Universality of group embeddability

Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the isometric embeddability between separable groups with a bounded bi-invariant complete metric are all invariantly universal analytic quasi-orders. This strengthens some results from [Wil14] and [FLR09].Comment: Minor corrections. 15 pages, submitte

An anonymous inter-network routing protocol for the Internet of Things

With the diffusion of the Internet of Things (IoT), computing is becoming increasingly pervasive, and different heterogeneous networks are integrated into larger systems. However, as different networks managed by different parties and with different security requirements are interconnected, security becomes a primary concern. IoT nodes, in particular, are often deployed “in the open”, where an attacker can gain physical access to the device. As nodes can be deployed in unsurveilled or even hostile settings, it is crucial to avoid escalation from successful attacks on a single node to the whole network, and from there to other connected networks. It is therefore necessary to secure the communication within IoT networks, and in particular, maintain context information private, including the network topology and the location and identity of the nodes. In this paper, we propose a protocol achieving anonymous routing between different interconnected networks, designed for the Internet of Things and based on the spatial Bloom filter (SBF) data structure. The protocol enables private communication between the nodes through the use of anonymous identifiers, which hide their location and identity within the network. As routing information is encrypted using a homomorphic encryption scheme, and computed only in the encrypted domain, the proposed routing strategy preserves context privacy, preventing adversaries from learning the network structure and topology. This, in turn, significantly reduces their ability to gain valuable network information from a successful attacks on a single node of the network, and reduces the potential for attack escalation

Bloom filter variants for multiple sets: a comparative assessment

In this paper we compare two probabilistic data structures for association queries derived from the well-known Bloom filter: the shifting Bloom filter (ShBF), and the spatial Bloom filter (SBF). With respect to the original data structure, both variants add the ability to store multiple subsets in the same filter, using different strategies. We analyse the performance of the two data structures with respect to false positive probability, and the inter-set error probability (the probability for an element in the set of being recognised as belonging to the wrong subset). As part of our analysis, we extended the functionality of the shifting Bloom filter, optimising the filter for any non-trivial number of subsets. We propose a new generalised ShBF definition with applications outside of our specific domain, and present new probability formulas. Results of the comparison show that the ShBF provides better space efficiency, but at a significantly higher computational cost than the SBF

Direct Product Primality Testing of Graphs is GI-hard

We investigate the computational complexity of the graph primality testing problem with respect to the direct product (also known as Kronecker, cardinal or tensor product). In [1] Imrich proves that both primality testing and a unique prime factorization can be determined in polynomial time for (finite) connected and nonbipartite graphs. The author states as an open problem how results on the direct product of nonbipartite, connected graphs extend to bipartite connected graphs and to disconnected ones. In this paper we partially answer this question by proving that the graph isomorphism problem is polynomial-time many-one reducible to the graph compositeness testing problem (the complement of the graph primality testing problem). As a consequence of this result, we prove that the graph isomorphism problem is polynomial-time Turing reducible to the primality testing problem. Our results show that connectedness plays a crucial role in determining the computational complexity of the graph primality testing problem

A Heuristic for Direct Product Graph Decomposition

In this paper we describe a heuristic for decomposing a directed graph into factors according to the direct product (also known as Kronecker, cardinal or tensor product). Given a directed, unweighted graph G with adjacency matrix Adj(G), our heuristic aims at identifying two graphs G 1 and G 2 such that G = G 1 × G 2 , where G 1 × G 2 is the direct product of G 1 and G 2 . For undirected, connected graphs it has been shown that graph decomposition is “at least as difficult” as graph isomorphism; therefore, polynomial-time algorithms for decomposing a general directed graph into factors are unlikely to exist. Although graph factorization is a problem that has been extensively investigated, the heuristic proposed in this paper represents – to the best of our knowledge – the first computational approach for general directed, unweighted graphs. We have implemented our algorithm using the MATLAB environment; we report on a set of experiments that show that the proposed heuristic solves reasonably- sized instances in a few seconds on general-purpose hardware. Although the proposed heuristic is not guaranteed to find a factorization, even if one exists; however, it always succeeds on all the randomly-generated instances used in the experimental evaluation

Distributed Smart City Services for Urban Ecosystems

A Smart City is a high-performance urban context, where citizens live independently and are more aware of the surrounding opportunities, thanks to forward-looking development of economy politics, governance, mobility and environment. ICT infrastructures play a key-role in this new research field being also a mean for society to allow new ideas to prosper and new, more efficient approaches to be developed. The aim of this work is to research and develop novel solutions, here called smart services, in order to solve several upcoming problems and known issues in urban areas and more in general in the modern society context. A specific focus is posed on smart governance and on privacy issues which have been arisen in the cellular age

The Italian mafias in the world: a systematic assessment of the mobility of criminal groups

This study complements existing literature on the mobility of criminal groups (mainly based on country case studies) with the first systematic assessment of the worldwide activities of the four main types of Italian mafias (Cosa Nostra, Camorra, ’Ndrangheta and Apulian mafias) from 2000 to 2012. Drawing from publicly available reports, a specific multiple correspondence analysis identifies the most important associations among mafias, activities, and countries. The results show that the mafias concentrate in a few countries; drug trafficking is the most frequent activity, whereas money laundering appears less important than expected; a stable mafia presence is reported in a few developed countries (mainly Germany, Canada, Australia, and the United States). The mafias show significant differences: the ’Ndrangheta tends to establish structured groups abroad, whereas the other mafias mainly participate in illicit trades

Probabilistic properties of the spatial bloom filters and their relevance to cryptographic protocols

The classical Bloom filter data structure is a crucial component of hundreds of cryptographic protocols. It has been used in privacy preservation and secure computation settings, often in conjunction with the (somewhat) homomorphic properties of ciphers such as Paillier's. In 2014, a new data structure extending and surpassing the capabilities of the classical Bloom filter has been proposed. The new primitive, called spatial Bloom filter (SBF) retains the hash-based membership-query design of the Bloom filter, but applies it to elements from multiple sets. Since its introduction, the SBF has been used in the design of cryptographic protocols for a number of domains, including location privacy and network security. However, due to the complex nature of this probabilistic data structure, its properties had not been fully understood. In this paper, we address this gap in knowledge and we fully explore the probabilistic properties of the SBF. In doing so, we define a number of metrics (such as emersion and safeness) useful in determining the parameters needed to achieve certain characteristics in a filter, including the false positive probability and inter-set error rate. This will in turn enable the design of more efficient cryptographic protocols based on the SBF, opening the way to their practical application in a number of security and privacy settings

Introduction to the special issue on privacy and security for location-based services and devices

The evolution of mobile phones into smartphones, and the diffusion of location-based services (LBS), are cornerstones of the digital era, but at the same time introduced a number of challenges to the privacy of individuals. Traditional information (as names, addresses and phone numbers) shared across the Internet with an increased number of services is now frequently coupled with positional data. With such detailed information, service providers are able to infer with alarming precision a number of sensitive information about their users, including religious, sexual and political preferences, as well as details of their social relationships and private life in general