3 research outputs found
Text-based Passwords Generated From Topological Graphic Passwords
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
Graph Homomorphisms Based On Particular Total Colorings of Graphs and Graphic Lattices
Lattice-based cryptography is not only for thwarting future quantum
computers, and is also the basis of Fully Homomorphic Encryption. Motivated
from the advantage of graph homomorphisms we combine graph homomorphisms with
graph total colorings together for designing new types of graph homomorphisms:
totally-colored graph homomorphisms, graphic-lattice homomorphisms from sets to
sets, every-zero graphic group homomorphisms from sets to sets. Our
graph-homomorphism lattices are made up by graph homomorphisms. These new
homomorphisms induce some problems of graph theory, for example, Number String
Decomposition and Graph Homomorphism Problem
Graphic Lattices and Matrix Lattices Of Topological Coding
Lattice-based Cryptography is considered to have the characteristics of
classical computers and quantum attack resistance. We will design various
graphic lattices and matrix lattices based on knowledge of graph theory and
topological coding, since many problems of graph theory can be expressed or
illustrated by (colored) star-graphic lattices. A new pair of the
leaf-splitting operation and the leaf-coinciding operation will be introduced,
and we combine graph colorings and graph labellings to design particular proper
total colorings as tools to build up various graphic lattices, graph
homomorphism lattice, graphic group lattices and Topcode-matrix lattices.
Graphic group lattices and (directed) Topcode-matrix lattices enable us to
build up connections between traditional lattices and graphic lattices. We
present mathematical problems encountered in researching graphic lattices, some
problems are: Tree topological authentication, Decompose graphs into
Hanzi-graphs, Number String Decomposition Problem, -gracefully total
numbers