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F[x]-lattice basis reduction algorithm and multisequence synthesis

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Abstract

By means ofF[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given multiple sequences over a fieldF. Its computational complexity isO(N 2) operations inF whereN is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomials is given. The set and exact number of all minimal polynomials are also described whenF is a finite field.

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References

  1. Berlekamp, E. R., Algebraic Coding Theory, New York: McGraw Hill, 1969.

    Google Scholar 

  2. Massey, J. L., Shift-register synthesis and BCH decoding, IEEE Trans. Inform. Theory, 1969, IT-15(1): 122–127.

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Sugiyama, Y., Kasahara, M., Hirasawa, S. et al., A method for solving key equation for decoding Goppa codes, Inform. Contr., 1975, 27: 87–99.

    Article  MATH  MathSciNet  Google Scholar 

  5. Feng, G. L., Tzeng, K. K., A generalized Euclidean algorithm for multisequence shift-register synthesis, IEEE Trans. Inform. Theory, 1989, 35(3): 584–594.

    Article  MATH  MathSciNet  Google Scholar 

  6. Feng, G. L., Tzeng, K. K., A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes, IEEE Trans. Inform. Theory, 1991, 37(5): 1274–1287.

    Article  MATH  MathSciNet  Google Scholar 

  7. Sakata, S., Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array, J. Symbolic Computation, 1988, 5: 321–337.

    Article  MATH  MathSciNet  Google Scholar 

  8. Lenstra, A. K., Lenstra, H. W., Lovosz, L., Factoring polynomials with rational coefficients, Math. Ann., 1982, 261: 515–534.

    Article  MATH  MathSciNet  Google Scholar 

  9. Shamir, A., A polynomial time algorithm for breaking the basic Merkle-Helllman cryptosystem, IEEE Trans. Inform. Theory, 1984, 30(5): 699–704.

    Article  MATH  MathSciNet  Google Scholar 

  10. Lagarias, J. C., Odlyzko, A. M., Soluting low density subset problems, J. Assoc. Comp. Mach., 1985, 32: 229–246.

    MATH  MathSciNet  Google Scholar 

  11. Coppersmith, D., Small solutions to polynomial equations and low exponent RSA vulnerabilities, Journal of Cryptology, 1997, 10: 233–260.

    Article  MATH  MathSciNet  Google Scholar 

  12. Schmidt, W. M., Construction and estimation of bases in function fields, J. Number Theory, 1991, 39(2): 181–224.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Information Engineering University, 450002, Zhengzhou, China

    Wang Liping & Zhu Yuefei

  2. State Key Laboratory of Information Security, 100039, Beijing, China

    Wang Liping & Zhu Yuefei

Authors
  1. Wang Liping
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  2. Zhu Yuefei
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Correspondence to Wang Liping.

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Wang, L., Zhu, Y. F[x]-lattice basis reduction algorithm and multisequence synthesis. Sci China Ser F 44, 321–328 (2001). https://doi.org/10.1007/BF02714735

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  • DOI: https://doi.org/10.1007/BF02714735

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