Publication 2009 Issue No. 4 - April Abstract - Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem
Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem
April 2009 (vol. 58 no. 4)
pp. 572-576
 ASCII Text x Murat Cenk, Ferruh Özbudak, "Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem," IEEE Transactions on Computers, vol. 58, no. 4, pp. 572-576, April, 2009.
 BibTex x @article{ 10.1109/TC.2008.207,author = {Murat Cenk and Ferruh Özbudak},title = {Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem},journal ={IEEE Transactions on Computers},volume = {58},number = {4},issn = {0018-9340},year = {2009},pages = {572-576},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2008.207},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder TheoremIS - 4SN - 0018-9340SP572EP576EPD - 572-576A1 - Murat Cenk, A1 - Ferruh Özbudak, PY - 2009KW - Finite field polynomial multiplicationKW - Chinese remainder theorem.VL - 58JA - IEEE Transactions on ComputersER -
Murat Cenk, Çankaya University, Ankara
Ferruh Özbudak, Nanyang Technical University, Singapore
Let $n$ and $\ell$ be positive integers and $f(x)$ be an irreducible polynomial over $\F_2$ such that $\ell deg(f(x))<2n-1.$ We obtain an effective upper bound for the multiplication complexity of $n$-term polynomials modulo $f(x)^\ell.$ This upper bound allows a better selection of the moduli when Chinese Remainder Theorem is used for polynomial multiplication over $\F_2$. We give improved formulae to multiply polynomials of small degree over $\F_2$. In particular we improve the best known multiplication complexities over $\F_2$ in the literature in some cases.

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Index Terms:
Finite field polynomial multiplication, Chinese remainder theorem.
Citation:
Murat Cenk, Ferruh Özbudak, "Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem," IEEE Transactions on Computers, vol. 58, no. 4, pp. 572-576, April 2009, doi:10.1109/TC.2008.207