  Topological graphic passwords (Topsnut-gpws) are one of graph-type passwords,
but differ from the existing graphical passwords, since Topsnut-gpws are saved
in computer by algebraic matrices. We focus on the transformation between
text-based passwords (TB-paws) and Topsnut-gpws in this article. Several
methods for generating TB-paws from Topsnut-gpws are introduced; these methods
are based on topological structures and graph coloring/labellings, such that
authentications must have two steps: one is topological structure
authentication, and another is text-based authentication. Four basic
topological structure authentications are introduced and many text-based
authentications follow Topsnut-gpws. Our methods are based on algebraic, number
theory and graph theory, many of them can be transformed into polynomial
algorithms. A new type of matrices for describing Topsnut-gpws is created here,
and such matrices can produce TB-paws in complex forms and longer bytes.
Estimating the space of TB-paws made by Topsnut-gpws is very important for
application. We propose to encrypt dynamic networks and try to face: (1)
thousands of nodes and links of dynamic networks; (2) large numbers of
Topsnut-gpws generated by machines rather than human's hands. As a try, we
apply spanning trees of dynamic networks and graphic groups (Topsnut-groups) to
approximate the solutions of these two problems. We present some unknown
problems in the end of the article for further research.
