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

Structures for parallel multipliers of a class of fields GF(2/sup m/) 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 th...

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Veröffentlicht in:IEEE transactions on computers Jg. 41; H. 8; S. 962 - 971
Hauptverfasser: Hasan, M.A., Wang, M., Bhargava, V.K.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 01.08.1992
Schlagworte:
Arithmetic
Complexity theory
Cryptography
Electrostatic precipitators
Error correction
Galois fields
Hardware
Message-oriented middleware
Modular construction
Polynomials
ISSN:0018-9340
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Zusammenfassung:Structures for parallel multipliers of a class of fields GF(2/sup m/) 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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ISSN:0018-9340
DOI:10.1109/12.156539