Quantifying Shannon's Work Function for Cryptanalytic Attacks

Attacks on cryptographic systems are limited by the available computational resources. A theoretical understanding of these resource limitations is needed to evaluate the security of cryptographic primitives and procedures. This study uses an Attacker versus Environment game formalism based on computability logic to quantify Shannon's work function and evaluate resource use in cryptanalysis. A simple cost function is defined which allows to quantify a wide range of theoretical and real computational resources. With this approach the use of custom hardware, e.g., FPGA boards, in cryptanalysis can be analyzed. Applied to real cryptanalytic problems, it raises, for instance, the expectation that the computer time needed to break some simple 90 bit strong cryptographic primitives might theoretically be less than two years.Comment: 19 page

Quantifying Resource Use in Computations

It is currently not possible to quantify the resources needed to perform a computation. As a consequence, it is not possible to reliably evaluate the hardware resources needed for the application of algorithms or the running of programs. This is apparent in both computer science, for instance, in cryptanalysis, and in neuroscience, for instance, comparative neuro-anatomy. A System versus Environment game formalism is proposed based on Computability Logic that allows to define a computational work function that describes the theoretical and physical resources needed to perform any purely algorithmic computation. Within this formalism, the cost of a computation is defined as the sum of information storage over the steps of the computation. The size of the computational device, eg, the action table of a Universal Turing Machine, the number of transistors in silicon, or the number and complexity of synapses in a neural net, is explicitly included in the computational cost. The proposed cost function leads in a natural way to known computational trade-offs and can be used to estimate the computational capacity of real silicon hardware and neural nets. The theory is applied to a historical case of 56 bit DES key recovery, as an example of application to cryptanalysis. Furthermore, the relative computational capacities of human brain neurons and the C. elegans nervous system are estimated as an example of application to neural nets.Comment: 26 pages, no figure

Spin injection across magnetic/non-magnetic interfaces with finite magnetic layers

We have reconsidered the problem of spin injection across ferromagnet/non-magnetic-semiconductor (FM/NMS) and dilute-magnetic-semiconductor/non-magnetic-semiconductor interfaces, for structures with \textit{finite} magnetic layers (FM or DMS). By using appropriate physical boundary conditions, we find expressions for the resistances of these structures which are in general different from previous results in the literature. When the magnetoresistance of the contacts is negligible, we find that the spin-accumulation effect alone cannot account for the $d$ dependence observed in recent magnetoresistance data. In a limited parameter range, our formulas predict a strong $d$ dependence arising from the magnetic contacts in systems where their magnetoresistances are sizable.Comment: 6 pages, 3 eps figs. (extended version- new title + two new figures added

Hall viscosity from gauge/gravity duality

In (2+1)-dimensional systems with broken parity, there exists yet another transport coefficient, appearing at the same order as the shear viscosity in the hydrodynamic derivative expansion. In condensed matter physics, it is referred to as "Hall viscosity". We consider a simple holographic realization of a (2+1)-dimensional isotropic fluid with broken spatial parity. Using techniques of fluid/gravity correspondence, we uncover that the holographic fluid possesses a nonzero Hall viscosity, whose value only depends on the near-horizon region of the background. We also write down a Kubo's formula for the Hall viscosity. We confirm our results by directly computing the Hall viscosity using the formula.Comment: 12 page

Generating topological order from a 2D cluster state using a duality mapping

In this paper we prove, extend and review possible mappings between the two-dimensional Cluster state, Wen's model, the two-dimensional Ising chain and Kitaev's toric code model. We introduce a two-dimensional duality transformation to map the two-dimensional lattice cluster state into the topologically-ordered Wen model. Then, we subsequently investigates how this mapping could be achieved physically, which allows us to discuss the rate at which a topologically ordered system can be achieved. Next, using a lattice fermionization method, Wen's model is mapped into a series of one-dimensional Ising interactions. Considering the boundary terms with this mapping then reveals how the Ising chains interact with one another. The relationships discussed in this paper allow us to consider these models from two different perspectives: From the perspective of condensed matter physics these mappings allow us to learn more about the relation between the ground state properties of the four different models, such as their entanglement or topological structure. On the other hand, we take the duality of these models as a starting point to address questions related to the universality of their ground states for quantum computation.Comment: 5 Figure

Depth-Resolved Composition and Electronic Structure of Buried Layers and Interfaces in a LaNiO3_3/SrTiO3_3 Superlattice from Soft- and Hard- X-ray Standing-Wave Angle-Resolved Photoemission

LaNiO$_3$ (LNO) is an intriguing member of the rare-earth nickelates in exhibiting a metal-insulator transition for a critical film thickness of about 4 unit cells [Son et al., Appl. Phys. Lett. 96, 062114 (2010)]; however, such thin films also show a transition to a metallic state in superlattices with SrTiO$_3$ (STO) [Son et al., Appl. Phys. Lett. 97, 202109 (2010)]. In order to better understand this transition, we have studied a strained LNO/STO superlattice with 10 repeats of [4 unit-cell LNO/3 unit-cell STO] grown on an (LaAlO$_3$)$_{0.3}$(Sr$_2$AlTaO$_6$)$_{0.7}$ substrate using soft x-ray standing-wave-excited angle-resolved photoemission (SWARPES), together with soft- and hard- x-ray photoemission measurements of core levels and densities-of-states valence spectra. The experimental results are compared with state-of-the-art density functional theory (DFT) calculations of band structures and densities of states. Using core-level rocking curves and x-ray optical modeling to assess the position of the standing wave, SWARPES measurements are carried out for various incidence angles and used to determine interface-specific changes in momentum-resolved electronic structure. We further show that the momentum-resolved behavior of the Ni 3d eg and t2g states near the Fermi level, as well as those at the bottom of the valence bands, is very similar to recently published SWARPES results for a related La$_{0.7}$Sr$_{0.3}$MnO$_3$/SrTiO$_3$ superlattice that was studied using the same technique (Gray et al., Europhysics Letters 104, 17004 (2013)), which further validates this experimental approach and our conclusions. Our conclusions are also supported in several ways by comparison to DFT calculations for the parent materials and the superlattice, including layer-resolved density-of-states results