An efficient lattice reduction method for F2-linear pseudorandom number generators using Mulders and Storjohann algorithm

Journal of Computational and Applied Mathematics

Volumn 236, Issue 2, 2011, Pages 141-149

  Harase, Shin ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Lattice reduction algorithm; Random number generation; Uniformity

Indexed keywords

EFFICIENT ALGORITHM; EQUIDISTRIBUTION; FAST ASSESSMENT; INITIAL STATE; LATTICE REDUCTION; LINEAR GENERATORS; MERSENNE TWISTERS; PARALLEL MACHINE; PARAMETER SET; PSEUDO RANDOM NUMBER GENERATORS; RANDOM NUMBERS; REDUCED BASIS; UNIFORMITY;

ALGORITHMS; COMPUTATIONAL COMPLEXITY; NUMBER THEORY;

RANDOM NUMBER GENERATION;

EID: 80051550676     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2011.06.005     Document Type: Article

References (21)

1. M. Matsumoto, and T. Nishimura Dynamic creation of pseudorandom number generators H. Niederreiter, J. Spanier, Monte Carlo and Quasi-Monte Carlo Methods 1998 2000 Springer-Verlag Berlin 56 69
2. T. Mulders, and A. Storjohann On lattice reduction for polynomial matrices J. Symbolic Comput. 35 2003 377 401 (Pubitemid 36530121)
3. 2-linear pseudorandom number generators Math. Comp. 80 2011 395 407
4. M. Matsumoto, and T. Nishimura Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator ACM Trans. Model. Comput. Simul. 8 1998 3 30
5. T. Nishimura Tables of 64-bit Mersenne Twisters ACM Trans. Model. Comput. Simul. 10 2000 348 357
6. F. Panneton, P. L'Ecuyer, and M. Matsumoto Improved long-period generators based on linear recurrences modulo 2 ACM Trans. Math. Software 32 2006 1 16 (Pubitemid 43924954)
7. F 2-linear random number generators C. Alexopoulos, D. Goldsman, J.R. Wilson, Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman 2009 Springer-Verlag 169 193
8. M. Matsumoto, M. Saito, H. Haramoto, and T. Nishimura Pseudorandom number generation: impossibility and compromise J. Univ. Comput. Sci. 12 2006 672 690 (Pubitemid 44180830)
9. M. Fushimi, and S. Tezuka The k-distribution of generalized feedback shift register pseudorandom numbers Commun. ACM 26 1983 516 523 (Pubitemid 13607254)
10. R. Couture, P. L'Ecuyer, and S. Tezuka On the distribution of k-dimensional vectors for simple and combined Tausworthe sequences Math. Comp. 60 1993 749 761
11. S. Tezuka The k-dimensional distribution of combined GFSR sequences Math. Comp. 62 1994 809 817
12. R. Couture, and P. L'Ecuyer Lattice computations for random numbers Math. Comp. 69 2000 757 765
13. A.K. Lenstra Factoring multivariate polynomials over finite fields J. Comput. System Sci. 30 1985 235 248
14. M. Saito, and M. Matsumoto SIMD-oriented fast Mersenne Twister: A 128-bit pseudorandom number generator A. Keller, S. Heinrich, H. Niederreiter, Monte Carlo and Quasi-Monte Carlo Methods 2006 2008 Springer-Verlag Berlin 607 622
15. L.-P. Wang, Y.-F. Zhu, and D.-Y. Pei On the lattice basis reduction multisequence synthesis algorithm IEEE Trans. Inform. Theory 50 2004 2905 2910
16. K. Mahler An analogue to Minkowski's geometry of numbers in a field of series Ann. of Math. 42 1941 488 522
17. K. Mahler On a theorem in the geometry of numbers in a space of Laurent series J. Number Theory 17 1983 403 416
18. W.M. Schmidt Construction and estimation of bases in function fields J. Number Theory 39 1991 181 224
19. S. Paulus Lattice basis reduction in function fields P.J. Buhler, Algorithmic Number Theory Lecture Notes in Computer Science vol. 1423 1998 Springer-Verlag Berlin 567 575 (Pubitemid 128093583)
20. S. Harase Maximally equidistributed pseudorandom number generators via linear output transformations Math. Comput. Simulation 79 2009 1512 1519
21. M. Matsumoto, and Y. Kurita Twisted GFSR generators II ACM Trans. Model. Comput. Simul. 4 1994 254 266