相关论文: Ramanujan graphs in cryptography

The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This…

Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total…

For a class $\mathcal{H}$ of graphs, #Sub$(\mathcal{H})$ is the counting problem that, given a graph $H\in \mathcal{H}$ and an arbitrary graph $G$, asks for the number of subgraphs of $G$ isomorphic to $H$. It is known that if $\mathcal{H}$…

Many applications, including provenance and some analyses of social networks, require path-based queries over graph-structured data. When these graphs contain sensitive information, paths may be broken, resulting in uninformative query…

Publishing graph data is widely desired to enable a variety of structural analyses and downstream tasks. However, it also potentially poses severe privacy leakage, as attackers may leverage the released graph data to launch attacks and…

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…

The Diophantine Equation Hard Problem (DEHP) is a potential cryptographic problem on the Diophantine equation $U=\sum \limits_{i=1}^n {V_i x_{i}}$. A proper implementation of DEHP would render an attacker to search for private parameters…

Graph Neural Networks (GNNs) have been predominant for graph learning tasks; however, recent studies showed that a well-known graph algorithm, Label Propagation (LP), combined with a shallow neural network can achieve comparable performance…

Quantum circuits composed of CNOT and $R_z$ are fundamental building blocks of many quantum algorithms, so optimizing the synthesis of such quantum circuits is crucial. We address this problem from a theoretical perspective by studying the…

The (strong) isometric path complexity is a recently introduced graph invariant that captures how arbitrary isometric paths (i.e., shortest paths) of a graph can be viewed as a union of a few ``rooted" isometric paths (i.e., isometric paths…

This paper analyzes security performance of an image encryption algorithm using 2D lag-complex Logistic map (LCLM), which adopts it as a pseudo-random number generator, and uses the sum of all pixel values of the plain-image as its initial…

We show a simple reduction which demonstrates the cryptographic hardness of learning a single periodic neuron over isotropic Gaussian distributions in the presence of noise. More precisely, our reduction shows that any polynomial-time…

Four algorithms giving rise to graceful graphs from a known (non)graceful graph are described. Some necessary conditions for a graph to be highly graceful and critical are given. Finally some conjectures are made on graceful, critical and…

Two graphs $G$ and $H$ are homomorphism indistinguishable over a family of graphs $\mathcal{F}$ if for all graphs $F \in \mathcal{F}$ the number of homomorphisms from $F$ to $G$ is equal to the number of homomorphism from $F$ to $H$. Many…

Karger (SIAM Journal on Computing, 1999) developed the first fully-polynomial approximation scheme to estimate the probability that a graph $G$ becomes disconnected, given that its edges are removed independently with probability $p$. This…

We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…

The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…

The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively…

The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first…

Lightweight block cipher design has largely focused on incremental optimization of established paradigms such as substitution--permutation networks, Feistel structures, and ARX constructions, where security derives from the algebraic…