Related papers: Ramanujan graphs in cryptography
This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph…
For two graphs $G_1$ and $G_2$, the size Ramsey number $\hat{r}(G_1,G_2)$ is the smallest positive integer $m$ for which there exists a graph $G$ of size $m$ such that for any red-blue edge-coloring of the graph $G$, $G$ contains either a…
Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its…
In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their…
The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Although several signcryption schemes are proposed over the years,…
Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall…
In 1994, P. Shor discovered quantum algorithms which can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, D-Wave demonstrated the first quantum computer. These events and further developments have brought a crisis to…
Motivated by applications to social network analysis (SNA), we study the problem of finding the maximum number of disjoint uni-color paths in an edge-colored graph. We show the NP-hardness and the approximability of the problem, and both…
In this paper, we relate a beautiful theory by Lov\'asz with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the Weisfeiler-Leman…
We propose a flexible procedure for large-scale image search by hash functions with kernels. Our method treats binary codes and pairwise semantic similarity as latent and observed variables, respectively, in a probabilistic model based on…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
We propose a notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed by L\'aszl\'o Lov\'asz and his coauthors. We prove that spectra of…
Post-quantum cryptography is inevitable. National Institute of Standards and Technology (NIST) starts standardizing quantum-resistant public-key cryptography (aka post-quantum cryptography). The reason is that investment in quantum…
Graph similarity learning (GSL), also referred to as graph matching in many scenarios, is a fundamental problem in computer vision, pattern recognition, and graph learning. However, previous GSL methods assume that graphs are homogeneous…
In this paper we construct explicit LPS-type Ramanujan graphs from each definite quaternion algebra over $\mathbb Q$ of class number 1, extending the constructions of Lubotzky, Phillips, Sarnak, and later Chiu, and answering in the…
A graph G is t-tough if any induced subgraph of it with x > 1 connected components is obtained from G by deleting at least tx vertices. Chvatal conjectured that there exists an absolute constant t_0 so that every t_0-tough graph is…
Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…
The Strong Exponential Time Hypothesis (SETH) is a standard assumption in (fine-grained) parameterized complexity and many tight lower bounds are based on it. We consider a number of reasonable weakenings of the SETH, with sources from (i)…