Publication 2003 Issue No. 11 - November Abstract - Fast Normal Basis Multiplication Using General Purpose Processors
Fast Normal Basis Multiplication Using General Purpose Processors
November 2003 (vol. 52 no. 11)
pp. 1379-1390
 ASCII Text x Arash Reyhani-Masoleh, M. Anwar Hasan, "Fast Normal Basis Multiplication Using General Purpose Processors," IEEE Transactions on Computers, vol. 52, no. 11, pp. 1379-1390, November, 2003.
 BibTex x @article{ 10.1109/TC.2003.1244936,author = {Arash Reyhani-Masoleh and M. Anwar Hasan},title = {Fast Normal Basis Multiplication Using General Purpose Processors},journal ={IEEE Transactions on Computers},volume = {52},number = {11},issn = {0018-9340},year = {2003},pages = {1379-1390},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1244936},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Fast Normal Basis Multiplication Using General Purpose ProcessorsIS - 11SN - 0018-9340SP1379EP1390EPD - 1379-1390A1 - Arash Reyhani-Masoleh, A1 - M. Anwar Hasan, PY - 2003KW - Finite field multiplicationKW - normal basisKW - software algorithmsKW - ECDSAKW - composite fields.VL - 52JA - IEEE Transactions on ComputersER -

Abstract—For cryptographic applications, normal bases have received considerable attention, especially for hardware implementation. In this article, we consider fast software algorithms for normal basis multiplication over the extended binary field GF (2^m). We present a vector-level algorithm which essentially eliminates the bit-wise inner products needed in the conventional approach to the normal basis multiplication. We then present another algorithm which significantly reduces the dynamic instruction counts. Both algorithms utilize the full width of the data-path of the general purpose processor on which the software is to be executed. We also consider composite fields and present an algorithm which can provide further speed-ups and an added flexibility toward hardware-software codesign of processors for very large finite fields.

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Index Terms:
Finite field multiplication, normal basis, software algorithms, ECDSA, composite fields.
Citation:
Arash Reyhani-Masoleh, M. Anwar Hasan, "Fast Normal Basis Multiplication Using General Purpose Processors," IEEE Transactions on Computers, vol. 52, no. 11, pp. 1379-1390, Nov. 2003, doi:10.1109/TC.2003.1244936