There's a paper by Michael Shub, On the intractability of Hilbert's Nullstellensatz and an algebraic version of $``{\rm NP}\ne{\rm P}?''$ available at http://www6.cityu.edu.hk/ma/people/smale/pap97.pdfOn the intractability of Hilbert's Nullstellensatz and an algebraic version of $``{\rm NP}\ne{\rm P}?''$.