2-Server PIR with sub-polynomial communication

A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the $i$th bit of an $n$-bit database replicated among two servers (which do not communicate) while not revealing any information about $i$ to either server. In this work we construct a 1-round 2-server PIR with total communication cost $n^{O({\sqrt{\log\log n/\log n}})}$. This improves over the currently known 2-server protocols which require $O(n^{1/3})$ communication and matches the communication cost of known 3-server PIR schemes. Our improvement comes from reducing the number of servers in existing protocols, based on Matching Vector Codes, from 3 or 4 servers to 2. This is achieved by viewing these protocols in an algebraic way (using polynomial interpolation) and extending them using partial derivatives

Outlaw distributions and locally decodable codes

Locally decodable codes (LDCs) are error correcting codes that allow for decoding of a single message bit using a small number of queries to a corrupted encoding. Despite decades of study, the optimal trade-off between query complexity and codeword length is far from understood. In this work, we give a new characterization of LDCs using distributions over Boolean functions whose expectation is hard to approximate (in L∞ norm) with a small number of samples. We coin the term “outlaw distributions” for such distributions since they “defy” the Law of Large Numbers. We show that the existence of outlaw distributions over sufficiently “smooth” functions implies the existence of constant query LDCs and vice versa. We give several candidates for outlaw distributions over smooth functions coming from finite field incidence geometry, additive combinatorics and hypergraph (non)expanders. We also prove a useful lemma showing that (smooth) LDCs which are only required to work on average over a random message and a random message index can be turned into true LDCs at the cost of only constant factors in the parameters

Epilepsy syndrome-associated balance dysfunction assessed by static posturography

AbstractPurposeTo compare subclinical balance dysfunction in patients with various epilepsy syndromes with apparently healthy subjects.MethodsTwenty-seven patients with localization-related epilepsy (LRE), 19 with primary generalized epilepsy (PGE), who had no subjective complaints of impaired balance and no abnormal neurologic findings on examination, and 22 apparently healthy subjects, underwent static posturography using the Posture Scale Analyzer (PSA) system.ResultsSway index was higher in patients compared to healthy subjects in all tests, significant for single leg stance (p=0.005). Patients with PGE had a higher sway index compared to patients with LRE in six of the tests, also significant for single leg stance (p=0.027). This difference was not affected by the type of AED treatment or disease duration.ConclusionPosturography can improve balance function assessment in patients with epilepsy, demonstrate subclinical impairment in seemingly asymptomatic patients, and further characterize balance deficits in different epilepsy syndromes

How to Extract Useful Randomness from Unreliable Sources

For more than 30 years, cryptographers have been looking for public sources of uniform randomness in order to use them as a set-up to run appealing cryptographic protocols without relying on trusted third parties. Unfortunately, nowadays it is fair to assess that assuming the existence of physical phenomena producing public uniform randomness is far from reality. It is known that uniform randomness cannot be extracted from a single weak source. A well-studied way to overcome this is to consider several independent weak sources. However, this means we must trust the various sampling processes of weak randomness from physical processes. Motivated by the above state of affairs, this work considers a set-up where players can access multiple potential sources of weak randomness, several of which may be jointly corrupted by a computationally unbounded adversary. We introduce SHELA (Somewhere Honest Entropic Look Ahead) sources to model this situation. We show that there is no hope of extracting uniform randomness from a SHELA source. Instead, we focus on the task of Somewhere-Extraction (i.e., outputting several candidate strings, some of which are uniformly distributed -- yet we do not know which). We give explicit constructions of Somewhere-Extractors for SHELA sources with good parameters. Then, we present applications of the above somewhere-extractor where the public uniform randomness can be replaced by the output of such extraction from corruptible sources, greatly outperforming trivial solutions. The output of somewhere-extraction is also useful in other settings, such as a suitable source of random coins for many randomized algorithms. In another front, we comprehensively study the problem of Somewhere-Extraction from a weak source, resulting in a series of bounds. Our bounds highlight the fact that, in most regimes of parameters (including those relevant for applications), SHELA sources significantly outperform weak sources of comparable parameters both when it comes to the process of Somewhere-Extraction, or in the task of amplification of success probability in randomized algorithms. Moreover, the low quality of somewhere-extraction from weak sources excludes its use in various efficient applications

Sub-logarithmic Distributed Oblivious RAM with Small Block Size

Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to securely execute RAM programs over data that is stored in an untrusted server. Distributed Oblivious RAM is a variant of ORAM, where the data is stored in $m>1$ servers. Extensive research over the last few decades have succeeded to reduce the bandwidth overhead of ORAM schemes, both in the single-server and the multi-server setting, from $O(\sqrt{N})$ to $O(1)$. However, all known protocols that achieve a sub-logarithmic overhead either require heavy server-side computation (e.g. homomorphic encryption), or a large block size of at least $\Omega(\log^3 N)$. In this paper, we present a family of distributed ORAM constructions that follow the hierarchical approach of Goldreich and Ostrovsky [GO96]. We enhance known techniques, and develop new ones, to take better advantage of the existence of multiple servers. By plugging efficient known hashing schemes in our constructions, we get the following results: 1. For any $m\geq 2$, we show an $m$-server ORAM scheme with $O(\log N/\log\log N)$ overhead, and block size $\Omega(\log^2 N)$. This scheme is private even against an $(m-1)$-server collusion. 2. A 3-server ORAM construction with $O(\omega(1)\log N/\log\log N)$ overhead and a block size almost logarithmic, i.e. $\Omega(\log^{1+\epsilon}N)$. We also investigate a model where the servers are allowed to perform a linear amount of light local computations, and show that constant overhead is achievable in this model, through a simple four-server ORAM protocol

Planar Point Sets Determine Many Pairwise Crossing Segments

We show that any set of $n$ points in general position in the plane determines $n^{1-o(1)}$ pairwise crossing segments. The best previously known lower bound, $\Omega\left(\sqrt n\right)$, was proved more than 25 years ago by Aronov, Erd\H os, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.Comment: A preliminary version to appear in the proceedings of STOC 201

No evidence of neural adaptations following chronic unilateral isometric training of the intrinsic muscles of the hand: a randomized controlled study

Purpose: To test whether long-term cortical adaptations occur bilaterally following chronic unilateral training with a simple motor task. / Methods: Participants (n = 34) were randomly allocated to a training or control groups. Only the former completed a 4-week maximal-intensity isometric training of the right first dorsal interosseus muscle through key pinching. Maximal strength was assessed bilaterally in four different movements progressively less similar to the training task: key, tip and tripod pinches, and handgrip. Transcranial magnetic stimulation was used to probe, in the left and right primary hand motor cortices, a number of standard tests of cortical excitability, including thresholds, intra-cortical inhibition and facilitation, transcallosal inhibition, and sensory-motor integration. / Results: Training increased strength in the trained hand, but only for the tasks specifically involving the trained muscle (key +8.5 %; p < 0.0005; tip +7.2 %; p = 0.02). However, the effect size was small and below the cutoff for meaningful change. Handgrip and tripod pinch were instead unaffected. There was a similar improvement in strength in the untrained hand, i.e., a cross-education effect (key +6.4 %; p = 0.02; tip +4.7 %; p = 0.007). Despite these changes in strength, no significant variation was observed in any of the neurophysiological parameters describing cortico-spinal and intra-cortical excitability, inter-hemispheric inhibition, and cortical sensory-motor integration. / Conclusions: A 4-week maximal-intensity unilateral training induced bilaterally spatial- and task-specific strength gains, which were not associated to direct or crossed cortical adaptations. The observed long-term stability of neurophysiological parameters might result from homeostatic plasticity phenomena, aimed at restoring the physiological inter-hemispheric balance of neural activity levels perturbed by the exercise. / Trial registration number: ClinicalTrials.gov identifier NCT02010398

Do Israelis understand the Hebrew bible?

The Hebrew Bible should be taught like a foreign language in Israel too, argues Ghil'ad Zuckermann, inter alia endorsing Avraham Ahuvia’s recently-launched translation of the Old Testament into what Zuckermann calls high-register 'Israeli'. According to Zuckermann, Tanakh RAM fulfills the mission of 'red 'el ha'am' not only in its Hebrew meaning (Go down to the people) but also – more importantly – in its Yiddish meaning ('red' meaning 'speak!', as opposed to its colorful communist sense). Ahuvia's translation is most useful and dignified. Given its high register, however, Zuckermann predicts that the future promises consequent translations into more colloquial forms of Israeli, a beautifully multi-layered and intricately multi-sourced language, of which to be proud.Ghil'ad Zuckerman