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VLSI aspects on inversion in finite fields
Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
2002 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

Different algorithms and architectures for inversion in finite extension fields are studied. The investigation is restricted to fields of characteristic two. Based on a simple transistor model, various architectures are compared with respect to delay, area requirement, and energy consumption.

Both polynomial and normal basis representations are considered. A special investigation is made on representations of fields as tower fields. New architectures are presented and compared with previously known architectures. For tower fields, a thorough investigation is made for the case where the extension degree is a power of two. In that case the investigation is based on a classification of all possible bases of the field over its largest subfield.

It is noted that normal bases, generated by irreducible all-one polynomials, are closely related to the polynomial bases which are generated by the same polynomials. Based on this observation, it is shown how architectures considered for polynomial basis representation can be modified for use with corresponding normal bases.

A list of minimum weight irreducible polynomials over F2 is also given.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2002. , 163 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 731
Keyword [en]
VLSI, Inversion, Finite Fields, Area, Delay, Power dissipation, Irreducible polynomials, Polynomial basis, Triangular basis, Normal basis, Dual basis, Tower fields.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-42327Local ID: 62620ISBN: 91-7373-256-7OAI: diva2:263183
Public defence
2002-02-08, Visionen, Hus B, Linköpings Universitet, Linköping, 10:15 (Swedish)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-02-13

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Olofsson, Mikael
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