Issue No. 04 - April (2009 vol. 58)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.207
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.
Finite field polynomial multiplication, Chinese remainder theorem.
Murat Cenk, Ferruh Özbudak, "Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem", IEEE Transactions on Computers, vol. 58, no. , pp. 572-576, April 2009, doi:10.1109/TC.2008.207