On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1719, Issue , 1999, Pages 87-93

  Griffin, Frances ^a   Niederreiter, Harald ^b   Shparlinski, Igor E ^a  

^a MACQUARIE UNIVERSITY   (Australia)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM NUMBER GENERATION;

DISCREPANCY BOUNDS; FIRST ORDER; NONLINEAR CONGRUENTIAL METHOD; PSEUDO-RANDOM NUMBERS;

ALGEBRA;

EID: 84957613068     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46796-3_9     Document Type: Conference Paper

References (20)

1. T. Cochrane, 'Trigonometric approximation and uniform distribution modulo 1', Proc. Amer. Math. Soc., 103 (1988), 695-702.
2. P. Deligne, 'Applications de la formule des traces aux sommes trigonometriques', Lect. Notes in Mathematics, Springer-Verlag, Berlin, 569 (1977), 168-232.
3. M. Drmota and R.F. Tichy, Sequences, discrepancies and applications, Springer- Verlag, Berlin, 1997.
4. J. Eichenauer-Herrmann, E. Herrmann and S. Wegenkittl, 'A survey of quadratic and inversive congruential pseudorandom numbers', Lect. Notes in Statistics, Springer-Verlag, Berlin, 127 (1998), 66-97.
5. M. Flahive and H. Niederreiter, 'On inversive congruential generators for pseudorandom numbers', Finite Fields, Coding Theory, and Advances in Communications and Computing (G.L. Mullen and P.J.-S. Shiue, eds.), Marcel Dekker, New York, 1993, 75-80.
6. J. B. Friedlander, D. Lieman and I. E. Shparlinski, 'On the distribution of the RSA generator', Proc. SETA '98 (C.S. Ding, T. Helleseth and H. Niederreiter, eds.), Springer-Verlag, Singapore, (to appear).
7. J. B. Friedlander and I. E. Shparlinski, 'On the distribution of the power generator', Preprint, 1999.
8. J. Gutierrez, H. Niederreiter and I. E. Shparlinski, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatsh. Math., (to appear).
9. D. Knuth, The art of computer programming, Vol. 2, 3rd ed., Addison-Wesley, Reading, MA, 1998.
10. R. Lidl and H. Niederreiter, 'Finite fields and their applications', Handbook of Algebra (M. Hazewinkel, ed.), Vol. 1, Elsevier, Amsterdam, 1996, 321-363.
11. R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997.
12. G. Marsaglia, 'The structure of linear congruential sequences', Applications of Number Theory to Numerical Analysis (S.K. Zaremba, ed.), Academic Press, New York, 1972, 249-285.
13. H. Niederreiter, Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, 1992.
14. H. Niederreiter, 'Finite fields, pseudorandom numbers, and quasirandom points', Finite Fields, Coding Theory, and Advances in Communications and Computing (G.L. Mullen and P.J.-S. Shiue, eds.), Marcel Dekker, New York, 1993, 375-394.
15. H. Niederreiter, 'New developments in uniform pseudorandom number and vector generation', Lect. Notes in Statistics, Springer-Verlag, Berlin, 106 (1995), 87-120.
16. H. Niederreiter and I. E. Shparlinski, 'On the distribution of inversive congru- ential pseudorandom numbers in parts of the period', Preprint, 1998.
17. H. Niederreiter and I. E. Shparlinski, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and Their Appl., 5 (1999), 246-253.
18. H. Niederreiter and I. E. Shparlinski, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Preprint, 1999.
19. H. Niederreiter and I. E. Shparlinski, 'Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus', Acta Arith., (to appear).
20. S. B. Steckin, 'An estimate of a complete rational exponential sum', Trudy Mat. Inst. Steklov., 143 (1977), 188-207 (in Russian).