Linear-Time Zero-Knowledge Proofs for Arithmetic Circuit Satisfiability

We give computationally efficient zero-knowledge proofs of knowledge for arithmetic circuit satisfiability over a large field. For a circuit with N addition and multiplication gates, the prover only uses O(N)O(N) multiplications and the verifier only uses O(N)O(N) additions in the field. If the commitments we use are statistically binding, our zero-knowledge proofs have unconditional soundness, while if the commitments are statistically hiding we get computational soundness. Our zero-knowledge proofs also have sub-linear communication if the commitment scheme is compact. Our construction proceeds in three steps. First, we give a zero-knowledge proof for arithmetic circuit satisfiability in an ideal linear commitment model where the prover may commit to secret vectors of field elements, and the verifier can receive certified linear combinations of those vectors. Second, we show that the ideal linear commitment proof can be instantiated using error-correcting codes and non-interactive commitments. Finally, by choosing efficient instantiations of the primitives we obtain linear-time zero-knowledge proofs

Foundations of Fully Dynamic Group Signatures

Group signatures are a central cryptographic primitive that has received a considerable amount of attention from the cryptographic community. They allow members of a group to anonymously sign on behalf of the group. Membership is overseen by a designated group manager. There is also a tracing authority that can revoke anonymity by revealing the identity of the signer if and when needed, to enforce accountability and deter abuse. For the primitive to be applicable in practice, it needs to support fully dynamic groups, i.e. users can join and leave at any time. In this work we take a close look at existing security definitions for fully dynamic group signatures. We identify a number of shortcomings in existing security definitions and fill the gap by providing a formal rigorous security model for the primitive. Our model is general and is not tailored towards a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. In the process, we identify a subtle issue inherent to one design paradigm, where new members might try to implicate older ones by means of back-dated signatures. This is not captured by existing models. We propose some inexpensive fixes for some existing constructions to avoid the issue

Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

Particle Swarm Optimization is an evolutionary method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The evolution is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of the inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is illustrated on the minimum labelling Steiner tree problem: given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes, whose edges have the smallest number of distinct labels

Foundations of Fully Dynamic Group Signatures

Group signatures allow members of a group to anonymously sign on behalf of the group. Membership is administered by a designated group manager. The group manager can also reveal the identity of a signer if and when needed to enforce accountability and deter abuse. For group signatures to be applicable in practice, they need to support fully dynamic groups, i.e., users may join and leave at any time. Existing security definitions for fully dynamic group signatures are informal, have shortcomings, and are mutually incompatible. We fill the gap by providing a formal rigorous security model for fully dynamic group signatures. Our model is general and is not tailored toward a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. We consider both the case where the group management and tracing signatures are administered by the same authority, i.e., a single group manager, and also the case where those roles are administered by two separate authorities, i.e., a group manager and an opening authority. We also show that a specialization of our model captures existing models for static and partially dynamic schemes. In the process, we identify a subtle gap in the security achieved by group signatures using revocation lists. We show that in such schemes new members achieve a slightly weaker notion of traceability. The flexibility of our security model allows to capture such relaxation of traceability

Italian/Americans and the American Racial System: Contadini to Settler Colonists?

This thesis explores the relationship between ethnicity and race, “whiteness,” in the American racial system through the lens of Italian/Americans. Firstly, it overviews the current scholarship on Italian/Americans and whiteness. Secondly, it analyzes methodologies that are useful for understanding race in an American context. Thirdly, it presents a case study on the Columbus symbol and the battle over identity that arose out of, and continues over, this symbol. Finally, this thesis provides suggestions using the case study and methodologies to open up new ways of understanding Italian/Americans and the American racial system

DAMA/NaI results

The DAMA/NaI set-up of the DAMA experiment has been operative during seven annual cycles and has investigated several rare processes. In particular, it has been realised in order to investigate the model independent annual modulation signature for Dark Matter particles in the galactic halo. With the total exposure collected in the seven annual cycles (107731 kg day) a model independent evidence for the presence of a Dark Matter particle component in the galactic halo has been pointed out at 6.3 sigma C.L.. Some of the many possible corollary model dependent quests for the candidate particle have been presented as well.Comment: Contributed paper to the Rencontres de Moriond "Electroweak Interactions and Unified Theories", La Thuile, Aosta Valley, Italy, March 200

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

Investigating electron interacting dark matter

Some extensions of the Standard Model provide Dark Matter candidate particles which can have a dominant coupling with the lepton sector of the ordinary matter. Thus, such Dark Matter candidate particles ($\chi^{0}$) can be directly detected only through their interaction with electrons in the detectors of a suitable experiment, while they are lost by experiments based on the rejection of the electromagnetic component of the experimental counting rate. These candidates can also offer a possible source of the 511 keV photons observed from the galactic bulge. In this paper this scenario is investigated. Some theoretical arguments are developed and related phenomenological aspects are discussed. Allowed intervals and regions for the characteristic phenomenological parameters of the considered model and of the possible mediator of the interaction are also derived considering the DAMA/NaI data.Comment: 16 pages, 6 figures. Accepted for publication in PRD. One typo correcte