p and q are about the same size (it is not essential but clearly you don't construct N from an easy to achieve prime number) 1

...

QS (Quadratic Sieve) with complexity of 1

...

A vector space that consist of two smaller vector spaces X,Y is denoted as 1

The operators over this space are bilinear operators over each of the sub spaces. 1In terms of matrices tensor product has the following form: 1