Speeding up the Arithmetic Operations over Optimal Extension Fields in the Lagrange Representation Using DFT

Author

Qi, Minglong ; Zhong, Luo ; Guo, Qingping

Author_Institution

Coll. of Comput. Sci. & Technol., Wuhan Univ. of Technol., Wuhan, China

fYear

2010

fDate

30-31 Jan. 2010

Firstpage

39

Lastpage

42

Abstract

In this paper, efficient algorithms of the arithmetic operations over Optimal Extension Field have been considered. An arbitrary field element is represented by the Lagrange Representation, and transformation forward and backward between the Lagrange Representation and the vector of polynomial coefficients of the field element has been speeded up by applying DFT (discrete Fourier transform) over a ring. Our contribution is of establishing modular multiplication and inversion algorithms over Optimal Extension Field in the Lagrange Representation using the discrete Fourier transform.

Keywords

discrete Fourier transforms; matrix multiplication; polynomials; DFT; Lagrange representation; arithmetic operations; discrete Fourier transform; inversion algorithms; optimal extension field; optimal extension fields; polynomial coefficients; vector; Cost accounting; Digital arithmetic; Discrete Fourier transforms; Fourier transforms; Galois fields; Information technology; Lagrangian functions; Marine technology; Polynomials; Underwater communication; Discrete Fourier transform; Optimal Extension Field; multiplicative inverse algorithm; the Lagrange Representation;

fLanguage

English

Publisher

ieee

Conference_Titel

Innovative Computing & Communication, 2010 Intl Conf on and Information Technology & Ocean Engineering, 2010 Asia-Pacific Conf on (CICC-ITOE)

Conference_Location

Macao

Print_ISBN

978-1-4244-5634-5

Electronic_ISBN

978-1-4244-5635-2

Type

conf

DOI

10.1109/CICC-ITOE.2010.17

Filename

5439298