An Improved BKW Algorithm for LWE with Applications to Cryptography and Lattices

In this paper, we study the Learning With Errors problem and its binary variant, where secrets and errors are binary or taken in a small interval. We introduce a new variant of the Blum, Kalai and Wasserman algorithm, relying on a quantization step that generalizes and fine-tunes modulus switching. In general this new technique yields a significant gain in the constant in front of the exponent in the overall complexity. We illustrate this by solving p within half a day a LWE instance with dimension n = 128, modulus $q = n^2$, Gaussian noise $\alpha = 1/(\sqrt{n/\pi} \log^2 n)$ and binary secret, using $2^{28}$ samples, while the previous best result based on BKW claims a time complexity of $2^{74}$ with $2^{60}$ samples for the same parameters. We then introduce variants of BDD, GapSVP and UniqueSVP, where the target point is required to lie in the fundamental parallelepiped, and show how the previous algorithm is able to solve these variants in subexponential time. Moreover, we also show how the previous algorithm can be used to solve the BinaryLWE problem with n samples in subexponential time $2^{(\ln 2/2+o(1))n/\log \log n}$. This analysis does not require any heuristic assumption, contrary to other algebraic approaches; instead, it uses a variant of an idea by Lyubashevsky to generate many samples from a small number of samples. This makes it possible to asymptotically and heuristically break the NTRU cryptosystem in subexponential time (without contradicting its security assumption). We are also able to solve subset sum problems in subexponential time for density $o(1)$, which is of independent interest: for such density, the previous best algorithm requires exponential time. As a direct application, we can solve in subexponential time the parameters of a cryptosystem based on this problem proposed at TCC 2010.Comment: CRYPTO 201

See-Saw Masses for Quarks and Leptons in SU(5)

We build on a recent paper by Grinstein, Redi and Villadoro, where a see-saw like mechanism for quark masses was derived in the context of spontaneously broken gauged flavour symmetries. The see-saw mechanism is induced by heavy Dirac fermions which are added to the Standard Model spectrum in order to render the flavour symmetries anomaly-free. In this letter we report on the embedding of these fermions into multiplets of an SU(5) grand unified theory and discuss a number of interesting consequences.Comment: 15 pages, 4 figures (v3: outline restructured, modified mechanism to cancel anomalies

A guideline for analyzing circadian wheel-running behavior in rodents under different lighting conditions

Most behavioral experiments within circadian research are based on the analysis of locomotor activity. This paper introduces scientists to chronobiology by explaining the basic terminology used within the field. Furthermore, it aims to assist in designing, carrying out, and evaluating wheel-running experiments with rodents, particularly mice. Since light is an easily applicable stimulus that provokes strong effects on clock phase, the paper focuses on the application of different lighting conditions

Effort estimation of FLOSS projects: A study of the Linux kernel

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 SpringerEmpirical research on Free/Libre/Open Source Software (FLOSS) has shown that developers tend to cluster around two main roles: “core” contributors differ from “peripheral” developers in terms of a larger number of responsibilities and a higher productivity pattern. A further, cross-cutting characterization of developers could be achieved by associating developers with “time slots”, and different patterns of activity and effort could be associated to such slots. Such analysis, if replicated, could be used not only to compare different FLOSS communities, and to evaluate their stability and maturity, but also to determine within projects, how the effort is distributed in a given period, and to estimate future needs with respect to key points in the software life-cycle (e.g., major releases). This study analyses the activity patterns within the Linux kernel project, at first focusing on the overall distribution of effort and activity within weeks and days; then, dividing each day into three 8-hour time slots, and focusing on effort and activity around major releases. Such analyses have the objective of evaluating effort, productivity and types of activity globally and around major releases. They enable a comparison of these releases and patterns of effort and activities with traditional software products and processes, and in turn, the identification of company-driven projects (i.e., working mainly during office hours) among FLOSS endeavors. The results of this research show that, overall, the effort within the Linux kernel community is constant (albeit at different levels) throughout the week, signalling the need of updated estimation models, different from those used in traditional 9am–5pm, Monday to Friday commercial companies. It also becomes evident that the activity before a release is vastly different from after a release, and that the changes show an increase in code complexity in specific time slots (notably in the late night hours), which will later require additional maintenance efforts

Revisiting the Hardness of Binary Error LWE

Binary error LWE is the particular case of the learning with errors (LWE) problem in which errors are chosen in $\{0,1\}$. It has various cryptographic applications, and in particular, has been used to construct efficient encryption schemes for use in constrained devices. Arora and Ge showed that the problem can be solved in polynomial time given a number of samples quadratic in the dimension $n$. On the other hand, the problem is known to be as hard as standard LWE given only slightly more than $n$ samples. In this paper, we first examine more generally how the hardness of the problem varies with the number of available samples. Under standard heuristics on the Arora--Ge polynomial system, we show that, for any $\epsilon >0$, binary error LWE can be solved in polynomial time $n^{O(1/\epsilon)}$ given $\epsilon\cdot n^{2}$ samples. Similarly, it can be solved in subexponential time $2^{\tilde O(n^{1-\alpha})}$ given $n^{1+\alpha}$ samples, for $0<\alpha<1$. As a second contribution, we also generalize the binary error LWE to problem the case of a non-uniform error probability, and analyze the hardness of the non-uniform binary error LWE with respect to the error rate and the number of available samples. We show that, for any error rate $0 < p < 1$, non-uniform binary error LWE is also as hard as worst-case lattice problems provided that the number of samples is suitably restricted. This is a generalization of Micciancio and Peikert\u27s hardness proof for uniform binary error LWE. Furthermore, we also discuss attacks on the problem when the number of available samples is linear but significantly larger than $n$, and show that for sufficiently low error rates, subexponential or even polynomial time attacks are possible

An expression signature of the angiogenic response in gastrointestinal neuroendocrine tumours: correlation with tumour phenotype and survival outcomes.

BACKGROUND: Gastroenteropancreatic neuroendocrine tumours (GEP-NETs) are heterogeneous with respect to biological behaviour and prognosis. As angiogenesis is a renowned pathogenic hallmark as well as a therapeutic target, we aimed to investigate the prognostic and clinico-pathological role of tissue markers of hypoxia and angiogenesis in GEP-NETs. METHODS: Tissue microarray (TMA) blocks were constructed with 86 tumours diagnosed from 1988 to 2010. Tissue microarray sections were immunostained for hypoxia inducible factor 1α (Hif-1α), vascular endothelial growth factor-A (VEGF-A), carbonic anhydrase IX (Ca-IX) and somatostatin receptors (SSTR) 1–5, Ki-67 and CD31. Biomarker expression was correlated with clinico-pathological variables and tested for survival prediction using Kaplan–Meier and Cox regression methods. RESULTS: Eighty-six consecutive cases were included: 51% male, median age 51 (range 16–82), 68% presenting with a pancreatic primary, 95% well differentiated, 51% metastatic. Higher grading (P=0.03), advanced stage (P<0.001), high Hif-1α and low SSTR-2 expression (P=0.03) predicted for shorter overall survival (OS) on univariate analyses. Stage, SSTR-2 and Hif-1α expression were confirmed as multivariate predictors of OS. Median OS for patients with SSTR-2+/Hif-1α-tumours was not reached after median follow up of 8.8 years, whereas SSTR-2-/Hif-1α+ GEP-NETs had a median survival of only 4.2 years (P=0.006). CONCLUSION: We have identified a coherent expression signature by immunohistochemistry that can be used for patient stratification and to optimise treatment decisions in GEP-NETs independently from stage and grading. Tumours with preserved SSTR-2 and low Hif-1α expression have an indolent phenotype and may be offered less aggressive management and less stringent follow up

Direct Integration and Non-Perturbative Effects in Matrix Models

We show how direct integration can be used to solve the closed amplitudes of multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of non-holomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic modular ring of the group $\Gamma(2)$. On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model.Comment: 51 pages, 8 figure

Composite Leptoquarks at the LHC

If electroweak symmetry breaking arises via strongly-coupled physics, the observed suppression of flavour-changing processes suggests that fermion masses should arise via mixing of elementary fermions with composite fermions of the strong sector. The strong sector then carries colour charge, and may contain composite leptoquark states, arising either as TeV scale resonances, or even as light, pseudo-Nambu-Goldstone bosons. The latter, since they are coupled to colour, get a mass of the order of several hundred GeV, beyond the reach of current searches at the Tevatron. The same generic mechanism that suppresses flavour-changing processes suppresses leptoquark-mediated rare processes, making it conceivable that the many stringent constraints may be evaded. The leptoquarks couple predominantly to third-generation quarks and leptons, and the prospects for discovery at LHC appear to be good. As an illustration, a model based on the Pati-Salam symmetry is described, and its embedding in models with a larger symmetry incorporating unification of gauge couplings, which provide additional motivation for leptoquark states at or below the TeV scale, is discussed.Comment: 10 pp, version to appear in JHE

The Rossiter-McLaughlin effect in Exoplanet Research

The Rossiter-McLaughlin effect occurs during a planet's transit. It provides the main means of measuring the sky-projected spin-orbit angle between a planet's orbital plane, and its host star's equatorial plane. Observing the Rossiter-McLaughlin effect is now a near routine procedure. It is an important element in the orbital characterisation of transiting exoplanets. Measurements of the spin-orbit angle have revealed a surprising diversity, far from the placid, Kantian and Laplacian ideals, whereby planets form, and remain, on orbital planes coincident with their star's equator. This chapter will review a short history of the Rossiter-McLaughlin effect, how it is modelled, and will summarise the current state of the field before describing other uses for a spectroscopic transit, and alternative methods of measuring the spin-orbit angle.Comment: Review to appear as a chapter in the "Handbook of Exoplanets", ed. H. Deeg & J.A. Belmont

Measuring the effects of acupuncture and homoeopathy in general practice: An uncontrolled prospective documentation approach

BACKGROUND: Despite the increasing demand for acupuncture and homoeopathy in Germany, little is known about the effects of these treatments in routine care. We set up a pragmatic documentation study in general practice funded within the scope of project launched by a German health insurer. Patients were followed-up for up to four years. METHODS: The aim of the project was to study the effects and benefits of acupuncture and/or homoeopathy, and to assess patient satisfaction within a prospective documentation of over 5000 acupuncture and over 900 homoeopathy patients. As data sources, we used the documentation made available by therapists on every individual visit and a standardised quality-of-life questionnaire (MOS SF-36); these were complemented by questions concerning the patient's medical history and by questions on patient satisfaction. The health insurer provided us with data on work absenteeism. RESULTS: Descriptive analyses of the main outcomes showed benefit of treatment with middle to large-sized effects for the quality of life questionnaire SF-36 and about 1 point improvement on a rating scale of effects, given by doctors. Data on the treatment and the patients' and physicians' background suggests chronically ill patients treated by fairly regular schemes. CONCLUSION: Since the results showed evidence of a subjective benefit for patients from acupuncture and homoeopathy, this may account for the increase in demand for these treatments especially when patients are chronically ill and unsatisfied with the conventional treatment given previously