Publication 2003 Issue No. 12 - December Abstract - Parallel Multipliers Based on Special Irreducible Pentanomials
Parallel Multipliers Based on Special Irreducible Pentanomials
December 2003 (vol. 52 no. 12)
pp. 1535-1542
 ASCII Text x Francisco Rodr?guez-Henr?quez, ?etin Kaya Ko?, "Parallel Multipliers Based on Special Irreducible Pentanomials," IEEE Transactions on Computers, vol. 52, no. 12, pp. 1535-1542, December, 2003.
 BibTex x @article{ 10.1109/TC.2003.1252850,author = {Francisco Rodr?guez-Henr?quez and ?etin Kaya Ko?},title = {Parallel Multipliers Based on Special Irreducible Pentanomials},journal ={IEEE Transactions on Computers},volume = {52},number = {12},issn = {0018-9340},year = {2003},pages = {1535-1542},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1252850},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Parallel Multipliers Based on Special Irreducible PentanomialsIS - 12SN - 0018-9340SP1535EP1542EPD - 1535-1542A1 - Francisco Rodr?guez-Henr?quez, A1 - ?etin Kaya Ko?, PY - 2003KW - Finite fields arithmeticKW - parallel multipliersKW - pentanomialsKW - multipliers for GF(2^m).VL - 52JA - IEEE Transactions on ComputersER -

Abstract—The state-of-the-art Galois field GF(2^m) multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally spaced polynomial (ESP). Unfortunately, there exist only a few irreducible ESPs in the range of interest for most of the applications, e.g., error-correcting codes, computer algebra, and elliptic curve cryptography. Furthermore, it is not always possible to find an irreducible trinomial of degree m in this range. For those cases where neither an irreducible trinomial nor an irreducible ESP exists, the use of irreducible pentanomials has been suggested. Irreducible pentanomials are abundant, and there are several eligible candidates for a given m. In this paper, we promote the use of two special types of irreducible pentanomials. We propose new Mastrovito and dual basis multiplier architectures based on these special irreducible pentanomials and give rigorous analyses of their space and time complexity.

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Index Terms:
Finite fields arithmetic, parallel multipliers, pentanomials, multipliers for GF(2^m).
Citation:
Francisco Rodr?guez-Henr?quez, ?etin Kaya Ko?, "Parallel Multipliers Based on Special Irreducible Pentanomials," IEEE Transactions on Computers, vol. 52, no. 12, pp. 1535-1542, Dec. 2003, doi:10.1109/TC.2003.1252850