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Multi-Continued Fraction Algorithms and Their Applications to Sequences

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Book cover Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

Pseudorandom sequences have a wide applications. In stream ciphers, the key stream usually is a pseudorandom sequence over a finite field F q :

$$ \alpha=(a_1, a_2, \cdots, a_i, \cdots),\; a_i\in F_q $$

This work is partly supported by NSFC (Grant No. 60473025 and 90604011).

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References

  1. Massey, J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Information Theory 15, 173–180 (1969)

    Article  MathSciNet  Google Scholar 

  2. Mills, W.H.: Continued fractions and linear recurrences. Math. Computation 29(129), 173–180 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  3. Lasjaunias, A.: Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic. J. Number Theorey 65, 206–225 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Jones, W.B., Thron, W.J.: Continued fractions, analytic theory and applications. In: Rota, G. (ed.) Encyclopedia of Mathematics and Its Applications, vol. 11

    Google Scholar 

  5. Schmidt, W.M.: On continued fraction and diophantine approximation in power series fields. Acta Arith. 95, 139–166 (2000)

    MATH  MathSciNet  Google Scholar 

  6. Bernstein, L.: The Jacobi-Perron algorithm: its theory and application. In: LNM207. Springer, Berlin (1971)

    Google Scholar 

  7. Podsypanin, E.V.: A generalization of continued fraction alogrithm that is related to ViggoBorun algorithm (Russian). Studies in Number Theory (LOMI), Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov 67 4, 184–194 (1977)

    MathSciNet  Google Scholar 

  8. Ito, S., Keane, M., Ohtsuki, M.: Almost everywhere exponential convergence of the modified Jocobi-Perron algorithm. Ergod.Th. & Dynam. Sys. 13, 319–334 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ito, S., Fujii, J., Higashino, H., Yasutomi, S.-I.: On simultaneous approximation to (α, α 2) with α 3 + − 1 = 0. J. Number Theory 99, 255–283 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Meester, R.: A Simple proof of the exponential convergence of the modified Jacobi-Perron algorithm. Ergod.Th. &Dynam. Sys. 19, 1077–1083 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Feng, K., Wang, F.: The Jacobi-Perron algorithm on function fields. Algebra Colloq. 1(2), 149–158 (1994)

    MATH  MathSciNet  Google Scholar 

  12. Inoue, K.: On the exponential convergence of Jacobi-Perron algorithm over F(x)d. JP Journal of Algebra, Number Theory and Application 1(3), 27–41 (2003)

    Google Scholar 

  13. Dai, Z.D., Wang, K.P., Ye, D.F.: m-Continued fraction expansions of multi-Laurent series. ADVANCE IN MATHEMATICS(CHINA) 33(2), 246–248 (2004)

    Google Scholar 

  14. Dai, Z.D., Wang, K.P., Ye, D.F.: Multi-continued fraction algorithm on multi-formal Laurent Series. ACTA ARITHMETICA, 1–21 (2006)

    Google Scholar 

  15. Dai, Z.D., Jiang, S.Q., Imamura, K., Gong, G.: Asymptotic behavior of normalized linear complexity of ultimately non-periodic binary sequences. IEEE Trans. Infor. Theory 50, 2911–2915 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Dai, Z.-D., Imamura, K., Yang, J.-H.: Asymptotic behavior of normalized linear complexity of multi-sequences. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 129–142. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Dai, Z.-D., Feng, X., Yang, J.-H.: Multi-continued fraction algorithm and generalized B-M algorithm over F 2. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 339–354. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Dai, Z.D., Yang, J.H.: Multi-continued fraction algorithm and generalized B-M algorithm over F q . Finite Fields and Their Application (accepted)

    Google Scholar 

  19. Xing, C.: Multi-sequences with almost perfect linear complexity profile and function fields over finite fields. Journal of Complexity 16, 661–675 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  20. Niederreiter, H.: Some computable complexity measure for binary sequences. In: Sequences and Their Applications, pp. 67–78. Springer, London (1999)

    Google Scholar 

  21. Wang, L.P., Niederreiter, H.: Enumeration results on the joint linear complexity profile of multisequences, Finite Fields and Their Application, doi:10.1016/j.ffa.2005.03.005

    Google Scholar 

  22. Niederreiter, H., Wang, L.-P.: Proof of a conjecture on the joint linear complexity profile of multisequences. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 13–22. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Feng, X.T., Wang, Q.L., Dai, Z.D.: Multi-sequences with d-perfect property. Journal of Complexity 21(2), 230–242 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  24. Dai, Q.L., Dai, Z.D.: A proof that JPA and MJPA on multi-formal Layrent series can not garrentee the optimal rational approximation. Journal of the Graduate School of the Chinese Academy of Science (in Chinese) 22, 51–58 (2005)

    Google Scholar 

  25. Feng, X., Dai, Z.-D.: Expected value of the linear complexity of two-dimensional binary sequences. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 113–128. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Dai, Z.D., Feng, X.T.: Expected value of the normalized linear complexity of multi-sequences over the binary fields (preprint)

    Google Scholar 

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Dai, Z. (2006). Multi-Continued Fraction Algorithms and Their Applications to Sequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_3

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  • DOI: https://doi.org/10.1007/11863854_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

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