Introduction to finite fields and their applications
Introduction to finite fields and their applications
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Pseudorandom vector generation by the inversive method
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A table of primitive binary polynomials
Mathematics of Computation
Some linear and nonlinear methods for pseudorandom number generation
WSC '95 Proceedings of the 27th conference on Winter simulation
Inversive and linear congruential pseudorandom number generators in empirical tests
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the statistical independence of compound pseudorandom numbers over part of the period
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the Average Distribution of Inversive Pseudorandom Numbers
Finite Fields and Their Applications
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A new algorithm, the digital inversive method, for generating uniform pseudorandom numbers is introduced. This algorithm starts from an inversive recursion in a large finite field and derives pseudorandom numbers from it by the digital method. If the underlying finite field has q elements, then the sequences of digital inversive pseudorandom numbers with maximum possible period length q can be characterized. Sequences of multiprecision pseudorandom numbers with very large period lengths are easily obtained by this new method. Digital inversive pseudorandom numbers satisfy statistical independence properties that are close to those of truly random numbers in the sense of asymptotic discrepancy. If q is a power of 2, then the digital inversive method can be implemented in a very fast manner.