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On "A New Representation of Elements of Finite Fields GF (2^m) Yielding Small Complexity Arithmetic Circuits"
December 2002 (vol. 51 no. 12)
pp. 1460-1461
ASCII Text
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Willi Geiselmann, Jörn Müller-Quade, Rainer Steinwandt, "On "A New Representation of Elements of Finite Fields GF (2^m) Yielding Small Complexity Arithmetic Circuits"," IEEE Transactions on Computers, vol. 51, no. 12, pp. 1460-1461, December, 2002.
 
 
BibTex
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@article{ 10.1109/TC.2002.1146713,
author = {Willi Geiselmann and Jörn Müller-Quade and Rainer Steinwandt},
title = {On "A New Representation of Elements of Finite Fields GF (2^m) Yielding Small Complexity Arithmetic Circuits"},
journal ={IEEE Transactions on Computers},
volume = {51},
number = {12},
issn = {0018-9340},
year = {2002},
pages = {1460-1461},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2002.1146713},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - On "A New Representation of Elements of Finite Fields GF (2^m) Yielding Small Complexity Arithmetic Circuits"
IS - 12
SN - 0018-9340
SP1460
EP1461
EPD - 1460-1461
A1 - Willi Geiselmann,
A1 - Jörn Müller-Quade,
A1 - Rainer Steinwandt,
PY - 2002
KW - Galois field arithmetic
KW - VLSI implementation.
VL - 51
JA - IEEE Transactions on Computers
ER -
 

Abstract—We characterize the smallest n with GF (2) [X] /(X^n+1) containing an isomorphic copy of GF(2^m). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. The representation considered there can often be improved significantly.

[1] G. Drolet, “A New Representation of Elements of Finite Fields$\big. {\rm GF}(2^m)\bigr.$Yielding Small Complexity Arithmetic Circuits,” IEEE Trans. Computers, vol. 47, no. 9, pp. 938-946, Sept. 1998.[2] T. Itoh and S. Tsujii, “Structure of Parallel Multipliers for a Class of Finite Fields$GF(2^m)$,” Information and Computation, vol. 83, pp. 21-40, 1989.[3] J.K. Wolf, “Efficient Circuits for Multiplying in$\big. {\rm GF}(2^m)\bigr.$for Certain Values of$\big. m\bigr.$,” Discrete Math., vols. 106/107, pp. 497-502, 1992.[4] J.H. Silverman, “Fast Multiplication in Finite Fields$\big. {\rm GF}(2^N)\bigr.$,” Proc. Cryptographic Hardware and Embedded Systems, First Int'l Workshop (CHES '99), ÇK. Koçand C. Paar, eds., pp. 122-134, 1999.[5] H. Wu, M.A. Hasan, and I.F. Blake, “Highly Regular Architectures for Finite Field Computation Using Redundant Basis,” Proc. Cryptographic Hardware and Embedded Systems, First Int'l Workshop (CHES '99), ÇK. Koçand C. Paar, eds., pp. 269-279, 1999.[6] J.H. Silverman, “Rings of Low Multiplicative Complexity,” Finite Fields and Their Applications, vol. 6, no. 2, pp. 175-191, 2000.[7] W. Geiselmann and H. Lukhaub, “Redundant Representation of Finite Fields,” Proc. Public Key Cryptography, Fourth Int'l Workshop Practice and Theory in Public Key Cryptosystems (PKC 2001), K. Kim, ed. pp. 339-352, 2001.[8] W. Bosma, J. Cannon, and C. Playoust, “The Magma Algebra System I: The User Language,” J. Symbolic Computation, vol. 24, pp. 235-265, 1997.

Index Terms:
Galois field arithmetic, VLSI implementation.
Citation:
Willi Geiselmann, Jörn Müller-Quade, Rainer Steinwandt, "On "A New Representation of Elements of Finite Fields GF (2^m) Yielding Small Complexity Arithmetic Circuits"," IEEE Transactions on Computers, vol. 51, no. 12, pp. 1460-1461, Dec. 2002, doi:10.1109/TC.2002.1146713
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