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Parallel linear congruential generators with prime moduli
 Parallel Computing
, 1998
"... Abstract. Linear congruential generators (LCGs) remain the most popular method of pseudorandom number generation on digital computers. Ease of implementation has favored implementing LCGs with poweroftwo moduli. However, prime modulus LCGs are superior in quality to poweroftwo modulus LCGs, and ..."
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Abstract. Linear congruential generators (LCGs) remain the most popular method of pseudorandom number generation on digital computers. Ease of implementation has favored implementing LCGs with poweroftwo moduli. However, prime modulus LCGs are superior in quality to poweroftwo modulus LCGs
Beware of Linear Congruential Generators with Multipliers of the form ...
 ACM Transactions on Mathematical Software
, 1999
"... INTRODUCTION Wu [1997] proposed a cleverlooking way to select the parameters and implement a linear congruential generator (LCG): Take a Mersenne prime modulus m, i.e., a prime of the form m = 2 e \Gamma 1 (see [Knuth 1997] for more on Mersenne primes), and a multiplier of the form a = \Sigma2 ..."
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Cited by 11 (4 self)
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INTRODUCTION Wu [1997] proposed a cleverlooking way to select the parameters and implement a linear congruential generator (LCG): Take a Mersenne prime modulus m, i.e., a prime of the form m = 2 e \Gamma 1 (see [Knuth 1997] for more on Mersenne primes), and a multiplier of the form a = \Sigma2
Linear Congruential Generators over Elliptic Curves
 Preprint CS94 143 , Dept. of Comp. Sci., Cornegie Mellon Univ
, 1994
"... Random numbers are useful in many applications such as Monte Carlo simulation, randomized algorithms, games, and password generation. It is important to be able to prove facts about about pseudorandom number generators, both about the distribution and the predictability of the pseudorandom numbers. ..."
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Cited by 8 (0 self)
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random numbers. This report was submitted in partial fulfillment of the requirements for the Senior Honors Research Program in the School of Computer Science at Carnegie Mellon University. Keywords: cryptography, pseudorandom number generation, elliptic curves, linear congruential generators 1 Introduction
Using Linear Congruential Generators for Cryptographic Purposes
"... We try to provide an alternative attitude toward the use of a Linear Congruential Generator (LCG here after) in generating pseudorandom numbers for some cryptographic purpose. In particular, we choose email encryption as our cryptographic application. Our encryption will be considered secure if the ..."
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Cited by 3 (1 self)
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We try to provide an alternative attitude toward the use of a Linear Congruential Generator (LCG here after) in generating pseudorandom numbers for some cryptographic purpose. In particular, we choose email encryption as our cryptographic application. Our encryption will be considered secure
Tables Of Linear Congruential Generators Of Different Sizes And Good Lattice Structure
, 1999
"... . We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8; 9; : : : ; 64; 127; 128, we take as a modulus m the largest prime smaller than 2 ` , and provide a list of multipliers a ..."
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Cited by 60 (19 self)
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. We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8; 9; : : : ; 64; 127; 128, we take as a modulus m the largest prime smaller than 2 ` , and provide a list of multipliers a
Deterministically broken Periodicity of Linear Congruential Generators using QuasiCrystals
, 1999
"... We describe the design of a family of aperiodic pseudorandom number generator (APRNG). These deterministic generators are based on linear congruential generators (LCGs) and, unlike any other deterministic PRNG, lead to nonperiodic pseudorandom sequences. An APRNG consists of several LCGs whose combi ..."
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We describe the design of a family of aperiodic pseudorandom number generator (APRNG). These deterministic generators are based on linear congruential generators (LCGs) and, unlike any other deterministic PRNG, lead to nonperiodic pseudorandom sequences. An APRNG consists of several LCGs whose
On lattice profile of the elliptic curve linear congruential generators. Periodica Mathematica Hungarica
 In press
, 2012
"... Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the b ..."
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Cited by 1 (0 self)
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the behavior of the linear congruential generators on elliptic curves (abbr. ECLCG) under this new lattice test and prove that the ECLCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k
Intrinsic Relations in the Structure of Linear Congruential Generators modulo 2
, 1992
"... We show two different general relationships that exist among terms of the linear congruential generator x i+1 = ax i + b mod 2 fi that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result. 1. Introducti ..."
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We show two different general relationships that exist among terms of the linear congruential generator x i+1 = ax i + b mod 2 fi that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result. 1
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