Title :
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
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;
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
DOI :
10.1109/CICC-ITOE.2010.17
