Journal ArticleDOI
Modular construction of low complexity parallel multipliers for a class of finite fields GF(2/sup m/)
TLDR
Structures for parallel multipliers of a class of fields GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynmials (ESP) are presented and it is shown that it is advantageous to use the ESP-based parallel multiplier.Abstract:
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. >read more
Citations
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Journal ArticleDOI
Optimal and Suboptimal Power Allocation Schemes for OFDM-based Cognitive Radio Systems
TL;DR: An optimal power loading algorithm for an OFDM-based cognitive radio (CR) system is investigated and shows that for a given interference threshold, the proposed optimal scheme allows CR base station to transmit more power in order to achieve a higher transmission rate than the classical loading algorithms.
Journal ArticleDOI
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
Arash Reyhani-Masoleh,M.A. Hasan +1 more
TL;DR: A new formulation for polynomial basis multiplication in terms of the reduction matrix Q is derived and a generalized architecture for the multiplier is developed and the time and gate complexities of the proposed multiplier are analyzed as a function of degree m and the Reduction matrix Q.
Journal ArticleDOI
Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields
Çetin Kaya Koç,Berk Sunar +1 more
TL;DR: A new low-complexity bit-parallel canonical basis multiplier for the field GF(2m) generated by an all-one-polynomial is presented and extended to obtain a new bit-Parallel normal basis multiplier.
Journal ArticleDOI
A new architecture for a parallel finite field multiplier with low complexity based on composite fields
TL;DR: A bit parallel structure for a multiplier withLow complexity in Galois fields is introduced and a complete set of primitive field polynomials for composite fields is provided which perform module reduction with low complexity.
Journal ArticleDOI
A modified Massey-Omura parallel multiplier for a class of finite fields
TL;DR: By removing the redundancy, a modified parallel multiplier is presented which is modular and has a lower circuit complexity.
References
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MonographDOI
Introduction to finite fields and their applications
Rudolf Lidl,Harald Niederreiter +1 more
TL;DR: An introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications, especially information theory, algebraic coding theory and cryptology and a chapter on applications within mathematics, such as finite geometries.
Journal ArticleDOI
A fast algorithm for computing multiplicative inverses in GF(2 m ) using normal bases
Toshiya Itoh,Shigeo Tsujii +1 more
TL;DR: The fast algorithm proposed in this paper also uses normal bases, and computes multiplicative inverses iterating multiplications in GF(2 m ).
Journal ArticleDOI
VLSI Architectures for Computing Multiplications and Inverses in GF(2 m )
TL;DR: In this article, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m) with the simple squaring property of the normal basis representation used together with this multiplier.
Journal ArticleDOI
Structure of parallel multipliers for a class of fields GF(2 m )
Toshiya Itoh,Shigeo Tsujii +1 more
TL;DR: A configuration of parallel multipliers for GF (2 m) based on irreducible AOPs and ESPs based on canonical bases is presented and it is shown a necessary and sufficient condition for ESPs to be irReducible over GF ( 2) and the uniqueness of the irredUCible ESPs overGF (2).