Sequence-type Colorings of Topological Coding Towards Information Security

Topological cryptography wants number of new colorings of graphs for resisting attack from supercomputer and quantum computers in the near future. Needless to say, one want random text-based strings as passwords or crypt digital files, also, want such forms of “one public key vs two or more private keys” and “one private key vs two or more public keys”. We define some sequence-type colorings and set-ordered sequence-type colorings defined on number sequences, also, these colorings are parameterized colorings with certain randomness. An algorithm, called LEAF-adding algorithm, is designed for proving “Each tree admits a set-ordered graceful total coloring”, which helps us to show trees admitting graceful sequence total colorings. Moreover, we discuss colorings based on abstract sequences, and construct connections between sequence-type colorings by the abstract substitution and the mapping homomorphism. At the end of the article we present “Text-Based String Partition Problem” for proving our sequence-type colorings having “provable security”.