorithm for testing primitivity of such trinomials. The algorithm has been used to find primitive trinomials of very high degree, e.g. r = 3021377. For certain r, primitive trinomials of degree r do not exist. We show how to overcome this difficulty by finding almost primitive trinomials polynomials with a primitive factor of degree r and overall degree slightly greater than r. In most applications, almost primitive trinomials are almost as useful as primitive trinomials.
Primitive Trinomials and Random Number Generators
, 2001
"... In this talk, which describes joint work with Samuli Larvala and Paul Zimmermann, we consider the problem of testing trinomials over GF(2) for irreducibility or primitivity. In particular, we consider trinomials whose degree is the exponent of a Mersenne prime. We describe a new algorithm for test ..."
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In this talk, which describes joint work with Samuli Larvala and Paul Zimmermann, we consider the problem of testing trinomials over GF(2) for irreducibility or primitivity. In particular, we consider trinomials whose degree is the exponent of a Mersenne prime. We describe a new algorithm for testing such trinomials. The algorithm is significantly faster than the standard algorithm, and has been used to find primitive trinomials of degree 3021377. Previously, the highest degree known was 859433. One of the applications is to pseudorandom number generators. Using the new primitive trinomials, we can obtain uniform random number generators with extremely long period and good statistical properties in all dimensions less than 3021377.
unknown title
, 1991
"... Abstract. All of the primitive trinomials over GF(2) with degree p given by ..."
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Abstract. All of the primitive trinomials over GF(2) with degree p given by