Finding a basis conversion matrix using a polynomial basis derived by a small multiplicative cyclic group

Yasuyuki Nogami, Hidehiro Kato, Kenta Nekado, Satoshi Uehara, Yoshitaka Morikawa

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Several methods for finding a basis conversion matrix between two different bases in an extension field Fp m have been proposed. Among them, the one based on Gauss period normal basis (GNB) is on average the most efficient. However, since it needs to construct a certain tower field F(p m) n, some inefficient cases in which the towering degree n becomes large have been reported. This paper first determines that such inefficient cases are caused by the GNB condition. In order to overcome this inefficiency, we propose a method that does not use any GNB in the target extension field Fp m, but instead uses a certain polynomial basis in Fp m derived by a certain small cyclic group in F(p m) n. This causes relaxation of the condition for the towering degree n. In addition, our experimental results show that the proposed method substantially accelerates the computation time for finding a basis conversion matrix.

Original languageEnglish
Article number6172234
Pages (from-to)4936-4947
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number7
Publication statusPublished - Jun 25 2012



  • Basis conversion
  • Gauss period normal basis (GNB)
  • extension field
  • public key cryptography

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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