相关论文: Girth of the Cayley graph and Cayley hash function…
We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily big finite Heesch number.
Cryptographic hash functions from expander graphs were proposed by Charles, Goren, and Lauter in [CGL] based on the hardness of finding paths in the graph. In this paper, we propose a new candidate for a hash function based on the hardness…
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups, the only geodetic Cayley graphs are odd cycles and…
Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process,…
We consider fuzzy, or continuous, bits, which take values in [0;1] and (-1;1] instead of {0;1}, and operations on them (NOT, XOR etc.) and on their sequences (ADD), to obtain the generalization of cryptographic hash functions, CHFs, for the…
We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.
This paper presents several algorithms for hashing directed graphs. The algorithms given are capable of hashing entire graphs as well as assigning hash values to specific nodes in a given graph. The notion of node symmetry is made precise…
We present a version of quantum hash function based on non-binary discrete functions. The proposed quantum procedure is "classical-quantum", that is, it takes a classical bit string as an input and produces a quantum state. The resulting…
We present here new mechanisms for hashing data via binary embeddings. Contrary to most of the techniques presented before, the embedding matrix of our mechanism is highly structured. That enables us to perform hashing more efficiently and…
Minwise hashing (MinHash) is an important and practical algorithm for generating random hashes to approximate the Jaccard (resemblance) similarity in massive binary (0/1) data. The basic theory of MinHash requires applying hundreds or even…
We introduce a novel, \textit{fully} quantum hash (FQH) function within the quantum walk on a cycle framework. We incorporate deterministic quantum computation with a single qubit to replace classical post-processing, thus increasing the…
Searching on bipartite graphs is basal and versatile to many real-world Web applications, e.g., online recommendation, database retrieval, and query-document searching. Given a query node, the conventional approaches rely on the similarity…
We explicitly construct random hash functions for privacy amplification (extractors) that require smaller random seed lengths than the previous literature, and still allow efficient implementations with complexity $O(n\log n)$ for input…
A mixed graph is called \emph{second kind hermitian integral}(or \emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of second kind are integers. A mixed graph is called \emph{Eisenstein integral} if the eigenvalues of…
A mixed graph is said to be HS-\emph{integral} if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called \emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency matrix are…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
Over the recent months it has become clear that the current generation of cryptographic hashing algorithms are insufficient to meet future needs. The ASH family of algorithms provides modifications to the existing SHA-2 family. These…
Recently, $\varepsilon$-almost dual universal$_2$ hash functions has been proposed as a new and wider class of hash functions. Using this class of hash functions, several efficient hash functions were proposed. This paper evaluates the…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
Hash functions like SHA-1 or MD5 are one of the most important cryptographic primitives, especially in the field of information integrity. Considering the fact that increasing methods have been proposed to break these hash algorithms, a…