Random Permutation Statistics and An Improved Slide-Determine Attack on KeeLoq

KeeLoq is a lightweight block cipher which is extensively used in the automotive industry. Its periodic structure, and overall simplicity makes it vulnerable to many different attacks. Only certain attacks are considered as really "practical" attacks on KeeLoq: the brute force, and several other attacks which require up to 2p16 known plaintexts and are then much faster than brute force, developed by Courtois et al., and (faster attack) by Dunkelman et al. On the other hand, due to the unusually small block size, there are yet many other attacks on KeeLoq, which require the knowledge of as much as about 2p32 known plaintexts but are much faster still. There are many scenarios in which such attacks are of practical interest, for example if a master key can be recovered, see Section 2 in [11] for a detailed discussion. The fastest of these attacks is an attack by Courtois, Bard and Wagner from that has a very low complexity of about 2p28 KeeLoq encryptions on average. In this paper we will propose an improved and refined attack which is faster both on average and in the best case. We also present an exact mathematical analysis of probabilities that arise in these attacks using the methods of modern analytic combinatorics

Giant disk galaxies : Where environment trumps mass in galaxy evolution

We identify some of the most HI massive and fastest rotating disk galaxies in the local universe with the aim of probing the processes that drive the formation of these extreme disk galaxies. By combining data from the Cosmic Flows project, which has consistently reanalyzed archival galaxy HI profiles, and 3.6$\mu$m photometry obtained with the Spitzer Space Telescope, with which we can measure stellar mass, we use the baryonic Tully-Fisher (BTF) relationship to explore whether these massive galaxies are distinct. We discuss several results, but the most striking is the systematic offset of the HI-massive sample above the BTF. These galaxies have both more gas and more stars in their disks than the typical disk galaxy of similar rotational velocity. The "condensed" baryon fraction, $f_C$, the fraction of the baryons in a dark matter halo that settle either as cold gas or stars into the disk, is twice as high in the HI-massive sample than typical, and almost reaches the universal baryon fraction in some cases, suggesting that the most extreme of these galaxies have little in the way of a hot baryonic component or cold baryons distributed well outside the disk. In contrast, the star formation efficiency, measured as the ratio of the mass in stars to that in both stars and gas, shows no difference between the HI-massive sample and the typical disk galaxies. We conclude that the star formation efficiency is driven by an internal, self-regulating process, while $f_C$ is affected by external factors. We also found that the most massive HI detected galaxies are located preferentially in filaments. We present the first evidence of an environmental effect on galaxy evolution using a dynamical definition of a filament.Comment: 14 pages, in press MNRA

The mid-infrared Tully-Fisher relation: Spitzer Surface Photometry

The availability of photometric imaging of several thousand galaxies with the Spitzer Space Telescope enables a mid-infrared calibration of the correlation between luminosity and rotation in spiral galaxies. The most important advantage of the new calibration in the 3.6 micron band, IRAC ch.1, is photometric consistency across the entire sky. Additional advantages are minimal obscuration, observations of flux dominated by old stars, and sensitivity to low surface brightness levels due to favorable backgrounds. Through Spitzer cycle 7 roughly 3000 galaxies had been observed and images of these are available at the Spitzer archive. In cycle 8 a program called Cosmic Flows with Spitzer has been initiated that will increase by 1274 the available sample of spiral galaxies with inclinations greater than 45 degrees from face-on suitable for distance measurements. This paper describes procedures based on the photometry package Archangel that are being employed to analyze both the archival and the new data in a uniform way. We give results for 235 galaxies, our calibrator sample for the Tully-Fisher relation. Galaxy magnitudes are determined with uncertainties held below 0.05 mag for normal spiral systems. A subsequent paper will describe the calibration of the [3.6] luminosity-rotation relation.Comment: Accepted for publication in The Astronomical Journal, 12 pages, 9 figure

The Calibration of the WISE W1 and W2 Tully-Fisher Relation

In order to explore local large-scale structures and velocity fields, accurate galaxy distance measures are needed. We now extend the well-tested recipe for calibrating the correlation between galaxy rotation rates and luminosities -- capable of providing such distance measures -- to the all-sky, space-based imaging data from the Wide-field Infrared Survey Explorer (WISE) W1 ($3.4\mu$m) and W2 ($4.6\mu$m) filters. We find a linewidth to absolute magnitude correlation (known as the Tully-Fisher Relation, TFR) of $\mathcal{M}^{b,i,k,a}_{W1} = -20.35 - 9.56 (\log W^i_{mx} - 2.5)$ (0.54 magnitudes rms) and $\mathcal{M}^{b,i,k,a}_{W2} = -19.76 - 9.74 (\log W^i_{mx} - 2.5)$ (0.56 magnitudes rms) from 310 galaxies in 13 clusters. We update the I-band TFR using a sample 9% larger than in Tully & Courtois (2012). We derive $\mathcal{M}^{b,i,k}_I = -21.34 - 8.95 (\log W^i_{mx} - 2.5)$ (0.46 magnitudes rms). The WISE TFRs show evidence of curvature. Quadratic fits give $\mathcal{M}^{b,i,k,a}_{W1} = -20.48 - 8.36 (\log W^i_{mx} - 2.5) + 3.60 (\log W^i_{mx} - 2.5)^2$ (0.52 magnitudes rms) and $\mathcal{M}^{b,i,k,a}_{W2} = -19.91 - 8.40 (\log W^i_{mx} - 2.5) + 4.32 (\log W^i_{mx} - 2.5)^2$ (0.55 magnitudes rms). We apply an I-band -- WISE color correction to lower the scatter and derive $\mathcal{M}_{C_{W1}} = -20.22 - 9.12 (\log W^i_{mx} - 2.5)$ and $\mathcal{M}_{C_{W2}} = -19.63 - 9.11 (\log W^i_{mx} - 2.5)$ (both 0.46 magnitudes rms). Using our three independent TFRs (W1 curved, W2 curved and I-band), we calibrate the UNION2 supernova Type Ia sample distance scale and derive $H_0 = 74.4 \pm 1.4$(stat) $\pm\ 2.4$(sys) kms$^{-1}$ Mpc$^{-1}$ with 4% total error.Comment: 22 page, 21 figures, accepted to ApJ, Table 1 data at http://spartan.srl.caltech.edu/~neill/tfwisecal/table1.tx

The Mid-Infrared Tully-Fisher Relation: Calibration of the SNIa Scale and Ho

This paper builds on a calibration of the SNIa absolute distance scale begun with a core of distances based on the correlation between galaxy rotation rates and optical Ic band photometry. This new work extends the calibration through the use of mid-infrared photometry acquired at 3.6 microns with Spitzer Space Telescope. The great virtue of the satellite observations is constancy of the photometry at a level better than 1% across the sky. The new calibration is based on 39 individual galaxies and 8 clusters that have been the sites of well observed SNIa. The new 3.6 micron calibration is not yet as extensively based as the Ic band calibration but is already sufficient to justify a preliminary report. Distances based on the mid-infrared photometry are 2% greater in the mean than reported at Ic band. This difference is only marginally significant. The Ic band result is confirmed with only a small adjustment. Incorporating a 1% decrease in the LMC distance, the present study indicates Ho = 75.2 +/- 3.0 km/s/Mpc.Comment: Accepted for publication in The Astrophysical Journal Letters, 6 pages, 2 figure