4.1 Euclidean Division
نویسنده
چکیده
We saw in Lecture 3 how to efficiently multiply integers, and, using Kronecker substitution, how to efficiently multiply polynomials with integer coefficients. This gives us what we need to multiply elements in finite fields, provided that we have a way to reduce the result to our standard representations of Fp ' Z/pZ and Fq ' Fp[x]/(f), using integers in [0, p− 1] and polynomials of degree less than deg f , respectively. In both cases we use Euclidean division.
منابع مشابه
PartII Number Theory
1 Division 3 1.1 Division Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Greatest common divisor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fundamental theorem of arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . ....
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