Another Look at XCB

XCB is a tweakable enciphering scheme (TES) which was first proposed in 2004. The scheme was modified in 2007. We call these two versions of XCB as XCBv1 and XCBv2 respectively. XCBv2 was later proposed as a standard for encryption of sector oriented storage media in IEEE-std 1619.2 2010. There is no known proof of security for XCBv1 but the authors provided a concrete security bound for XCBv2 and a ``proof\u27\u27 for justifying the bound. In this paper we show that XCBv2 is not secure as a TES by showing an easy distinguishing attack on it. For XCBv2 to be secure, the message space should contain only messages whose lengths are multiples of the block length of the block cipher. For such restricted message spaces also, the bound that the authors claim is not justified. We show this by pointing out some errors in the proof. For XCBv2 on full block messages, we provide a new security analysis. The resulting bound that can be proved is much worse than what has been claimed by the authors. Further, we provide the first concrete security bound for XCBv1, which holds for all message lengths. In terms of known security bounds, both XCBv1 and XCBv2 are worse compared to existing alternative TES

Factorisation and holomorphic blocks in 4d

We study N=1 theories on Hermitian manifolds of the form M^4=S^1xM^3 with M^3 a U(1) fibration over S^2, and their 3d N=2 reductions. These manifolds admit an Heegaard-like decomposition in solid tori D^2xT^2 and D^2xS^1. We prove that when the 4d and 3d anomalies are cancelled the matrix integrands in the Coulomb branch partition functions can be factorised in terms of 1-loop factors on D^2xT^2 and D^2xS^1 respectively. By evaluating the Coulomb branch matrix integrals we show that the 4d and 3d partition functions can be expressed as sums of products of 4d and 3d holomorphic blocks.Comment: 57 page

Implications of Unitarity and Charge Breaking Minima in Left-Right Symmetric Model

We examine the usefulness of the unitarity conditions in Left-Right symmetric model which can translate into giving a stronger constraint on the model parameters together with the criteria derived from vacuum stability and perturbativity. In this light, we demonstrate the bounds on the masses of the physical scalars present in the model and find the scenario where multiple scalar modes are in the reach of Large Hadron Collider. We also analyse the additional conditions that can come from charge breaking minima in this context.Comment: v2: Accepted for publication in Phys. Rev. D, reference added, minor change in the text, 16 pages, 2 figure

Parametrized Homology via Zigzag Persistence

This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or, equivalently, as a persistence diagram. By defining persistence in terms of finite rectangle measures, we classify barcode intervals into four classes. Each of these conveys how the homological features perish at both ends of the interval over which they are defined

Cross-border Mergers and Hollowing-out

The purpose of our paper is to examine the profitability and social desirability of both domestic and foreign mergers in a location-quantity competition model, where we allow for the possibility of hollowing-out of the target firm. We refer to hollowing-out as the situation where the target firm is shut down following a merger with a domestic or foreign acquirer. Our analysis shows that mergers have ambiguous effects on the profitability of merged firms and on social welfare. Hollowing-out occurs in very few instances in our framework. One such instance is the case of firms located side-by-side in the same cluster and only if it is very costly to transfer the more efficient technology of the acquirer to the domestic target firm. This happens regardless of the origin of the acquirer, domestic or foreign. We also show that there are instances when a cross-border merger with hollowing out is not profitable but it is socially desirable.Economic models; International topics; Market structure and pricing

A New Look at the Ashtekar-Magnon Energy Condition

In 1975, Ashtekar and Magnon showed that an energy condition selects a unique quantization procedure for certain observers in general, curved spacetimes. We generalize this result in two important ways, by eliminating the need to assume a particular form for the (quantum) Hamiltonian, and by considering the surprisingly nontrivial extension to nonminimal coupling.Comment: REVTeX, 10 page