Number-Based Strings And Degree-sequences Of Topological Cryptography

Based on the problems that quantum computer is not good at computing, various anti-quantum-computing ciphers have been designed to resist the threat of the forthcoming quantum computing to the public key cryptosystem. We design several topological authentications on number-based strings and degree-sequences in topological coding by sequence-type operations, leaf-type operations, vertex-type operations, cycle-type operations, where number-based strings are considered as public keys in topological authentications. The decomposition of degree-sequences of graphs are determined completely, and we build up the connections between degree-sequences and various graphic lattices, as well as the complexity of decomposing a number-based string into a degree-sequence is NP-hard.