On the Communication Complexity of Secure Computation

Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful information theoretic tools to prove lower bounds on the communication complexity of MPC. We restrict ourselves to a 3-party setting in order to bring out the power of these tools without introducing too many complications. Our techniques include the use of a data processing inequality for residual information - i.e., the gap between mutual information and G\'acs-K\"orner common information, a new information inequality for 3-party protocols, and the idea of distribution switching by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case. Using these techniques we obtain tight bounds on communication complexity by MPC protocols for various interesting functions. In particular, we show concrete functions that have "communication-ideal" protocols, which achieve the minimum communication simultaneously on all links in the network. Also, we obtain the first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of Feige, Kilian and Naor (1994), who had shown that such functions exist. We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.Comment: 37 page

Inclusive-photon production and its dependence on photon isolation in pp collisions at s√ = 13 TeV using 139 fb−1 of ATLAS data

Measurements of differential cross sections are presented for inclusive isolated-photon production in pp collisions at a centre-of-mass energy of 13 TeV provided by the LHC and using 139 fb−1 of data recorded by the ATLAS experiment. The cross sections are measured as functions of the photon transverse energy in different regions of photon pseudorapidity. The photons are required to be isolated by means of a fixed-cone method with two different cone radii. The dependence of the inclusive-photon production on the photon isolation is investigated by measuring the fiducial cross sections as functions of the isolation-cone radius and the ratios of the differential cross sections with different radii in different regions of photon pseudorapidity. The results presented in this paper constitute an improvement with respect to those published by ATLAS earlier: the measurements are provided for different isolation radii and with a more granular segmentation in photon pseudorapidity that can be exploited in improving the determination of the proton parton distribution functions. These improvements provide a more in-depth test of the theoretical predictions. Next-to-leading-order QCD predictions from JETPHOX and SHERPA and next-to-next-to-leading-order QCD predictions from NNLOJET are compared to the measurements, using several parameterisations of the proton parton distribution functions. The measured cross sections are well described by the fixed-order QCD predictions within the experimental and theoretical uncertainties in most of the investigated phase-space region

Charged-hadron production in pp, p+Pb, Pb+Pb, and Xe+Xe collisions at sNN−−−√ = 5 TeV with the ATLAS detector at the LHC

This paper presents measurements of charged-hadron spectra obtained in pp, p+Pb, and Pb+Pb collisions at s√ or sNN−−−√ = 5.02 TeV, and in Xe+Xe collisions at sNN−−−√ = 5.44 TeV. The data recorded by the ATLAS detector at the LHC have total integrated luminosities of 25 pb−1, 28 nb−1, 0.50 nb−1, and 3 μb−1, respectively. The nuclear modification factors RpPb and RAA are obtained by comparing the spectra in heavy-ion and pp collisions in a wide range of charged-particle transverse momenta and pseudorapidity. The nuclear modification factor RpPb shows a moderate enhancement above unity with a maximum at pT ≈ 3 GeV; the enhancement is stronger in the Pb-going direction. The nuclear modification factors in both Pb+Pb and Xe+Xe collisions feature a significant, centrality-dependent suppression. They show a similar distinct pT-dependence with a local maximum at pT ≈ 2 GeV and a local minimum at pT ≈ 7 GeV. This dependence is more distinguishable in more central collisions. No significant |η|-dependence is found. A comprehensive comparison with several theoretical predictions is also provided. They typically describe RAA better in central collisions and in the pT range from about 10 to 100 GeV

A century of trends in adult human height

Being taller is associated with enhanced longevity, and higher education and earnings. We reanalysed 1472 population-based studies, with measurement of height on more than 18.6 million participants to estimate mean height for people born between 1896 and 1996 in 200 countries. The largest gain in adult height over the past century has occurred in South Korean women and Iranian men, who became 20.2 cm (95% credible interval 17.5-22.7) and 16.5 cm (13.3-19.7) taller, respectively. In contrast, there was little change in adult height in some sub-Saharan African countries and in South Asia over the century of analysis. The tallest people over these 100 years are men born in the Netherlands in the last quarter of 20th century, whose average heights surpassed 182.5 cm, and the shortest were women born in Guatemala in 1896 (140.3 cm; 135.8-144.8). The height differential between the tallest and shortest populations was 19-20 cm a century ago, and has remained the same for women and increased for men a century later despite substantial changes in the ranking of countries

Rising rural body-mass index is the main driver of the global obesity epidemic in adults

Body-mass index (BMI) has increased steadily in most countries in parallel with a rise in the proportion of the population who live in cities 1,2 . This has led to a widely reported view that urbanization is one of the most important drivers of the global rise in obesity 3�6 . Here we use 2,009 population-based studies, with measurements of height and weight in more than 112 million adults, to report national, regional and global trends in mean BMI segregated by place of residence (a rural or urban area) from 1985 to 2017. We show that, contrary to the dominant paradigm, more than 55 of the global rise in mean BMI from 1985 to 2017�and more than 80 in some low- and middle-income regions�was due to increases in BMI in rural areas. This large contribution stems from the fact that, with the exception of women in sub-Saharan Africa, BMI is increasing at the same rate or faster in rural areas than in cities in low- and middle-income regions. These trends have in turn resulted in a closing�and in some countries reversal�of the gap in BMI between urban and rural areas in low- and middle-income countries, especially for women. In high-income and industrialized countries, we noted a persistently higher rural BMI, especially for women. There is an urgent need for an integrated approach to rural nutrition that enhances financial and physical access to healthy foods, to avoid replacing the rural undernutrition disadvantage in poor countries with a more general malnutrition disadvantage that entails excessive consumption of low-quality calories. © 2019, The Author(s)

Scalable Byzantine agreement with a random beacon

Abstract. We present two Monte Carlo algorithms for efficiently computing Byzantine agreement in the partially synchronous communication model. The algorithms assume the existence of a random beacon, which is a stream of random bits known to all processors. Both algorithms terminate in O(1) expected time. The first algorithm sends O(B + n log n) messages in total, where B is the maximum number of messages sent by the bad processors in any round and n is the number of processors. It ensures all processors reach agreement. The second algorithm sends Õ(1) messages per processor, and is thus load-balanced, and ensures all but a o(1) fraction of the processors reach agreement. Both algorithms succeed with probability 1 − O(1/n k), even against an adaptive adversary that takes over up to a 1/3 − ɛ fraction of the processors, for any fixed positive values ɛ and k. We prove the correctness of both algorithms and provide empirical evidence that they require significantly less bandwidth than state of the art for networks of size greater than 4,000 processors. Our algorithms work in the full-information model and thus make no cryptographic assumptions.