Quote:
Originally Posted by frmky
SNFS requires two polynomials, a degree polynomial , and a linear polynomial, , which share a common root modulo the number you are factoring. The difficulty is given by the size of .

Strictly speaking it does not require that one of the polynomials be linear. Any two polynomials which share a common root mod N will work.
A linear polynomial is almost always used (but not exclusively) because of the difficulty of finding good polynomials when neither are linear.