Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

By applying Grover's quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehl\'{e}, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time $2^{1.799n + o(n)}$, improving upon the classical time complexity of $2^{2.465n + o(n)}$ of Pujol and Stehl\'{e} and the $2^{2n + o(n)}$ of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time $2^{0.312n + o(n)}$, improving upon the classical time complexity of $2^{0.384n + o(n)}$ of Wang et al. These quantum complexities will be an important guide for the selection of parameters for post-quantum cryptosystems based on the hardness of the shortest vector problem.Comment: 19 page

ROYALE: A Framework for Universally Composable Card Games with Financial Rewards and Penalties Enforcement

While many tailor made card game protocols are known, the vast majority of those suffer from three main issues: lack of mechanisms for distributing financial rewards and punishing cheaters, lack of composability guarantees and little flexibility, focusing on the specific game of poker. Even though folklore holds that poker protocols can be used to play any card game, this conjecture remains unproven and, in fact, does not hold for a number of protocols (including recent results). We both tackle the problem of constructing protocols for general card games and initiate a treatment of such protocols in the Universal Composability (UC) framework, introducing an ideal functionality that captures general card games constructed from a set of core card operations. Based on this formalism, we introduce Royale, the first UC-secure general card games which supports financial rewards/penalties enforcement. We remark that Royale also yields the first UC-secure poker protocol. Interestingly, Royale performs better than most previous works (that do not have composability guarantees), which we highlight through a detailed concrete complexity analysis and benchmarks from a prototype implementation

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.

An outflow in the Seyfert ESO 362-G18 revealed by Gemini-GMOS/IFU Observations

We present two-dimensional stellar and gaseous kinematics of the inner 0.7 $\times$ 1.2 kpc$^{2}$ of the Seyfert galaxy ESO 362-G18, derived from optical spectra obtained with the GMOS/IFU on the Gemini South telescope at a spatial resolution of $\approx$170 pc and spectral resolution of 36 km s$^{-1}$. ESO 362-G18 is a strongly perturbed galaxy of morphological type Sa or S0/a, with a minor merger approaching along the NE direction. Previous studies have shown that the [OIII] emission shows a fan-shaped extension of $\approx$ 10\arcsec\ to the SE. We detect the [OIII] doublet, [NII] and H${\alpha}$ emission lines throughout our field of view. The stellar kinematics is dominated by circular motions in the galaxy plane, with a kinematic position angle of $\approx$137$^{\circ}$. The gas kinematics is also dominated by rotation, with kinematic position angles ranging from 122$^{\circ}$ to 139$^{\circ}$. A double-Gaussian fit to the [OIII]$\lambda$5007 and H${\alpha}$ lines, which have the highest signal to noise ratios of the emission lines, reveal two kinematic components: (1) a component at lower radial velocities which we interpret as gas rotating in the galactic disk; and (2) a component with line of sight velocities 100-250 km s$^{-1}$ higher than the systemic velocity, interpreted as originating in the outflowing gas within the AGN ionization cone. We estimate a mass outflow rate of 7.4 $\times$ 10$^{-2}$ M$_{\odot}$ yr$^{-1}$ in the SE ionization cone (this rate doubles if we assume a biconical configuration), and a mass accretion rate on the supermassive black hole (SMBH) of 2.2 $\times$ 10$^{-2}$ M$_{\odot}$ yr$^{-1}$. The total ionized gas mass within $\sim$84 pc of the nucleus is 3.3 $\times$ 10$^{5}$ M$_{\odot}$; infall velocities of $\sim$34 km s$^{-1}$ in this gas would be required to feed both the outflow and SMBH accretion.Comment: 18 pages, 14 figure

Shorter Double-Authentication Preventing Signatures for Small Address Spaces

A recent paper by Derler, Ramacher, and Slamanig (IEEE EuroS&P 2018) constructs double-authentication preventing signatures ( DAP signatures , a specific self-enforcement enabled variant of signatures where messages consist of an address and a payload) that have---if the supported address space is not too large---keys and signatures that are considerably more compact than those of prior work. We embark on their approach to restrict attention to small address spaces and construct novel DAP schemes that beat their signature size by a factor of five and reduce the signing key size from linear to constant (the verification key size remains almost the same). We construct our DAP signatures generically from identification protocols, using a transform similar to but crucially different from that of Fiat and Shamir. We use random oracles. We don\u27t use pairings

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Gauging the effect of supermassive black holes feedback on quasar host galaxies

In order to gauge the role that active galactic nuclei play in the evolution of galaxies via the effect of kinetic feedback in nearby QSO 2’s (z ∼ 0.3), we observed eight such objects with bolometric luminosities Lbol∼1046ergs−1 using Gemini Multi-Object Spectrograph-integral field units. The emission lines were fitted with at least two Gaussian curves, the broadest of which we attributed to gas kinetically disturbed by an outflow. We found that the maximum extent of the outflow ranges from ∼1 to 8 kpc, being ∼0.5±0.3 times the extent of the [OIII] ionized gas region. Our ‘default’ assumptions for the gas density (obtained from the [SII] doublet) and outflow velocities resulted in peak mass outflow rates of M˙defout∼ 3–30 M⊙yr−1 and outflow power of E˙defout∼1041–1043ergs−1⁠. The corresponding kinetic coupling efficiencies are εdeff=E˙defout/Lbol∼7×10−4–0.5 per cent, with the average efficiency being only 0.06 per cent (0.01 per cent median), implying little feedback powers from ionized gas outflows in the host galaxies. We investigated the effects of varying assumptions and calculations on M˙out and E˙out regarding the ionized gas densities, velocities, masses, and inclinations of the outflow relative to the plane of the sky, resulting in average uncertainties of 1 dex. In particular, we found that better indicators of the [OIII] emitting gas density than the default [SII] line ratio, such as the [ArIV] λλ4711,40 line ratio, result in almost an order of magnitude decrease in the εf