Multiple Polynomials
In practice, many different polynomials are used for y, since only one polynomial will not typically provide enough (x, y) pairs that are smooth over the factor base. The polynomials used must have a special form, since they need to be squares modulo n. The polynomials must all have a similar form to the original y(x) = x2 − n:
Assuming is a multiple of A, so that the polynomial y(x) can be written as . If then A is a square, only the factor has to be considered.
This approach (called MPQS, Multiple Polynomial Quadratic Sieve) is ideally suited for parallelization, since each processor involved in the factorization can be given n, the factor base and a collection of polynomials, and it will have no need to communicate with the central processor until it is finished with its polynomials.
Read more about this topic: Quadratic Sieve
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