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Let n and lscr be positive integers and f(x) be an irreducible polynomial over IF2 such that lscrdeg(f(x)) < 2n -1. We obtain an effective upper bound for the multiplication complexity of n-term polynomials modulo f(x)lscr. This upper bound allows a better selection of the moduli when Chinese Remainder Theorem is used for polynomial multiplication over IF2. We give improved formulae to multiply polynomials of small degree over IF2. In particular we improve the best known multiplication complexities over IF2 in the literature in some cases.