Statistical Zero Research Articles

Robustness for Space-Bounded Statistical Zero Knowledge

We show that the space-bounded Statistical Zero Knowledge classes \({{{\sf SZK}_{\sf L}}} \) and \({{{\sf {NISZK}_{\sf {L}}}}} \) are surprisingly robust, in that the power of the verifier and simulator can be strengthened or weakened without affecting the resulting class. Coupled with other recent characterizations of these classes [5], this can be viewed as lending support to the conjecture that these classes may coincide with the non-space-bounded classes \({{{\sf SZK}}} \) and \({{{\sf {NISZK}_{\sf {L}}}}} \) , respectively.

Gender differences in agricultural productivity in Côte d'Ivoire: Distribution, drivers, and changes over time

AbstractThis paper analyzes changes in agricultural productivity gender gaps in Côte d'Ivoire between 2008 and 2016 using decomposition methods. The analysis finds that the gender gap went from 40% in food crops and 17% in exports crops in 2008, to 19% in food crops and a statistical zero in export crops in 2016. The overall gender gap decreased by 15 percentage points over this period, and is statistically insignificant in 2016 once accounting for whether households farm export crops. Moreover, our results show that while some drivers of the gender gap remain stable across the decade (including total land cultivated, and pesticide and fertilizer use), others change their contribution (number of plots, crop choice and household labor). Despite substantial improvements, female‐headed households in the bottom half of the distribution remain disadvantaged. Our results indicate that strengthening women's access to agricultural labor and adoption of export crops are policy priorities to reach gender parity.

Cryptographic hardness under projections for time-bounded Kolmogorov complexity

A version of time-bounded Kolmogorov complexity, denoted KT, has received attention in the past several years, due to its close connection to circuit complexity and to the Minimum Circuit Size Problem MCSP. Essentially all results about the complexity of MCSP hold also for MKTP (the problem of computing the KT complexity of a string). Both MKTP and MCSP are hard for SZK (Statistical Zero Knowledge) under BPP-Turing reductions; neither is known to be NP-complete.Recently, some hardness results for MKTP were proved that are not (yet) known to hold for MCSP. In particular, MKTP is hard for DET (a subclass of P) under nonuniform ≤mNC0 reductions. In this paper, we improve this, to show that MKTP‾ is hard for the (apparently larger) class NISZKL under not only ≤mNC0 reductions but even under projections. Also MKTP‾ is hard for NISZK under ≤mP/poly reductions. Here, NISZK is the class of problems with non-interactive zero-knowledge proofs, and NISZKL is the non-interactive version of the class SZKL that was studied by Dvir et al.As an application, we provide several improved worst-case to average-case reductions to problems in NP, and we obtain a new lower bound on MKTP (which is currently not known to hold for MCSP).

Sensitivity of Logic Learning Machine for Reliability in Safety-Critical Systems

Nowadays, artificial intelligence (AI) is bursting in many fields, including critical ones, giving rise to reliable AI that means ensuring safety of autonomous decisions. As the false negatives may have a safety impact (e.g., in a mobility scenario, prediction of no collision, but collision in reality), the aim is to push them as close to zero as possible, thus designing “safety regions” in the feature space with statistical zero error. We show here how sensitivity analysis of an explainable AI model drives such statistical assurance. We test and compare the proposed algorithms on two different datasets (physical fatigue and vehicle platooning) and achieve quite different conclusions in terms of achievable performance that strongly depend on the level of noise in the dataset rather than on the algorithms at hand.

An identification system based on the explicit isomorphism problem

We propose a new identification system based on algorithmic problems related to computing isomorphisms between central simple algebras. We design a statistical zero knowledge protocol which relies on the hardness of computing isomorphisms between orders in division algebras which generalizes a protocol by Hartung and Schnorr, which relies on the hardness of integral equivalence of quadratic forms.

Variable data measurement systems analysis: advances in gage bias and linearity referencing and acceptability

Measurement systems analysis (MSA) is a set of requirements and procedures adopted by the automotive industry and other disciplines to evaluate the accuracy and precision of measurement systems through assessing and quantifying the random and systematic errors and assigning appropriate dispositions for tolerance and performance acceptance. The methodology of variable data MSA comprises studies of a system's stability, bias, linearity and gage repeatability and reproducibility (GR&R). This paper describes advances in referencing and criteria for estimation of uncertainty errors, dispositions, and acceptability of MSA bias and linearity, proposing an extension to the basic statistical zero null-hypothesis to include overlap between confidence intervals and uncertainty associated with the reference standards used in bias and linearity studies.

On the Power of Statistical Zero Knowledge

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 18 December 2017Accepted: 29 October 2018Published online: 22 October 2019Keywordsoracle separation, statistical zero knowledge proof, perfect zero knowledge proof, hardness amplificationAMS Subject Headings68Q05, 68Q15Publication DataISSN (print): 0097-5397ISSN (online): 1095-7111Publisher: Society for Industrial and Applied MathematicsCODEN: smjcat

The Supply and Demand Effects of Review Platforms

Review platforms such as Yelp and TripAdvisor aggregate crowd-sourced information about users' experiences with products and services. We analyze the impact of review platforms on the hotel industry using a panel of hotel prices, sales and reviews from five US states over a 10-year period from 2005-2014. We show that a hotel's demand is positively correlated with their average rating across TripAdvisor, Expedia and Hotels.com. Such correlations have grown over our sample period from a statistical zero in 2005 to a substantial level in 2014: a hotel rated one star higher on all the platforms on average has 27.8% higher demand. By contrast, an increase in average ratings has a negligible effect on hotels' pricing schedules (i.e. supply). A natural experiment in our data that caused abrupt changes in the ratings of some hotels but not others suggests that these associations are causal. Building on this causal interpretation, we estimate heterogeneous treatment effects: independent hotels stand to gain more from online reputation than chains, as do hotels that practice revenue management.

Zero knowledge and circuit minimization

We show that every problem in the complexity class SZK (Statistical Zero Knowledge) is efficiently reducible to the Minimum Circuit Size Problem (MCSP). In particular Graph Isomorphism lies in RPMCSP.This is the first theorem relating the computational power of Graph Isomorphism and MCSP, despite the long history these problems share, as candidate NP-intermediate problems.

The effect of bovine somatotropin on the cost of producing milk: Estimates using propensity scores

Annual farm-level data from New York dairy farms from the years 1994 through 2013 were used to estimate the cost effect from bovine somatotropin (bST) using propensity score matching. Cost of production was computed using the whole-farm method, which subtracts sales of crops and animals from total costs under the assumption that the cost of producing those products is equal to their sales values. For a farm to be included in this data set, milk receipts on that farm must have comprised 85% or more of total receipts, indicating that these farms are primarily milk producers. Farm use of bST, where 25% or more of the herd was treated, ranged annually from 25 to 47% of the farms. The average cost effect from the use of bST was estimated to be a reduction of $2.67 per 100kg of milk produced in 2013 dollars, although annual cost reduction estimates ranged from statistical zero to $3.42 in nominal dollars. Nearest neighbor matching techniques generated a similar estimate of $2.78 in 2013 dollars. These cost reductions estimated from the use of bST represented a cost savings of 5.5% per kilogram of milk produced. Herd-level production increase per cow from the use of bST over 20yr averaged 1,160kg.

Statistical Zero Knowledge and quantum one-way functions

One-way functions are a fundamental notion in cryptography, since they are the necessary condition for the existence of secure encryption schemes. Most examples of such functions, including Factoring, Discrete Logarithm or the RSA function, however, can be inverted with the help of a quantum computer. Hence, it is very important to study the possibility of quantum one-way functions, i.e. functions which are easily computable by a classical algorithm but are hard to invert even by a quantum adversary. In this paper, we provide a set of problems that are good candidates for quantum one-way functions. These problems include Graph Non-Isomorphism, Approximate Closest Lattice Vector and Group Non-Membership. More generally, we show that any hard instance of Circuit Quantum Sampling gives rise to a quantum one-way function. By the work of Aharonov and Ta-Shma [D. Aharonov, A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge, in: Proceedings of STOC02 — Symposium on the Theory of Computing, 2001], this implies that any language in Statistical Zero Knowledge which is hard-on-average for quantum computers leads to a quantum one-way function. Moreover, extending the result of Impagliazzo and Luby [R. Impagliazzo, M. Luby, One-way functions are essential for complexity based cryptography, in: Proceedings of FOCS89 — Symposium on Foundations of Computer Science, 1989] to the quantum setting, we prove that quantum distributionally one-way functions are equivalent to quantum one-way functions.

Adiabatic Quantum State Generation

The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to this task by studying the problem of quantum state generation. We motivate this problem by showing that the entire class of statistical zero knowledge, which contains natural candidates for efficient quantum algorithms such as graph isomorphism and lattice problems, can be reduced to the problem of quantum state generation. To study quantum state generation, we define a paradigm which we call adiabatic state generation (ASG) and which is based on adiabatic quantum computation. The ASG paradigm is not meant to replace the standard quantum circuit model or to improve on it in terms of computational complexity. Rather, our goal is to provide a natural theoretical framework, in which quantum state generation algorithms could be designed. The new paradigm seems interesting due to its intriguing links to a variety of different areas: the analysis of spectral gaps and ground‐states of Hamiltonians in physics, rapidly mixing Markov chains, adiabatic computation, and approximate counting. To initiate the study of ASG, we prove several general lemmas that can serve as tools when using this paradigm. We demonstrate the application of the paradigm by using it to turn a variety of (classical) approximate counting algorithms into efficient quantum state generators of nontrivial quantum states, including, for example, the uniform superposition over all perfect matchings in a bipartite graph.

A complete problem for statistical zero knowledge

We present the first complete problem for SZK, the class of promise problems possessing statistical zero-knowledge proofs (against an honest verifier). The problem, called Statistical Difference, is to decide whether two efficiently samplable distributions are either statistically close or far apart. This gives a new characterization of SZK that makes no reference to interaction or zero knowledge .We propose the use of complete problems to unify and extend the study of statistical zero knowledge. To this end, we examine several consequences of our Completeness Theorem and its proof, such as:---A way to make every (honest-verifier) statistical zero-knowledge proof very communication efficient, with the prover sending only one bit to the verifier (to achieve soundness error 1/2).---Simpler proofs of many of the previously known results about statistical zero knowledge, such as the Fortnow and Aiello--Hεstad upper bounds on the complexity of SZK and Okamoto's result that SZK is closed under complement.---Strong closure properties of SZK that amount to constructing statistical zero-knowledge proofs for complex assertions built out of simpler assertions already shown to be in SZK.---New results about the various measures of "knowledge complexity," including a collapse in the hierarchy corresponding to knowledge complexity in the "hint" sense.---Algorithms for manipulating the statistical difference between efficiently samplable distributions, including transformations that "polarize" and "reverse" the statistical relationship between a pair of distributions.

On the Knowledge Complexity of ${\cal{N}P}$

We show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class . Thus, if the polynomial time hierarchy does not collapse, then -complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict languages being proven with even one bit of knowledge. Our result is a common generalization of two previous results: The first asserts that statistical zero knowledge is contained in [11, 2], while the second asserts that the languages recognizable in logarithmic statistical knowledge complexity are in [19]. Next, we consider the relation between the error probability and the knowledge complexity of an interactive proof. Note that reducing the error probability via repetition is not free: it may increase the knowledge complexity. We show that if the negligible error probability is less than (where k(n) is the knowledge complexity) then the language proven is in the third level of the polynomial time hierarchy (specifically, it is in ). In the standard setting of negligible error probability, there exist PSPACE-complete languages which have sub-linear knowledge complexity. However, if we insist, for example, that the error probability is less than , then PSPACE-complete languages do not have sub-quadratic knowledge complexity, unless . In order to prove our main result, we develop an AM protocol for checking that a samplable distribution D has a given entropy h. For any fractions , the verifier runs in time polynomial in and and fails with probability at most to detect an additive error in the entropy. We believe that this protocol is of independent interest. Subsequent to our work Goldreich and Vadhan [16] established that the problem of comparing the entropies of two samplable distributions if they are noticeably different is a natural complete promise problem for the class of statistical zero knowledge ( ).

ARC Length Difference Method in the Selection of Primary Sources of Combined Extragalactic Radio Source Catalogues

The coordinates of common extragalactic radio sources will be different if the orientations of individual frames are different. If coordinates in each of the frames are in good consistence, i.e. small or non local relative deformations exist, common arcs in frames will be equal to each other (within precision) whether the orientations of the frames coincide or not. In addition, if relative deformations exist between frames, these deformations will be reflected partly on the difference of the lengths of common arcs. It is inferred that we can select candidates for primary objects by comparing the lengths of common arcs in individual frames. We call this as the Arc Length Difference (ALD) selection method.Considering that it is unrealistic to distinguish between positions with or without deformations beforehand (Arias et al., 1988), and that an arc length difference gives us nothing definite about the consistency of a specified source in frames because of the variable values and the statistical zero mean of the differences (Li & Jin, 1994), we take the Mean value of all the Absolute Arc Length Differences (MAALD) related to each specified source as the criterion for the recognition of deformation. The large the deformation for a particular source is, the larger (statistically) the absolute value of the arc length difference or the MAALD related to this source will be. Taking all the MAALDs of all the common objects of two frames as a random series, and deleting large MAALDs in this series by means of statistics, we can select candidates for primary objects which have better internal and external consistencies in frames.Here we make emphasis on the following two aspects of the ALD method. First, if we take all the absolute values of the arc length differences as a random series and perform statistical deletion on this series, there will come out the situation that among all the absolute values related to a specified source some will be deleted and others will be kept because of the variable value nature of the arc length difference. Therefore the characteristics of consistency of the source will be concealed and we will be faced to the ambiguous case to decide whether the source should be deleted or not. The effect of the variable value nature of the arc length difference can be avoided and the characteristics of consistency of a source is highlighted by using the mean of all the absolute values related to this source. Second, since the value of MAALD is the mean of all the absolute arc length differences related to a source, a specified arc length difference will enter into two MAALDs, so that all the MAALDs are then interweaved with one another. After one of the MAALDs is deleted, the rest will be changed accordingly. So we emphasize a progressive process to avoid a large number of sources being deleted in a single step.Our tests show that the ALD selection method is stable and reliable. It can emphasize the characteristics of each source on the premise of the consistency of all the sources and the selection results of this method can reflect appropriately the total number of sources, the position precision, the sky coverage and so on of individual frames.

Effect of Certain Dietary Sugars on Hamster Caries ,

The comparative effect of various dietary sugars on hamster dental caries was studied. A strain of hamster which does not normally present caries unless infected with a cariogenic organism was inoculated with AHT-type human cariogenic streptococcus and fed diets high in either sucrose, fructose, glucose, lactose or a glucose-fructose mixture. All of the sugars tested supported caries, but the total caries scores varied from a statistical zero at 100 days on the basal diet (no added carbohydrate) to a high score on sucrose. Sucrose was the most cariogenic sugar tested — or at least supported the most rapidly progressive carious process. Given sufficient time fructose, lactose and glucose — in decreasing order of activity — also supported dental destruction under this experimental regime. High dietary sucrose was not essential for the development of periodontal lesions or of microbial deposits along the gingival margin of the tooth (gingival plaque). Microbial deposits on the tooth crown (coronal plaque), however, formed primarily on the sucrose diet. The formation of large amounts of coronal plaque was not essential to carious attack upon the smooth surfaces of the tooth. Apparently sugars other than sucrose were also capable of supporting smooth surface caries.