New Encryption Techniques From Lattice Thought In Topological Cryptography

摘要

For answering the similarity authentication problem: "For a given public key-graph G colored by a coloring , find a private key-graph H admitting a coloring such that G and H admit one of some similarities, and a particular text-based string induced from a Topcode-matrix of G is authenticated with another particular text-based string induced from a Topcode-matrix of H". For new new encryption techniques and measuring various similarities between graphs, we define some particular W-similarities, such as: isomorphic subgraph similarity, subgraph Topcode-matrix similarity, isomorphic colored subgraph similarity, subgraph degree-sequence ε-distance similarity, subgraph m-editable similarity, graphic base H-similarity, etc. Moreover, we introduce several graph operations, graph-splitting group matchings and graphic lattices an so on, such that our topological encryption techniques can be used in the calculating era of supercomputer and quantum computer.