Square form factorization, II

We propose a new subexponential time integer factoring algorithm called SQUFOF2, based on ideas of D. Shanks and R. de Vogelaere. It begins by using a sieve like that in the multiple polynomial Quadratic Sieve to construct a square value of a binary quadratic form. It uses this value to produce a square form. Then it factors the integer $N$ as the original SQUFOF does by taking an inverse square root and following a nonprincipal cycle to a symmetry point. This marriage with the Quadratic Sieve transforms SQUFOF from an $O(N^{1/4})$ algorithm into one with subexponential time. On the way we prove new facts about the infrastructure distance, which is used in the time complexity analysis.