Publication 2002 Issue No. 3 - March Abstract - On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)
On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)
March 2002 (vol. 51 no. 3)
pp. 346-351
 ASCII Text x M. Elia, M. Leone, "On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)," IEEE Transactions on Computers, vol. 51, no. 3, pp. 346-351, March, 2002.
 BibTex x @article{ 10.1109/12.990131,author = {M. Elia and M. Leone},title = {On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)},journal ={IEEE Transactions on Computers},volume = {51},number = {3},issn = {0018-9340},year = {2002},pages = {346-351},doi = {http://doi.ieeecomputersociety.org/10.1109/12.990131},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)IS - 3SN - 0018-9340SP346EP351EPD - 346-351A1 - M. Elia, A1 - M. Leone, PY - 2002KW - finite fieldsKW - parallel multiplierKW - optimal normal basisVL - 51JA - IEEE Transactions on ComputersER -

A lower bound to the number of AND gates used in parallel multipliers for $GF(2/supm/)$, under the condition that time complexity be minimum, is determined. In particular, the exact minimum number of AND gates for Primitive Normal Bases and Optimal Normal Bases of Type II multipliers is evaluated. This result indirectly suggests that space complexity is essentially a quadratic function of $m$ when time complexity is kept minimum.

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Index Terms:
finite fields, parallel multiplier, optimal normal basis
Citation:
M. Elia, M. Leone, "On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)," IEEE Transactions on Computers, vol. 51, no. 3, pp. 346-351, March 2002, doi:10.1109/12.990131