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Complete Mapping Polynomials over Finite Field F 16

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Arithmetic of Finite Fields (WAIFI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4547))

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Abstract

A polynomial f(x) over F q , the finite field with q elements, is called a complete mapping polynomial if the two mappings F q →F q respectively defined by f(x) and f(x) + x are one-to-one. In this correspondence, complete mapping polynomials over F 16 are considered. The nonexistence of the complete mapping polynomial of degree 9 and the existence of the ones of degree 8 and 11 are proved; the result that the reduced degree of complete mapping polynomials over F 16 are 1, 4, 8, 10, 11, 12, 13 is presented; and by searching with computer, the degree distribution of complete mapping polynomials over the field is given.

Supported by National Natural Science Foundation of China (60373087, 60473023, 90104005, 60673071).

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References

  • Niederreiter, H., Robinson, K.H.: Bol loops of order pq. Math. proc. cambridge philos. soc. 89, 241–256 (1981)

    MATH  MathSciNet  Google Scholar 

  • Niederreiter, H., Robinson, K.H.: Complete mappings of finite fields. J. Austral. Math. Soc. Ser.A 33, 197–212 (1982)

    MATH  MathSciNet  Google Scholar 

  • Wan, D.: On a problem of Niederreiter and Robinson about finite fields. J.Austral. Math. Soc. Ser. A 41, 336–338 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Lidl, R., Niederreiter, H.: Finite Fields, encyclopedia of mathematics and its application. Addison-Wesley Publishing Company, London (1983)

    Google Scholar 

  • Zhihui Li: The Research on Permutation Theory in Block Cipher System. Ph.D thesis, Northwestern Polytechnical University (2002)

    Google Scholar 

  • Lang, S.: Algebraic number theory, 2nd edn. GTM110. Springer, Berlin Heidelberg New York (1994)

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Author information

Authors and Affiliations

  1. School of Computer, Wuhan University, Wuhan, Hubei, 430072, China

    Yuan Yuan, Yan Tong & Huanguo Zhang

Authors
  1. Yuan Yuan
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  2. Yan Tong
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  3. Huanguo Zhang
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Editor information

Claude Carlet Berk Sunar

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© 2007 Springer-Verlag Berlin Heidelberg

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Yuan, Y., Tong, Y., Zhang, H. (2007). Complete Mapping Polynomials over Finite Field F 16 . In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_12

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  • DOI: https://doi.org/10.1007/978-3-540-73074-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73073-6

  • Online ISBN: 978-3-540-73074-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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