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Issue No.04 - April (2009 vol.58)

pp: 572-576

Murat Cenk , Çankaya University, Ankara

Ferruh Özbudak , Nanyang Technical University, Singapore

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.207

ABSTRACT

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.

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.2008.207REFERENCES

- [2] A. Karatsuba and Y. Ofman, “Multiplication of Multidigit Numbers by Automata,”
Soviet Physics—Doklady, vol. 7, pp. 595-596, 1963.- [5] A. Weimerskirch and C. Paar,
Generalizations of the Karatsuba Algorithm for Polynomial Multiplication, http://eprint.iacr.org/2006224, 2008.- [6] S. Winograd,
Arithmetic Complexity of Computations. SIAM, 1980. |