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Sign of Permutation Induced by Nagata Automorphism over Finite Fields

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  • Keisuke Hakuta
  • Tsuyoshi Takagi

Abstract

This paper proves that the Nagata automorphism over a finite field can be mimicked by a tame automorphism which is a composition of four elementary automorphisms. By investigating the sign of the permutations induced by the above elementary automorphisms, one can see that if the Nagata automorphism is defined over a prime field of characteristic two, the Nagata automorphism induces an odd permutation, and otherwise, the Nagata automorphism induces an even permutation.

Suggested Citation

  • Keisuke Hakuta & Tsuyoshi Takagi, 2017. "Sign of Permutation Induced by Nagata Automorphism over Finite Fields," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(5), pages 54-60, October.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:5:p:54
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    More about this item

    Keywords

    polynomial automorphism; finite field; permutation; nagata automorphism; multivariate polynomial cryptography;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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