Integer-Decomposing Topological Authentication Problem For Post-Quantum Cryptosystem

For overcoming possibly attacks from super-computers and quantum computers, we proposed the Integer-Decomposing Topological Authentication Problem (IDTAP) in Topological Coding: Decompose an even integer m to form a number-based string m 1 m 2 ⋯m p (as a public key) holding m = m 1 + m 2 + ⋯+ m p , such that d = (m 1 ,m 2 ,…,m p ) is just the degree-sequence of a graph G (as a private key). For the goal of answering IDTAP, we investigate some operations on graph degree-sequences, and show particular degree-sequences, such as perfect degree-sequence, unique graph degree-sequence corresponds, right-angled degree sequence base, degree-sequence homomorphism. We define degree-sequence lattices, degree-sequence accompany graphic lattices, and present: "A degree-sequence lattice is equivalent to a non-negative integer lattice", and our star-tree lattices can describe graphs.