A course in number theory and cryptography
A course in number theory and cryptography
Random number generators for MIMD parallel processors
Journal of Parallel and Distributed Computing
Random number generators for parallel processors
Journal of Computational and Applied Mathematics - Random numbers and simulation
On a new class of pseudorandom numbers for simulation methods
Journal of Computational and Applied Mathematics
An analysis of Lehmer's Euclidean GCD algorithm
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Linear and inversive pseudorandom numbers for parallel and distributed simulation
PADS '98 Proceedings of the twelfth workshop on Parallel and distributed simulation
Are there hyperbolas in the scatter plots of inversive congruential pseudorandom numbers?
Journal of Computational and Applied Mathematics - 9/4/98
Tables of linear congruential generators of different sizes and good lattice structure
Mathematics of Computation
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
ACM Transactions on Mathematical Software (TOMS)
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Grid Datafarm Architecture for Petascale Data Intensive Computing
CCGRID '02 Proceedings of the 2nd IEEE/ACM International Symposium on Cluster Computing and the Grid
Parallel linear congruential generators with Sophie-Germain moduli
Parallel Computing
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Improved long-period generators based on linear recurrences modulo 2
ACM Transactions on Mathematical Software (TOMS)
Pseudorandom number generation on the GPU
GH '06 Proceedings of the 21st ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model
Journal of Computational Physics
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Monte Carlo (MC) simulations are considered to be ideal for parallelization because a large Monte Carlo problem can often be easily broken up into many small, essentially independent, subproblems. Many Monte Carlo applications are suitable for grid computing environments. In such an environment, the number of substreams is not known in advance in the computing task. This is a challenge for generating random sequences by using the traditional splitting method, which is aimed at ways of partitioning the full period of a single sequence into parallel substreams. Explicit inversive congruential generator(EICG)[1] with prime modulus has some very compelling properties for parallel Monte Carlo simulations. EICG is an excellent pseudorandom number generator for parallalizing via parameterizing. This paper describes an implementation of parallel random number sequences by varying a set of different parameters instead of splitting a single random sequence. Comparisons with linear and nonlinear generators in the library: SPRNG[2] are presented.