Orthogonality relations in Quantum Tomography

Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums) that are measured for the quantum estimation. In particular we analyze the reconstruction of operators of spin systems.Comment: 10 pages, 2 figure

An Algebraic Model For Quorum Systems

Quorum systems are a key mathematical abstraction in distributed fault-tolerant computing for capturing trust assumptions. A quorum system is a collection of subsets of all processes, called quorums, with the property that each pair of quorums have a non-empty intersection. They can be found at the core of many reliable distributed systems, such as cloud computing platforms, distributed storage systems and blockchains. In this paper we give a new interpretation of quorum systems, starting with classical majority-based quorum systems and extending this to Byzantine quorum systems. We propose an algebraic representation of the theory underlying quorum systems making use of multivariate polynomial ideals, incorporating properties of these systems, and studying their algebraic varieties. To achieve this goal we will exploit properties of Boolean Groebner bases. The nice nature of Boolean Groebner bases allows us to avoid part of the combinatorial computations required to check consistency and availability of quorum systems. Our results provide a novel approach to test quorum systems properties from both algebraic and algorithmic perspectives.Comment: 15 pages, 3 algorithm

Unidirectional Quorum-based Cycle Planning for Efficient Resource Utilization and Fault-Tolerance

In this paper, we propose a greedy cycle direction heuristic to improve the generalized $\mathbf{R}$ redundancy quorum cycle technique. When applied using only single cycles rather than the standard paired cycles, the generalized $\mathbf{R}$ redundancy technique has been shown to almost halve the necessary light-trail resources in the network. Our greedy heuristic improves this cycle-based routing technique's fault-tolerance and dependability. For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Optimal communication quorum sets forming optical cycles based on light-trails have been shown to flexibly and efficiently route both point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle routing techniques will use pairs of cycles to achieve both routing and fault-tolerance, which uses substantial resources and creates the potential for underutilization. Instead, we use a single cycle and intentionally utilize $\mathbf{R}$ redundancy within the quorum cycles such that every point-to-point communication pairs occur in at least $\mathbf{R}$ cycles. Without the paired cycles the direction of the quorum cycles becomes critical to the fault tolerance performance. For this we developed a greedy cycle direction heuristic and our single fault network simulations show a reduction of missing pairs by greater than 30%, which translates to significant improvements in fault coverage.Comment: Computer Communication and Networks (ICCCN), 2016 25th International Conference on. arXiv admin note: substantial text overlap with arXiv:1608.05172, arXiv:1608.05168, arXiv:1608.0517

A Touch of Evil: High-Assurance Cryptographic Hardware from Untrusted Components

The semiconductor industry is fully globalized and integrated circuits (ICs) are commonly defined, designed and fabricated in different premises across the world. This reduces production costs, but also exposes ICs to supply chain attacks, where insiders introduce malicious circuitry into the final products. Additionally, despite extensive post-fabrication testing, it is not uncommon for ICs with subtle fabrication errors to make it into production systems. While many systems may be able to tolerate a few byzantine components, this is not the case for cryptographic hardware, storing and computing on confidential data. For this reason, many error and backdoor detection techniques have been proposed over the years. So far all attempts have been either quickly circumvented, or come with unrealistically high manufacturing costs and complexity. This paper proposes Myst, a practical high-assurance architecture, that uses commercial off-the-shelf (COTS) hardware, and provides strong security guarantees, even in the presence of multiple malicious or faulty components. The key idea is to combine protective-redundancy with modern threshold cryptographic techniques to build a system tolerant to hardware trojans and errors. To evaluate our design, we build a Hardware Security Module that provides the highest level of assurance possible with COTS components. Specifically, we employ more than a hundred COTS secure crypto-coprocessors, verified to FIPS140-2 Level 4 tamper-resistance standards, and use them to realize high-confidentiality random number generation, key derivation, public key decryption and signing. Our experiments show a reasonable computational overhead (less than 1% for both Decryption and Signing) and an exponential increase in backdoor-tolerance as more ICs are added