Publication 2003 Issue No. 4 - April Abstract - Efficient Multiplication Beyond Optimal Normal Bases
Efficient Multiplication Beyond Optimal Normal Bases
April 2003 (vol. 52 no. 4)
pp. 428-439
 ASCII Text x Arash Reyhani-Masoleh, M. Anwar Hasan, "Efficient Multiplication Beyond Optimal Normal Bases," IEEE Transactions on Computers, vol. 52, no. 4, pp. 428-439, April, 2003.
 BibTex x @article{ 10.1109/TC.2003.1190584,author = {Arash Reyhani-Masoleh and M. Anwar Hasan},title = {Efficient Multiplication Beyond Optimal Normal Bases},journal ={IEEE Transactions on Computers},volume = {52},number = {4},issn = {0018-9340},year = {2003},pages = {428-439},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1190584},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Efficient Multiplication Beyond Optimal Normal BasesIS - 4SN - 0018-9340SP428EP439EPD - 428-439A1 - Arash Reyhani-Masoleh, A1 - M. Anwar Hasan, PY - 2003KW - Finite fieldsKW - multiplicationKW - normal basesKW - composite fieldsKW - optimal bases.VL - 52JA - IEEE Transactions on ComputersER -

Abstract—In cryptographic applications, the use of normal bases to represent elements of the finite field {\rm GF}( 2^{m}) is quite advantageous, especially for hardware implementation. In this article, we consider an important field operation, namely, multiplication which is used in many cryptographic functions. We present a class of algorithms for normal basis multiplication in {\rm GF}( 2^{m}). Our proposed multiplication algorithm for composite finite fields requires a significantly lower number of bit level operations and, hence, can reduce the space complexity of cryptographic systems.

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Index Terms:
Finite fields, multiplication, normal bases, composite fields, optimal bases.
Citation:
Arash Reyhani-Masoleh, M. Anwar Hasan, "Efficient Multiplication Beyond Optimal Normal Bases," IEEE Transactions on Computers, vol. 52, no. 4, pp. 428-439, April 2003, doi:10.1109/TC.2003.1190584