Resumo: We reduce the problem of factoring a Blum integer to the problem
of (numerically) integrating a certain meromorphic function. We
provide two algorithms to address this problem, one based on the residue
theorem and the other in the (generalized) Cauchy's argument principle.
In the former algorithm, we show that computing the residue of the
function at a certain pole leads to obtain the factors of a Blum
integer. In the latter, we consider a contour integral that simplifies
to an integral over the real numbers for which we are able to obtain an
analytical solution with several branches. The computational hardness
amounts to discovering the branch of the solution that gives the precise
integral. Joint on going work with Vitor Rocha Vieira (CFIF/DF-IST). |