Efficient Construction of Gate Circuit for Computing Multiplicative Inverses over GF (2m)

Masakatu MORII; Masao KASAHARA

Efficient Construction of Gate Circuit for Computing Multiplicative Inverses over GF (2^m)

Masakatu MORII, Masao KASAHARA

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The theory of finite fields has been successfully applied to the constructing of the various algebraic codes, digital signal processing, and techniques of cryptography. Especially the theories on four operations are very important, because it is strongly related to the size and the throughput of the gate circuits for the various encoders and decoders. In this paper we shall give a new method for constructing the gate circuit that yields the multiplicative inverses over GF (2^m). The method is based on a new algorithm for computing multiplicative inverses in GF (2^m). The operations needed for our algorithm are rarely performed on GF (2^m), but primarily on the subfields of GF (2^m). When performing the multiplication and division over finite fields, the idea of using the subfield has been given wide attention. However the conventional algorithms taking advantage of this idea are not necessarily efficient from the practical point of view. We see that our algorithm proved superior to the conventional methods when GF (2^m) has the subfield GF (2²).

Publication: IEICE TRANSACTIONS on transactions Vol.E72-E No.1 pp.37-42

Publication Date: 1989/01/25

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Type of Manuscript: PAPER

Category: Information Theory and Coding Theory

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Masakatu MORII
Masao KASAHARA

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Masakatu MORII, Masao KASAHARA, "Efficient Construction of Gate Circuit for Computing Multiplicative Inverses over GF (2m)" in IEICE TRANSACTIONS on transactions, vol. E72-E, no. 1, pp. 37-42, January 1989, doi: .
Abstract: The theory of finite fields has been successfully applied to the constructing of the various algebraic codes, digital signal processing, and techniques of cryptography. Especially the theories on four operations are very important, because it is strongly related to the size and the throughput of the gate circuits for the various encoders and decoders. In this paper we shall give a new method for constructing the gate circuit that yields the multiplicative inverses over GF (2^m). The method is based on a new algorithm for computing multiplicative inverses in GF (2^m). The operations needed for our algorithm are rarely performed on GF (2^m), but primarily on the subfields of GF (2^m). When performing the multiplication and division over finite fields, the idea of using the subfield has been given wide attention. However the conventional algorithms taking advantage of this idea are not necessarily efficient from the practical point of view. We see that our algorithm proved superior to the conventional methods when GF (2^m) has the subfield GF (2²).
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e72-e_1_37/_p

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@ARTICLE{e72-e_1_37,
author={Masakatu MORII, Masao KASAHARA, },
journal={IEICE TRANSACTIONS on transactions},
title={Efficient Construction of Gate Circuit for Computing Multiplicative Inverses over GF (2m)},
year={1989},
volume={E72-E},
number={1},
pages={37-42},
abstract={The theory of finite fields has been successfully applied to the constructing of the various algebraic codes, digital signal processing, and techniques of cryptography. Especially the theories on four operations are very important, because it is strongly related to the size and the throughput of the gate circuits for the various encoders and decoders. In this paper we shall give a new method for constructing the gate circuit that yields the multiplicative inverses over GF (2^m). The method is based on a new algorithm for computing multiplicative inverses in GF (2^m). The operations needed for our algorithm are rarely performed on GF (2^m), but primarily on the subfields of GF (2^m). When performing the multiplication and division over finite fields, the idea of using the subfield has been given wide attention. However the conventional algorithms taking advantage of this idea are not necessarily efficient from the practical point of view. We see that our algorithm proved superior to the conventional methods when GF (2^m) has the subfield GF (2²).},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - Efficient Construction of Gate Circuit for Computing Multiplicative Inverses over GF (2m)
T2 - IEICE TRANSACTIONS on transactions
SP - 37
EP - 42
AU - Masakatu MORII
AU - Masao KASAHARA
PY - 1989
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E72-E
IS - 1
JA - IEICE TRANSACTIONS on transactions
Y1 - January 1989
AB - The theory of finite fields has been successfully applied to the constructing of the various algebraic codes, digital signal processing, and techniques of cryptography. Especially the theories on four operations are very important, because it is strongly related to the size and the throughput of the gate circuits for the various encoders and decoders. In this paper we shall give a new method for constructing the gate circuit that yields the multiplicative inverses over GF (2^m). The method is based on a new algorithm for computing multiplicative inverses in GF (2^m). The operations needed for our algorithm are rarely performed on GF (2^m), but primarily on the subfields of GF (2^m). When performing the multiplication and division over finite fields, the idea of using the subfield has been given wide attention. However the conventional algorithms taking advantage of this idea are not necessarily efficient from the practical point of view. We see that our algorithm proved superior to the conventional methods when GF (2^m) has the subfield GF (2²).
ER -