Modular construction of low complexity parallel multipliers for a class of finite fields GF(2m)

TitleModular construction of low complexity parallel multipliers for a class of finite fields GF(2m)
Publication TypeJournal Article
Year of Publication1992
AuthorsHasan, M. A., M. Wang, and V. K. Bhargava
JournalComputers, IEEE Transactions on
Pagination962 -971
Date Publishedaug.
Keywordscomplexity, computational complexity, digital arithmetic, equally spaced polynomials, exponentiation, finite fields, inversion, irreducible all one polynomials, multiplication algorithms, multiplying circuits, number theory, parallel multipliers, squaring algorithms

Structures for parallel multipliers of a class of fields GF(2m) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and the corresponding irreducible ESPs have been exploited to construct ESP-based multipliers of large fields by a regular expansion of the basic modules of the AOP-based multiplier of a small field. Some features of the structures also enable a fast implementation of squaring and multiplication algorithms and therefore make fast exponentiation and inversion possible. It is shown that, if for a certain degree, an irreducible AOP as well as an irreducible ESP exist, then from the complexity point of view, it is advantageous to use the ESP-based parallel multiplier


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