論文

査読有り
2018年3月

Three theorems on odd degree Chebyshev polynomials and more generalized permutation polynomials over a ring of module $$2^w$$ 2 w

Japan Journal of Industrial and Applied Mathematics
  • Atsushi

35
1
開始ページ
49
終了ページ
69
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1007/s13160-017-0275-7
出版者・発行元
Springer Tokyo

Odd degree Chebyshev polynomials over a ring of modulo 2 w have two kinds of period. One is an “orbital period”. Odd degree Chebyshev polynomials are bijection over the ring. Therefore, when an odd degree Chebyshev polynomial iterates affecting a factor of the ring, we can observe an orbit over the ring. The “ orbital period ” is a period of the orbit. The other is a “degree period”. It is observed when changing the degree of Chebyshev polynomials with a fixed argument of polynomials. Both kinds of period have not been completely studied. In this paper, we clarify completely both of them. The knowledge about them enables us to efficiently solve degree decision problem of Chebyshev polynomial over the ring, and so a key-exchange protocol with Chebyshev polynomial over the ring is not secure. In addition, we generalize the discussion and show that a key-exchange protocol with more generalized permutation polynomials which belong to a certain class is not secure.

リンク情報
DOI
https://doi.org/10.1007/s13160-017-0275-7
ID情報
  • DOI : 10.1007/s13160-017-0275-7
  • ISSN : 1868-937X
  • ORCIDのPut Code : 78091657
  • SCOPUS ID : 85030830248

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