Fast lattice reduction for F2-linear pseudorandom number generators

Mathematics of Computation

Volumn 80, Issue 273, 2010, Pages 395-407

  Harase, Shin ^a   Matsumoto, Makoto ^a   Saito, Mutsuo ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649369839     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-2010-02391-9     Document Type: Article

References (18)

1. R. Couture and P. L'Ecuyer, Lattice computations for random numbers, Math. Comput. 69 (2000), no. 230, 757-765.
2. R. Couture, P. L'Ecuyer, and S. Tezuka, On the distribution of k-dimensional vectors for simple and combined tausworthe sequences, Math. Comput. 60 (1993), 749-761.
3. M. Fushimi and S. Tezuka, The k-distribution of generalized feedback shift register pseudorandom numbers, Commun. ACM 26 (1983), no. 7, 516-523.
4. S. Harase, Maximally equidistributed pseudorandom, number generators via linear output transformations, Math. Comput. Simul. 79 (2009), no. 5, 1512-1519.
5. P. L'Ecuyer and R. Couture, An implementation of the lattice and spectral tests for multiple recursive linear random number generators, INFORMS Journal on Computing 9 (1997), no. 2, 206-217.
6. 2-linear random number generators, Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman (C. Alexopoulos, D. Goldsman, and J. R. Wilson, eds.), Springer-Verlag, 2009, pp. 169-193.
7. A. K. Lenstra, Factoring multivariate polynomials over finite fields, Journal of Computer and System Sciences 30 (1985), no. 2, 235 - 248.
8. K. Mahler, An analogue to Minkowski's geometry of numbers in a field of series, The Annals of Mathematics 42 (1941), no. 2, 488-522.
9. K. Mahler, On a theorem in the geometry of numbers in a space of Laurent series, Journal of Number Theory 17 (1983), no. 3, 403-416.
10. J. L. Massey, Shift-register synthesis and BCH decoding, IEEE Trans. Inform. Theory IT-15 (1969), 122-127.
11. M. Matsumoto and T. Nishimura, Mersenne twister: a 623-dimensionally equidistributed uniform, pseudo-random, number generator, ACM Trans. Model. Comput. Simul. 8 (1998), no. 1, 3-30.
12. F. Panneton, P. L'Ecuyer, and M. Matsumoto, Improved long-period generators based on linear recurrences modulo 2, ACM Trans. Math. Softw. 32 (2006), no. 1, 1-16.
13. S. Paulus, Lattice basis reduction, in, function, fields., Algorithmic Number Theory. Lecture Notes in Computer Science (Berlin), vol. 1423, Springer-Verlag, 1998.
14. W. M. Schmidt, Construction, and estimation of bases in, function, fields, J. Number Theory 39 (1991), no. 2, 181 - 224.
15. S. Tezuka, The k-dimensional distribution of combined GFSR sequences, Math. Comput. 62 (1994), no. 206, 809 - 817.
16. L. Wang and H. Niederreiter, Successive minima profile, lattice profile, and joint linear complexity profile of pseudorandom multisequences, J. Complex. 24 (2008), no. 2, 144-153.
17. L. Wang and Y. Zhu, F[x]-lattice basis reduction, algorithm, and multisequence synthesis, Sci. in China Ser. F 44 (2001), 321-328.
18. L. Wang, Y. Zhu, and D.-Y. Pei, On the lattice basis reduction synthesis algorithm, IEEE Trans. Inform. Theory 50 (2004), no. 11, 2905-2910.