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A Combined Circuit for Multiplication and Inversion in ${\rm GF}(2^{m})$

Authors :
N. Takagi
K. Kobayashi
Source :
IEEE Transactions on Circuits and Systems II: Express Briefs. 55:1144-1148
Publication Year :
2008
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2008.

Abstract

A combined circuit for multiplication and inversion in ${rm GF}(2^{m})$ is proposed. In order to develop a combined circuit, we start with combining the most significant bit first multiplication algorithm and the modified extended Euclid's algorithm by focusing on the similarities between them. Since almost all hardware components of the circuits are shared by multiplication and inversion, the combined circuit can be implemented with significantly smaller hardware than that necessary to implement both multiplication and inversion separately. By logic synthesis, the area of the proposed circuit is estimated to be approximately over 15% smaller than that of previously proposed combined multiplication/division circuits.

Details

ISSN :
15583791 and 15497747
Volume :
55
Database :
OpenAIRE
Journal :
IEEE Transactions on Circuits and Systems II: Express Briefs
Accession number :
edsair.doi.dedup.....2ad4a04a498b9340302ef733647a352c
Full Text :
https://doi.org/10.1109/tcsii.2008.2003347