Successive minima profile, lattice profile, and joint linear complexity profile of pseudorandom multisequences

Journal of Complexity

Volumn 24, Issue 2, 2008, Pages 144-153

  Wang, Li Ping ^a   Niederreiter, Harald ^b  

^a TSINGHUA UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Joint linear complexity profile; Marsaglia's lattice test; Multisequences; Successive minima

Indexed keywords

LINEAR ALGEBRA; MATHEMATICAL MODELS; PROBLEM SOLVING;

JOINT LINEAR COMPLEXITY PROFILE; MARSAGLIA'S LATTICE TESTS; MULTISEQUENCES; SUCCESSIVE MINIMA;

COMPUTATIONAL COMPLEXITY;

EID: 40749091255     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2007.07.001     Document Type: Article

References (22)

1. Couture R., L'Ecuyer P., and Tezuka S. On the distribution of k-dimensional vectors for simple and combined Tausworthe sequences. Math. Comp. 60 (1993) 749-761 S11-S16
2. Dawson E., and Simpson L. Analysis and design issues for synchronous stream ciphers. In: Niederreiter H. (Ed). Coding Theory and Cryptology (2002), World Scientific, Singapore 49-90
3. Dorfer G. Lattice profile and linear complexity profile of pseudorandom number sequences. In: Mullen G.L., Poli A., and Stichtenoth H. (Eds). Finite Fields and Applications, Lecture Notes in Computer Science vol. 2948 (2004), Springer, Berlin 69-78
4. Dorfer G., Meidl W., and Winterhof A. Counting functions and expected values for the lattice profile at n. Finite Fields Appl. 10 (2004) 636-652
5. Dorfer G., and Winterhof A. Lattice structure and linear complexity profile of nonlinear pseudorandom number generators. Appl. Algebra Engrg. Comm. Comput. 13 (2003) 499-508
6. Dorfer G., and Winterhof A. Lattice structure of nonlinear pseudorandom number generators in parts of the period. In: Niederreiter H. (Ed). Monte Carlo and Quasi-Monte Carlo Methods 2002 (2004), Springer, Berlin 199-211
7. ECRYPT stream cipher project; available at: 〈http://www.ecrypt.eu.org/stream〉.
8. F.-W. Fu, H. Niederreiter, On the counting function of the lattice profile of periodic sequences, J. Complexity, to appear.
9. Hawkes P., and Rose G.G. Exploiting multiples of the connection polynomial in word-oriented stream ciphers. In: Okamoto T. (Ed). Advances in Cryptology-ASIACRYPT 2000, Lecture Notes in Computer Science vol. 1976 (2000), Springer, Berlin 303-316
10. Lenstra A.K. Factoring multivariate polynomials over finite fields. J. Comput. System Sci. 30 (1985) 235-248
11. Mahler K. An analogue to Minkowski's geometry of numbers in a field of series. Ann. of Math. 42 (1941) 488-522
12. Marsaglia G. The structure of linear congruential sequences. In: Zaremba S.K. (Ed). Applications of Number Theory to Numerical Analysis (1972), Academic Press, New York 249-285
13. Meidl W. Continued fraction for formal Laurent series and the lattice structure of sequences. Appl. Algebra Engrg. Comm. Comput. 17 (2006) 29-39
14. Meidl W. Enumeration results on linear complexity profiles and lattice profiles. J. Complexity 22 (2006) 275-286
15. W. Meidl, personal communication.
16. Niederreiter H. The probabilistic theory of the joint linear complexity of multisequences. In: Gong G., et al. (Ed). Sequences and Their Applications-SETA 2006, Lecture Notes in Computer Science vol. 4086 (2006), Springer, Berlin 5-16
17. Niederreiter H., and Winterhof A. Lattice structure and linear complexity of nonlinear pseudorandom numbers. Appl. Algebra Engrg. Comm. Comput. 13 (2002) 319-326
18. Rueppel R.A. Stream ciphers. In: Simmons G.J. (Ed). Contemporary Cryptology: The Science of Information Integrity (1992), IEEE Press, New York 65-134
19. Schmidt W.M. Construction and estimation of bases in function fields. J. Number Theory 39 (1991) 181-224
20. Wang L.-P. The vector key equation and multisequence shift register synthesis. In: Fossorier M., et al. (Ed). Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science vol. 3857 (2006), Springer, Berlin 68-75
21. Wang L.-P., and Zhu Y.-F. F [x]-lattice basis reduction algorithm and multisequence synthesis. Sci. China Ser. F 44 (2001) 321-328
22. Wang L.-P., Zhu Y.-F., and Pei D.-Y. On the lattice basis reduction multisequence synthesis algorithm. IEEE Trans. Inform. Theory 50 (2004) 2905-2910