Lattice structure and linear complexity profile of nonlinear pseudorandom number generators

Applicable Algebra in Engineering, Communications and Computing

Volumn 13, Issue 6, 2003, Pages 499-508

  Dorfer, Gerhard ^a,b   Winterhof, Arne ^b,c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Linear complexity profile; Marsaglia's lattice test; Nonlinear method; Pseudorandom number generator

Indexed keywords

COMPUTATIONAL METHODS; LINEAR SYSTEMS; NONLINEAR SYSTEMS; THEOREM PROVING;

LINEAR COMPLEXITY PROFILE;

RANDOM NUMBER GENERATION;

EID: 0038680378     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-003-0116-6     Document Type: Article

References (23)

1. Blackburn, S.R., Etzion, T., Paterson, K.G.: Permutation polynomials, de Bruijn sequences, and linear complexity. J. Comb. Th. A 76(1), 55-82 (1996)
2. Cusick, T.W., Ding, C., Renvall, A.: Stream Ciphers and Number Theory. Amsterdam: Elsevier 1998
3. Dieter, U.: Erzeugung von gleichverteilten Zufallsfolgen. Jahrbuch Überblicke Mathematik, pp. 25-44. Braunschweig: Vieweg 1993
4. Eichenauer, J., Grothe, H., Lehn, J.: Marsaglia's lattice test and non-linear congruential pseudo-random number generators. Metrika 35(3/4), 241-250 (1988)
5. Eichenauer-Herrmann, J., Herrmann, E., Wegenkittl, S.: A survey of quadratic and inversive congruential pseudorandom numbers. In: Niederreiter, H., et al. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 1996. Lecture Notes in Statistics 127, pp. 66-97. New York: Springer 1998
6. Eichenauer-Herrmann, J., Niederreiter, H.: Digital inversive pseudorandom numbers. ACM Trans. Modeling Comp. Simul. 4(4), 339-349 (1994)
7. Frieze, A.M., Håstad, J., Kannan, R., Lagarias, J.C., Shamir, A.: Reconstructing truncated integer variables satisfying linear congruences. SIAM J. Comput. 17(2), 262-280 (1988)
8. Jungnickel, D.: Finite Fields: Structure and Arithmetics. Mannheim: Bibliographisches Institut 1993
9. Lagarias, J.C.: Pseudorandom number generators in cryptography and number theory. In: Cryptology and computational number theory. Proc. Sympos. Appl. Math. 42, pp. 115-143. Providence, RI: Amer. Math. Soc. 1990
10. Levin, M.B.: Explicit digital inversive pseudorandom numbers. Math. Slovaca 50(5), 581-598 (2000)
11. Marsaglia, G.: The structure of linear congruential sequences. In: Zaremba, S.K. (ed.) Applications of Number Theory to Numerical Analysis, pp. 249-285. New York: Academic Press 1972
12. Massey, J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inform. Theory 15, 122-127 (1969)
13. Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. Boca Raton: CRC Press 1997
14. Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: SIAM 1992
15. Niederreiter, H.: New developments in uniform pseudorandom number and vector generation. In: Niederreiter, H., Shiue, P.J.-S. (eds.) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Lecture Notes in Statistics 106, pp. 87-120. New York: Springer 1995
16. Niederreiter, H.: Some computable complexity measures for binary sequences. In: Ding, C., Helleseth, T., Niederreiter, H. (eds.) Sequences and their Applications, pp. 67-78. London: Springer 1999
17. Niederreiter, H.: Design and analysis of nonlinear pseudorandom number generators. In: Monte Carlo Simulation, pp. 3-9. Rotterdam: A.A. Balkema Publishers 2001
18. Niederreiter, H., Shparlinski, I.E.: Recent advances in the theory of nonlinear pseudorandom number generators. In: Fang, K.-T., Hickernell, F.J., Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 86-102. Berlin: Springer 2002
19. Niederreiter, H., Winterhof, A.: Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators. Acta Arith. 93(4), 387-399 (2000)
20. Niederreiter, H., Winterhof, A.: On the lattice structure of pseudorandom numbers generated over arbitrary finite fields. Appl. Alg. Engrg. Comm. Comp. 12(3), 265-272 (2001)
21. Niederreiter, H., Winterhof, A.: Lattice structure and linear complexity of nonlinear pseudorandom numbers. Appl. Alg. Engrg. Comm. Comp. 13(4), 319-326 (2002)
22. Rueppel, R.A.: Analysis and Design of Stream Ciphers. Berlin: Springer 1986
23. Rueppel, R.A.: Stream ciphers. In: Contemporary Cryptology: The science of Information Integrity, pp. 65-134. New York: IEEE Press 1992