Division and bit-serial multiplication over GF(qm)

TitleDivision and bit-serial multiplication over GF(qm)
Publication TypeJournal Article
Year of Publication1992
AuthorsHasan, M. A., and V. K. Bhargava
JournalComputers and Digital Techniques, IEE Proceedings E
Volume139
Pagination230 - 236
Date Publishedmay.
ISSN0143-7062
Keywordsbit-serial multiplication, canonical basis representation, digital arithmetic, finite fields, irreducible polynomials, linear equations, polynomials
Abstract

Division and bit-serial multiplication in finite fields are considered. Using co-ordinates of the supporting elements it is shown that, when field elements are represented by polynomials, division over GF(qm) can be performed by solving a system of m linear equations over GF(q). For a canonical basis representation, a relationship between the division and the discrete-time Wiener-Hopf equation of degree m over GF(q) is derived. This relationship leads to a bit-serial multiplication scheme that can be easily realised for all irreducible polynomials.

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