相关论文: Cryptography and non commutative cohomology

Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…

In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology…

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…

This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…

In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…

We follow existing distributed systems frameworks employing methods from algebraic topology to formally define primitives of blockchain technology. We define the notion of cross chain liquidity, sharding and probability spaces between and…

The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

We consider cohomology of diagrams of algebras by Beck's approach, using comonads. We then apply this theory to computing the cohomology of $\Psi$-rings. Our main result is that there is a spectral sequence connecting the cohomology of the…

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be…

In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography.…

We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…

Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

We consider the level of information security provided by random linear network coding in network scenarios in which all nodes comply with the communication protocols yet are assumed to be potential eavesdroppers (i.e. "nice but curious").…

Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…

For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…