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Finding a Basis Conversion Matrix via Prime Gauss Period Normal Basis
Yasuyuki NOGAMI Ryo NAMBA Yoshitaka MORIKAWA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2009/06/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
public key cryptography, extension field, Gauss period normal basis, basis conversion,
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This paper proposes a method to construct a basis conversion matrix between two given bases in Fpm. In the proposed method, Gauss period normal basis (GNB) works as a bridge between the two bases. The proposed method exploits this property and construct a basis conversion matrix mostly faster than EDF-based algorithm on average in polynomial time. Finally, simulation results are reported in which the proposed method compute a basis conversion matrix within 30 msec on average with Celeron (2.00 GHz) when mlog p≈160.