Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions

How to generate provably true randomness with minimal assumptions? This question is important not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible in Nature. All current solutions require special structures in the initial source of randomness, or a certain independence relation among two or more sources. Both types of assumptions are impossible to test and difficult to guarantee in practice. Here we show how this fundamental limit can be circumvented by extractors that base security on the validity of physical laws and extract randomness from untrusted quantum devices. In conjunction with the recent work of Miller and Shi (arXiv:1402:0489), our physical randomness extractor uses just a single and general weak source, produces an arbitrarily long and near-uniform output, with a close-to-optimal error, secure against all-powerful quantum adversaries, and tolerating a constant level of implementation imprecision. The source necessarily needs to be unpredictable to the devices, but otherwise can even be known to the adversary. Our central technical contribution, the Equivalence Lemma, provides a general principle for proving composition security of untrusted-device protocols. It implies that unbounded randomness expansion can be achieved simply by cross-feeding any two expansion protocols. In particular, such an unbounded expansion can be made robust, which is known for the first time. Another significant implication is, it enables the secure randomness generation and key distribution using public randomness, such as that broadcast by NIST's Randomness Beacon. Our protocol also provides a method for refuting local hidden variable theories under a weak assumption on the available randomness for choosing the measurement settings.Comment: A substantial re-writing of V2, especially on model definitions. An abstract model of robustness is added and the robustness claim in V2 is made rigorous. Focuses on quantum-security. A future update is planned to address non-signaling securit

Predictable arguments of knowledge

We initiate a formal investigation on the power of predictability for argument of knowledge systems for NP. Specifically, we consider private-coin argument systems where the answer of the prover can be predicted, given the private randomness of the verifier; we call such protocols Predictable Arguments of Knowledge (PAoK). Our study encompasses a full characterization of PAoK, showing that such arguments can be made extremely laconic, with the prover sending a single bit, and assumed to have only one round (i.e., two messages) of communication without loss of generality. We additionally explore PAoK satisfying additional properties (including zero-knowledge and the possibility of re-using the same challenge across multiple executions with the prover), present several constructions of PAoK relying on different cryptographic tools, and discuss applications to cryptography

2DPHOT: A Multi-purpose Environment for the Two-dimensional Analysis of Wide-field Images

We describe 2DPHOT, a general purpose analysis environment for source detection and analysis in deep wide-field images. 2DPHOT is an automated tool to obtain both integrated and surface photometry of galaxies in an image, to perform reliable star-galaxy separation with accurate estimates of contamination at faint flux levels, and to estimate completeness of the image catalog. We describe the analysis strategy on which 2DPHOT is based, and provide a detailed description of the different algorithms implemented in the package. This new environment is intended as a dedicated tool to process the wealth of data from wide-field imaging surveys. To this end, the package is complemented by 2DGUI, an environment that allows multiple processing of data using a range of computing architectures.Comment: Accepted to PAS

Hubble Space Telescope Photometry of Globular Clusters in M81

We perform aperture photometry and profile fitting on 419 globular cluster (GC) candidates with mV \leq 23 mag identified in Hubble Space Telescope Advanced Camera for Surveys BVI imaging, and estimate the effective radii of the clusters. We identify 85 previously known spectroscopically-confirmed clusters, and newly identify 136 objects as good cluster candidates within the 3{\sigma} color and size ranges defined by the spectroscopically confirmed clusters, yielding a total of 221 probable GCs. The luminosity function peak for the 221 probable GCs with estimated total dereddening applied is V ~(20.26 \pm 0.13) mag, corresponding to a distance of ~3.7\pm0.3 Mpc. The blue and red GC candidates, and the metal-rich (MR) and metal-poor (MP) spectroscopically confirmed clusters, are similar in half-light radius, respectively. Red confirmed clusters are about 6% larger in median half-light radius than blue confirmed clusters, and red and blue good GC candidates are nearly identical in half-light radius. The total population of confirmed and "good" candidates shows an increase in half-light radius as a function of galactocentric distance.Comment: 42 figures, 14 pages, accepted to A

Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model

We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks. In an effort to reduce the setup assumptions required for efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks, we consider a model, which we call the Authenticated Public-Key (APK) model. The APK model seems to significantly reduce the setup assumptions made by the CRS model (as no trusted party or honest execution of a centralized algorithm are required), and can be seen as a slightly stronger variation of the Bare Public-Key (BPK) model from \cite{CGGM,MR}, and a weaker variation of the registered public-key model used in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK model. Our main result is a constant-round concurrent non-malleable zero-knowledge argument of knowledge for any polynomial-time relation (associated to a language in $\mathcal{NP}$), under the (minimal) assumption of the existence of a one-way function family. Furthermore,We show time-efficient instantiations of our protocol based on known number-theoretic assumptions. We also note a negative result with respect to further reducing the setup assumptions of our protocol to those in the (unauthenticated) BPK model, by showing that concurrently non-malleable zero-knowledge arguments of knowledge in the BPK model are only possible for trivial languages

[OII] emitters in the GOODS field at z~1.85: a homogeneous measure of evolving star formation

We present the results of a deep, near-infrared, narrow band imaging survey at a central wavelength of 1.062 microns (FWHM=0.01 microns) in the GOODS-South field using the ESO VLT instrument, HAWK-I. The data are used to carry out the highest redshift search for [OII]3727 emission line galaxies to date. The images reach an emission line flux limit (5 sigma) of 1.5 x 10^-17 erg cm^-2 s^-1, additionally making the survey the deepest of its kind at high redshift. In this paper we identify a sample of [OII]3727 emission line objects at redshift z~1.85 in a co-moving volume of ~4100 Mpc^3. Objects are selected using an observed equivalent width (EW_obs) threshold of EW_obs = 50 angstroms. The sample is used to derive the space density and constrain the luminosity function of [OII] emitters at z=1.85. We find that the space density of objects with observed [OII] luminosities in the range log(L_[OII]) > 41.74 erg s^-1 is log(rho)=-2.45+/-0.14 Mpc^-3, a factor of 2 greater than the observed space density of [OII] emitters reported at z~1.4. After accounting for completeness and assuming an internal extinction correction of A_Halpha=1 mag (equivalent to A_[OII]=1.87), we report a star formation rate density of rho* ~0.38+/-0.06 Msun yr^-1 Mpc^-3. We independently derive the dust extinction of the sample using 24 micron fluxes and find a mean extinction of A_[OII]=0.98+/-0.11 magnitudes (A_Halpha=0.52). This is significantly lower than the A_Halpha=1 (A[OII]=1.86) mag value widely used in the literature. Finally we incorporate this improved extinction correction into the star formation rate density measurement and report rho*~0.24+/-0.06 Msun yr^-1 Mpc^-3.Comment: 11 pages, 10 figures, accepted for publication in MNRA

Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack