Abstract
The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture. A graphic lattice is generated by a graphic base and graphical operations, where a graphic base is a group of disjointed, connected graphs holding linearly independent properties. We study the existence of graphic bases with odd-graceful total colorings and show graphic lattices by vertex-overlapping and edge-joining operations; we prove that these graphic lattices are closed to the odd-graceful total coloring.
Highlights
IntroductionTopological authentication is a new technique based on topological coding, a mixed branch of discrete mathematics, number theory, algebraic group, graph theory, and so on
We extend the theoretical tool of topological coding from graph labeling to graph coloring and define a new type of coloring for building graphic lattices and providing topological coding based on new coloring
This paper studies the existence of graphic bases with odd-graceful total colorings and shows graphic lattices by vertex-overlapping operations and edge-joining operations; further, we prove that these graphic lattices are closed to the odd-graceful total coloring
Summary
Topological authentication is a new technique based on topological coding, a mixed branch of discrete mathematics, number theory, algebraic group, graph theory, and so on. This technology is more and more widely used in real life; for example, the user identity authentication of the smart-phone adopts a graphic password [1,2]. The security of the lattice-based cryptology depends on the difficulty of the difficult problems in classical number theory and computational complexity theory [11], many difficult problems in the lattice have been proven to be NP-hard, so this mechanism is generally considered to be resistant to the attacks from quantum computers when it is used in cryptanalysis and design.
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