相关论文: Graph Homomorphisms Based On Particular Total Colo…

Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological…

In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…

Making topological authentication from theory to practical application is an important and challenging task. More and more researchers pay attention on coming quantum computation, privacy data protection, lattices and cryptography. Research…

We, for anti-quantum computing, will discuss various number-based strings, such as number-based super-strings, parameterized strings, set-based strings, graph-based strings, integer-partitioned and integer-decomposed strings, Hanzi-based…

We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…

Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in…

A homomorphism from a graph $X$ to a graph $Y$ is an adjacency preserving mapping $f:V(X) \rightarrow V(Y)$. We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph $X$ admits a…

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…

The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer…

The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining…

The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The…

As quantum computing technology continues to advance, post-quantum cryptographic methods capable of resisting quantum attacks have emerged as a critical area of focus. Given the potential vulnerability of existing homomorphic encryption…

Topological Coding consists of two different kinds of mathematics: topological structure and mathematical relation. The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

Homomorphic encryption is a method used in cryptopgraphy to create programs that can interact with encrypted data without ever leaving the data in the clear. This has many potential applications in cybersecurity. This paper uses…

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…

We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…

Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a…

We consider a database composed of a set of conceptual graphs. Using conceptual graphs and graph homomorphism it is possible to build a basic query-answering mechanism based on semantic search. Graph homomorphism defines a partial order…

In recent work by Johnson et al. (2022), a framework was described for the study of graph problems over classes specified by omitting each of a finite set of graphs as subgraphs. If a problem falls into the framework then its computational…