Publication 2005 Issue No. 4 - April Abstract - Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
April 2005 (vol. 54 no. 4)
pp. 485-490
 ASCII Text x Haining Fan, Yiqi Dai, "Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials," IEEE Transactions on Computers, vol. 54, no. 4, pp. 485-490, April, 2005.
 BibTex x @article{ 10.1109/TC.2005.64,author = {Haining Fan and Yiqi Dai},title = {Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials},journal ={IEEE Transactions on Computers},volume = {54},number = {4},issn = {0018-9340},year = {2005},pages = {485-490},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2005.64},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Fast Bit-Parallel GF(2^n) Multiplier for All TrinomialsIS - 4SN - 0018-9340SP485EP490EPD - 485-490A1 - Haining Fan, A1 - Yiqi Dai, PY - 2005KW - Finite fieldKW - multiplicationKW - polynomial basisKW - irreducible trinomial.VL - 54JA - IEEE Transactions on ComputersER -
Based on a new representation of GF(2^n), we present two multipliers for all irreducible trinomials. Space complexities of the multipliers match the best results. The time complexity of one multiplier is T_A + (1 + \left\lceil {\log _2 n}\right\rceil )T_X for all irreducible trinomials, where T_A and T_X are the delay of one 2-input AND and XOR gates, respectively.

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Index Terms:
Finite field, multiplication, polynomial basis, irreducible trinomial.
Citation:
Haining Fan, Yiqi Dai, "Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials," IEEE Transactions on Computers, vol. 54, no. 4, pp. 485-490, April 2005, doi:10.1109/TC.2005.64