On the lattice structure of the add-with-carry and subtract-with-borrow random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the lattice structure of certain linear congruential sequences related to AWC/SWB generators
Mathematics of Computation
Maximally equidistributed combined Tausworthe generators
Mathematics of Computation
Distribution properties of multiply-with-carry random number generators
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Tables of maximally equidistributed combined LFSR generators
Mathematics of Computation
Algebraic feedback shift registers
Theoretical Computer Science - Special issue: cryptography
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
Shift Register Sequences
Fast Software Encryption, Cambridge Security Workshop
Stateless key distribution for secure intra and inter-group multicast in mobile wireless network
Computer Networks: The International Journal of Computer and Telecommunications Networking
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
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In this (largely expository) article, we propose a simple modification of the multiply-with-carry random number generators of Marsaglia [1994] and Couture and L'Écuyer [1997]. The resulting generators are both efficient (since they may be configured with a base b which is a power of 2) and exhibit maximal period. These generators are analyzed using a simple but powerful algebraic technique involving b-adic numbers.