DocumentCode
1519450
Title
Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation
Author
Hasan, M. Anwar ; Negre, Christophe
Author_Institution
Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada
Volume
60
Issue
4
fYear
2011
fDate
4/1/2011 12:00:00 AM
Firstpage
602
Lastpage
607
Abstract
We study Dickson bases for binary field representation. Such a representation seems interesting when no optimal normal basis exists for the field. We express the product of two field elements as Toeplitz or Hankel matrix-vector products. This provides a parallel multiplier which is subquadratic in space and logarithmic in time. Using the matrix-vector formulation of the field multiplication, we also present sequential multiplier structures with linear space complexity.
Keywords
Hankel matrices; Toeplitz matrices; computational complexity; matrix multiplication; polynomial approximation; Dickson polynomial representation; Hankel matrix vector product; Toeplitz matrix vector product; binary field representation; field element; field multiplication; linear space complexity; low space complexity multiplication; matrix-vector formulation; optimal normal basis; parallel multiplier; sequential multiplier structure; Binary field; Dickson basis; Toeplitz matrix; multiplier; parallel; sequential.;
fLanguage
English
Journal_Title
Computers, IEEE Transactions on
Publisher
ieee
ISSN
0018-9340
Type
jour
DOI
10.1109/TC.2010.132
Filename
5487495
Link To Document