相关论文: Cryptography and non commutative cohomology

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Blockchain technology and, in particular, blockchain-based cryptocurrencies offer us information that has never been seen before in the financial world. In contrast to fiat currencies, all transactions of crypto-currencies and crypto-tokens…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…

In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…

A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…

Quantum homomorphic encryption, which allows computation by a server directly on encrypted data, is a fundamental primitive out of which more complex quantum cryptography protocols can be built. For such constructions to be possible,…

Homomorphic encryption is an encryption scheme that allows computations to be evaluated on encrypted inputs without knowledge of their raw messages. Recently Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for…

It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based…

We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalised tensor networks. This class specifically includes spin networks, the kinematic…

Security protocols are building blocks in secure communications. They deploy some security mechanisms to provide certain security services. Security protocols are considered abstract when analyzed, but they can have extra vulnerabilities…

Homomorphic encryption has largely been studied in context of public key cryptosystems. But there are applications which inherently would require symmetric keys. We propose a symmetric key encryption scheme with fully homomorphic evaluation…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We…

This paper demonstrates a topological meaning of quandle cocycle invariants of links with respect to finite connected quandles $X$, from a perspective of homotopy theory: Specifically, for any prime $\ell$ which does not divide the type of…

Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…

We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian $(\bb L^+)$. The squared distance of a node $i$ to the origin in this…

Recent advances in cryptography promise to enable secure statistical computation on encrypted data, whereby a limited set of operations can be carried out without the need to first decrypt. We review these homomorphic encryption schemes in…