Admissible and Asymptotically Optimal Linear Congruential Generators

2007 ◽  
Vol 13 (3) ◽  
Author(s):  
V. Nekrutkin ◽  
M. Samakhova
Keyword(s):  
Asymptotically Optimal ◽  
Linear Congruential Generators ◽  
Optimal Linear ◽  
Linear Congruential

scholarly journals On lattice profile of the elliptic curve linear congruential generators

2014 ◽  
Vol 68 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Zhixiong Chen ◽  
Domingo Gomez-Perez ◽  
Gottlieb Pirsic
Keyword(s):  
Elliptic Curve ◽  
Linear Congruential Generators ◽  
Linear Congruential

Feistel-inspired scrambling improves the quality of linear congruential generators

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Asia Aljahdali ◽  
Michael Mascagni
Keyword(s):  
Randomized Algorithms ◽  
Statistical Properties ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Pseudorandom Sequences ◽  
Linear Congruential Generators ◽  
Pseudorandom Number Generation ◽  
Linear Congruential ◽  
Test Suites

AbstractGenerating pseudorandom numbers is a prerequisite for many areas including Monte Carlo simulation and randomized algorithms. The performance of pseudorandom number generators (PRNGs) depends on the quality of the generated random sequences. They must be generated quickly and have good statistical properties. Several statistical test suites have been developed to evaluate a single stream of random numbers such as those from the TestU01 library, the DIEHARD test suite, the tests from the SPRNG package, and a set of tests designed to evaluate bit sequences developed at NIST. This paper presents a new pseudorandom number generation scheme that produces pseudorandom sequences with good statistical properties via a scrambling procedure motivated by cryptographic transformations. We will specifically apply this to a popular set of PRNGs called the Linear Congruential generators (LGCs). The scrambling technique is based on a simplified version of a Feistel network. The proposed method seeks to improve the quality of the LCGs output stream. We show that this Feistel-inspired scrambling technique breaks up the regularities that are known to exist in LCGs. The Feistel-inspired scrambling technique is modular, and can be applied to any 64-bit PRNG, and so we believe that it can serve as an inexpensive model for a scrambler that can be used with most PRNGs via post-processing.

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