| 摘要 |
A reduction operation is utilized in an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=t<m>+am-1t<m-1>+am-2t<m-2>+ . . . +a1t+a0, where the coefficients as are equal to either 1 or 0, and m is a field degree. The reduction operation includes partially reducing a result of the arithmetic operation on the two binary polynomials to produce a congruent polynomial of degree less than a chosen integer n, with m<=n. The partial reduction includes using a polynomial M'=(Mm(t)-t<m>)*t<n-m>, or a polynomial M''=Mm(t)*t<n-m >as part of reducing the result to the degree less than n and greater than or equal to m. The integer n can be the data path width of an arithmetic unit performing the arithmetic operation, a multiple of a digit size of a multiplier performing the arithmetic operation, a word size of a storage location, such as a register, or a maximum operand size of a functional unit in which the arithmetic operation is performed.
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