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59-462: Monowi ( / ˈ m ɒ n oʊ w aɪ / MON -oh-wye ) is an incorporated village in Boyd County, Nebraska, United States. It garnered national and international recognition after the 2010 United States census counted four residents of the village, one of them is Elsie Eiler . Although the 2020 census listed Monowi's population as two, this was confirmed to be an example of differential privacy in

118-471: A liquor license . She is required to produce a municipal road plan every year in order to secure state funding for the village's four street lights. Although the village is nearly abandoned, it does have a bar called the Monowi Tavern, operated by Eiler for passing travelers and tourists. In addition, Eiler maintains the five-thousand–volume Rudy's Library, founded in memory of her late husband. In 2018,

177-431: A Tracker, an adversary that could learn the confidential contents of a statistical database by creating a series of targeted queries and remembering the results. This and future research showed that privacy properties in a database could only be preserved by considering each new query in light of (possibly all) previous queries. This line of work is sometimes called query privacy, with the final result being that tracking

236-595: A collection of datasets, and f : D → R d {\displaystyle f\colon {\mathcal {D}}\rightarrow \mathbb {R} ^{d}} be a function. One definition of the sensitivity of a function, denoted Δ f {\displaystyle \Delta f} , can be defined by: Δ f = max ‖ f ( D 1 ) − f ( D 2 ) ‖ 1 , {\displaystyle \Delta f=\max \lVert f(D_{1})-f(D_{2})\rVert _{1},} where

295-697: A key technology underlying hashcash and bitcoin . Her publications include: She was elected as a Fellow of the American Academy of Arts and Sciences (AAAS) in 2008, as a member of the National Academy of Engineering in 2008, as a member of the National Academy of Sciences in 2014, as a fellow of the Association for Computing Machinery (ACM) in 2015, and as a member of the American Philosophical Society in 2016. Dwork received

354-458: A malicious user (often termed an adversary ) wants to find whether Chandler has diabetes or not. Suppose he also knows in which row of the database Chandler resides. Now suppose the adversary is only allowed to use a particular form of query Q i {\displaystyle Q_{i}} that returns the partial sum of the first i {\displaystyle i} rows of column X {\displaystyle X} in

413-496: A positive real number and A {\displaystyle {\mathcal {A}}} be a randomized algorithm that takes a dataset as input (representing the actions of the trusted party holding the data). Let im   A {\displaystyle {\textrm {im}}\ {\mathcal {A}}} denote the image of A {\displaystyle {\mathcal {A}}} . The algorithm A {\displaystyle {\mathcal {A}}}

472-416: A quarter by people who do not have the attribute A and three-quarters by people who actually possess it. Thus, if p is the true proportion of people with A , then we expect to obtain (1/4)(1- p ) + (3/4) p = (1/4) + p /2 positive responses. Hence it is possible to estimate p . In particular, if the attribute A is synonymous with illegal behavior, then answering "Yes" is not incriminating, insofar as

531-449: A single person, that person's data contributes 100%. If the database contains data from a hundred people, each person's data contributes just 1%. The key insight of differential privacy is that as the query is made on the data of fewer and fewer people, more noise needs to be added to the query result to produce the same amount of privacy. Hence the name of the 2006 paper, "Calibrating noise to sensitivity in private data analysis." Let ε be

590-449: A statistical database which limits the disclosure of private information of records in the database. For example, differentially private algorithms are used by some government agencies to publish demographic information or other statistical aggregates while ensuring confidentiality of survey responses, and by companies to collect information about user behavior while controlling what is visible even to internal analysts. Roughly, an algorithm

649-432: A strong guarantee that presence or absence of an individual will not affect the final output of the algorithm significantly. For example, assume we have a database of medical records D 1 {\displaystyle D_{1}} where each record is a pair ( Name , X ), where X {\displaystyle X} is a Boolean denoting whether a person has diabetes or not. For example: Now suppose

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708-499: Is ( ε × c ) {\displaystyle (\varepsilon \times c)} -differentially private. This could be generalized to group privacy, as the group size could be thought of as the Hamming distance h {\displaystyle h} between A {\displaystyle A} and B {\displaystyle B} (where A {\displaystyle A} contains

767-754: Is 1. This indicates that the "Has Diabetes" field in Chandler's row must be 1. This example highlights how individual information can be compromised even without explicitly querying for the information of a specific individual. Continuing this example, if we construct D 2 {\displaystyle D_{2}} by replacing (Chandler, 1) with (Chandler, 0) then this malicious adversary will be able to distinguish D 2 {\displaystyle D_{2}} from D 1 {\displaystyle D_{1}} by computing Q 5 − Q 4 {\displaystyle Q_{5}-Q_{4}} for each dataset. If

826-414: Is also extendable. We may want to protect databases differing in c {\displaystyle c} rows, which amounts to an adversary with arbitrary auxiliary information knowing if c {\displaystyle c} particular participants submitted their information. This can be achieved because if c {\displaystyle c} items change, the probability dilation

885-901: Is bounded by exp ⁡ ( ε c ) {\displaystyle \exp(\varepsilon c)} instead of exp ⁡ ( ε ) {\displaystyle \exp(\varepsilon )} , i.e., for D 1 and D 2 differing on c {\displaystyle c} items: Pr [ A ( D 1 ) ∈ S ] ≤ exp ⁡ ( ε c ) ⋅ Pr [ A ( D 2 ) ∈ S ] {\displaystyle \Pr[{\mathcal {A}}(D_{1})\in S]\leq \exp(\varepsilon c)\cdot \Pr[{\mathcal {A}}(D_{2})\in S]\,\!} Thus setting ε instead to ε / c {\displaystyle \varepsilon /c} achieves

944-518: Is differentially private if an observer seeing its output cannot tell whether a particular individual's information was used in the computation. Differential privacy is often discussed in the context of identifying individuals whose information may be in a database. Although it does not directly refer to identification and reidentification attacks, differentially private algorithms provably resist such attacks. The 2006 Cynthia Dwork , Frank McSherry , Kobbi Nissim , and Adam D. Smith article introduced

1003-420: Is given roughly the same privacy that would result from having their data removed. That is, the statistical functions run on the database should not be substantially affected by the removal, addition, or change of any individual in the data. How much any individual contributes to the result of a database query depends in part on how many people's data are involved in the query. If the database contains data from

1062-531: Is one of the inventors of differential privacy and proof-of-work . Dwork works at Harvard University , where she is Gordon McKay Professor of Computer Science, Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study , and Affiliated Professor at Harvard Law School and Harvard's Department of Statistics. Dwork was elected a member of the National Academy of Engineering in 2008 for fundamental contributions to distributed algorithms and

1121-442: Is said to provide (ε, δ)-differential privacy if, for all datasets D 1 {\displaystyle D_{1}} and D 2 {\displaystyle D_{2}} that differ on a single element (i.e., the data of one person), and all subsets S {\displaystyle S} of im   A {\displaystyle {\textrm {im}}\ {\mathcal {A}}} : where

1180-783: Is the original real valued query/function we planned to execute on the database. Now clearly T A ( x ) {\displaystyle {\mathcal {T}}_{\mathcal {A}}(x)\,\!} can be considered to be a continuous random variable, where which is at most e | f ( D 1 ) − f ( D 2 ) | λ ≤ e Δ ( f ) λ {\displaystyle e^{\frac {|f(D_{1})-f(D_{2})|}{\lambda }}\leq e^{\frac {\Delta (f)}{\lambda }}\,\!} . We can consider Δ ( f ) λ {\displaystyle {\frac {\Delta (f)}{\lambda }}\,\!} to be

1239-533: The ε {\displaystyle \varepsilon \,\!} -differential private algorithm we need to have λ = 1 / ε {\displaystyle \lambda =1/\varepsilon \,\!} . Though we have used Laplace noise here, other forms of noise, such as the Gaussian Noise, can be employed, but they may require a slight relaxation of the definition of differential privacy. A simple example, especially developed in

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1298-517: The 1930s , when it had a population of 150. Like many other small communities in the Great Plains , it lost its younger residents to cities that were experiencing growth and offering better jobs. During the 2000 census , the village had a total population of two; only one married couple, Rudy and Elsie Eiler, lived there. Rudy died in 2004, leaving his wife as the only resident in the village. In this capacity, she acts as mayor , and granted herself

1357-489: The 2020 census appeared to show that Monowi's population increased to two. However, Eiler denied that anyone had moved into the town, and a spokesperson for the United States Census Bureau said that the alleged second resident was actually a form of " noise ... add[ed] to the [census] data," in which some individuals are listed in a bordering tract to protect the anonymity of census respondents. According to

1416-960: The Gaussian distribution (which requires the L2 norm ) instead of the Laplace distribution . There are techniques (which are described below) using which we can create a differentially private algorithm for functions, with parameters that vary depending on their sensitivity. The Laplace mechanism adds Laplace noise (i.e. noise from the Laplace distribution , which can be expressed by probability density function noise ( y ) ∝ exp ⁡ ( − | y | / λ ) {\displaystyle {\text{noise}}(y)\propto \exp(-|y|/\lambda )\,\!} , which has mean zero and standard deviation 2 λ {\displaystyle {\sqrt {2}}\lambda \,\!} ). Now in our case we define

1475-586: The L1 norm . In the example of the medical database below, if we consider f {\displaystyle f} to be the function Q i {\displaystyle Q_{i}} , then the sensitivity of the function is one, since changing any one of the entries in the database causes the output of the function to change by either zero or one. This can be generalized to other metric spaces (measures of distance), and must be to make certain differentially private algorithms work, including adding noise from

1534-510: The social sciences , is to ask a person to answer the question "Do you own the attribute A ?", according to the following procedure: (The seemingly redundant extra toss in the first case is needed in situations where just the act of tossing a coin may be observed by others, even if the actual result stays hidden.) The confidentiality then arises from the refutability of the individual responses. But, overall, these data with many responses are significant, since positive responses are given to

1593-465: The Hamming distance between A {\displaystyle A} and B {\displaystyle B} for any two databases A , B {\displaystyle A,B} . If there is a mechanism M {\displaystyle M} that is ε {\displaystyle \varepsilon } -differentially private, then the composite mechanism M ∘ T {\displaystyle M\circ T}

1652-580: The U.S. Census Bureau, the village has a total area of 0.21 square miles (0.54 km), all land. The village is located in the far eastern portion of Boyd County, in the northeastern region of Nebraska. It is located between the Niobrara River and the larger Missouri River . The nearest community to Monowi is Lynch , located approximately 6.92 miles (11.14 km) away. The village is located approximately 193.97 miles (312.16 km) from Omaha . Census data for Monowi highlights its uniqueness, owing to

1711-407: The adversary were required to receive the values Q i {\displaystyle Q_{i}} via an ε {\displaystyle \varepsilon } -differentially private algorithm, for a sufficiently small ε {\displaystyle \varepsilon } , then he or she would be unable to distinguish between the two datasets. Composability refers to

1770-518: The amount of noise that needed to be added and proposing a generalized mechanism for doing so. This paper also created the first formal definition of differential privacy. Their work was a co-recipient of the 2016 TCC Test-of-Time Award and the 2017 Gödel Prize . Since then, subsequent research has shown that there are many ways to produce very accurate statistics from the database while still ensuring high levels of privacy . To date there are over 12 real-world deployments of differential privacy ,

1829-580: The census data; Eiler remains the town's sole resident. According to tradition, the name Monowi means "flower" in an unidentified Native American language. Monowi was so named after the many wildflowers growing at the original site of the village. Monowi was platted in 1903, when the Mason, Elkhorn and Missouri Valley Railroad was extended to that point. A post office was established in Monowi in 1902 and remained in operation until 1967. Monowi's peak years were in

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1888-499: The concept of the privacy loss budget . If all elements that access sensitive data of a complex mechanisms are separately differentially private, so will be their combination, followed by arbitrary post-processing. In general, ε-differential privacy is designed to protect the privacy between neighboring databases which differ only in one row. This means that no adversary with arbitrary auxiliary information can know if one particular participant submitted their information. However this

1947-401: The concept of ε-differential privacy, a mathematical definition for the privacy loss associated with any data release drawn from a statistical database . (Here, the term statistical database means a set of data that are collected under the pledge of confidentiality for the purpose of producing statistics that, by their production, do not compromise the privacy of those individuals who provided

2006-485: The data. She uses a systems-based approach to studying fairness in algorithms including those used for placing ads. Dwork has also made contributions in cryptography and distributed computing , and is a recipient of the Edsger W. Dijkstra Prize for her early work on the foundations of fault-tolerant systems . Her contributions in cryptography include non-malleable cryptography with Danny Dolev and Moni Naor in 1991,

2065-435: The data.) The definition of ε-differential privacy requires that a change to one entry in a database only creates a small change in the probability distribution of the outputs of measurements, as seen by the attacker. The intuition for the definition of ε-differential privacy is that a person's privacy cannot be compromised by a statistical release if their data are not in the database. In differential privacy, each individual

2124-575: The database. In order to find Chandler's diabetes status the adversary executes Q 5 ( D 1 ) {\displaystyle Q_{5}(D_{1})} and Q 4 ( D 1 ) {\displaystyle Q_{4}(D_{1})} , then computes their difference. In this example, Q 5 ( D 1 ) = 3 {\displaystyle Q_{5}(D_{1})=3} and Q 4 ( D 1 ) = 2 {\displaystyle Q_{4}(D_{1})=2} , so their difference

2183-476: The desired result (protection of c {\displaystyle c} items). In other words, instead of having each item ε-differentially private protected, now every group of c {\displaystyle c} items is ε-differentially private protected (and each item is ( ε / c ) {\displaystyle (\varepsilon /c)} -differentially private protected). One can think of differential privacy as bounding

2242-505: The error rates in a hypothesis test. Consider two hypotheses: Then, there are two error rates: Ideal protection would imply that both error rates are equal, but for a fixed (ε, δ) setting, an attacker can achieve the following rates: Since differential privacy is a probabilistic concept, any differentially private mechanism is necessarily randomized. Some of these, like the Laplace mechanism, described below, rely on adding controlled noise to

2301-401: The fact that the joint distribution of the outputs of (possibly adaptively chosen) differentially private mechanisms satisfies differential privacy. The other important property for modular use of differential privacy is robustness to post processing. This is defined to mean that for any deterministic or randomized function F {\displaystyle F} defined over the image of

2360-449: The first lattice-based cryptosystem with Miklós Ajtai in 1997, which was also the first public-key cryptosystem for which breaking a random instance is as hard as solving the hardest instance of the underlying mathematical problem ("worst-case/average-case equivalence"). With Naor she also first presented the idea of, and a technique for, combating e-mail spam by requiring a proof of computational effort, also known as proof-of-work —

2419-408: The function that we want to compute. Others, like the exponential mechanism and posterior sampling sample from a problem-dependent family of distributions instead. An important definition with respect to ε-differentially private mechanisms is sensitivity. Let d {\displaystyle d} be a positive integer, D {\displaystyle {\mathcal {D}}} be

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2478-403: The group and B {\displaystyle B} does not). In this case M ∘ T {\displaystyle M\circ T} is ( ε × c × h ) {\displaystyle (\varepsilon \times c\times h)} -differentially private. In 1977, Tore Dalenius formalized the mathematics of cell suppression . Tore Dalenius

2537-440: The impact of a query on the privacy of individuals in the database was NP-hard . In 2003, Kobbi Nissim and Irit Dinur demonstrated that it is impossible to publish arbitrary queries on a private statistical database without revealing some amount of private information, and that the entire information content of the database can be revealed by publishing the results of a surprisingly small number of random queries—far fewer than

2596-448: The invention of differential privacy in the early to mid 2000s, a strong privacy guarantee frequently permitting highly accurate data analysis. The definition of differential privacy relies on the notion of indistinguishability of the outputs irrespective of whether an individual has contributed their data or not. This is typically achieved by adding small amounts of noise either to the input data or to outputs of computations performed on

2655-460: The mathematics of the techniques themselves. In addition to standard defects of software artifacts that can be identified using testing or fuzzing , implementations of differentially private mechanisms may suffer from the following vulnerabilities: Cynthia Dwork Cynthia Dwork (born June 27, 1958 ) is an American computer scientist best known for her contributions to cryptography , distributed computing , and algorithmic fairness . She

2714-402: The maximum is over all pairs of datasets D 1 {\displaystyle D_{1}} and D 2 {\displaystyle D_{2}} in D {\displaystyle {\mathcal {D}}} differing in at most one element and ‖ ⋅ ‖ 1 {\displaystyle \lVert \cdot \rVert _{1}} denotes

2773-404: The mechanism A {\displaystyle {\mathcal {A}}} , if A {\displaystyle {\mathcal {A}}} satisfies ε-differential privacy, so does F ( A ) {\displaystyle F({\mathcal {A}})} . The property of composition permits modular construction and analysis of differentially private mechanisms and motivates

2832-423: The most noteworthy being: There are several public purpose considerations regarding differential privacy that are important to consider, especially for policymakers and policy-focused audiences interested in the social opportunities and risks of the technology: Because differential privacy techniques are implemented on real computers, they are vulnerable to various attacks not possible to compensate for solely in

2891-644: The numerical singularity of its population. As of 2010: The area is within Boyd County Public Schools. The area was previously within the Lynch Public Schools district in Lynch . The Lynch district consolidated into the Boyd County district in June 2017. Differential privacy Another way to describe differential privacy is as a constraint on the algorithms used to publish aggregate information about

2950-597: The output function of A {\displaystyle {\mathcal {A}}\,\!} as a real valued function (called as the transcript output by A {\displaystyle {\mathcal {A}}\,\!} ) as T A ( x ) = f ( x ) + Y {\displaystyle {\mathcal {T}}_{\mathcal {A}}(x)=f(x)+Y\,\!} where Y ∼ Lap ( λ ) {\displaystyle Y\sim {\text{Lap}}(\lambda )\,\!\,\!} and f {\displaystyle f\,\!}

3009-434: The person has a probability of a "Yes" response, whatever it may be. Although this example, inspired by randomized response , might be applicable to microdata (i.e., releasing datasets with each individual response), by definition differential privacy excludes microdata releases and is only applicable to queries (i.e., aggregating individual responses into one result) as this would violate the requirements, more specifically

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3068-462: The plausible deniability that a subject participated or not. A transformation T {\displaystyle T} is c {\displaystyle c} -stable if the Hamming distance between T ( A ) {\displaystyle T(A)} and T ( B ) {\displaystyle T(B)} is at most c {\displaystyle c} -times

3127-410: The presence of correlated data . According to this definition, differential privacy is a condition on the release mechanism (i.e., the trusted party releasing information about the dataset) and not on the dataset itself. Intuitively, this means that for any two datasets that are similar, a given differentially private algorithm will behave approximately the same on both datasets. The definition gives

3186-457: The privacy factor ε {\displaystyle \varepsilon \,\!} . Thus T {\displaystyle {\mathcal {T}}\,\!} follows a differentially private mechanism (as can be seen from the definition above). If we try to use this concept in our diabetes example then it follows from the above derived fact that in order to have A {\displaystyle {\mathcal {A}}\,\!} as

3245-679: The probability is taken over the randomness used by the algorithm. This definition is sometimes called "approximate differential privacy", with "pure differential privacy" being a special case when δ = 0 {\displaystyle \delta =0} . In the latter case, the algorithm is commonly said to satisfy ε-differential privacy (i.e., omitting δ = 0 {\displaystyle \delta =0} ). Differential privacy offers strong and robust guarantees that facilitate modular design and analysis of differentially private mechanisms due to its composability , robustness to post-processing , and graceful degradation in

3304-560: The security of cryptosystems. Dwork received her B.S.E. from Princeton University in 1979, graduating Cum Laude, and receiving the Charles Ira Young Award for Excellence in Independent Research. Dwork received her Ph.D. from Cornell University in 1983 for research supervised by John Hopcroft . Dwork is known for her research placing privacy-preserving data analysis on a mathematically rigorous foundation, including

3363-422: The village was featured in commercials for Arby's and Prudential . The village was also used as a starting place for the biggest advertisement poster in the world, which was finished on June 13, 2018. After the 1990 United States census , Eiler had observed that Monowi's population had been miscounted, and contacted radio broadcaster Paul Harvey to publicize the error. Years later, preliminary information from

3422-409: Was a Swedish statistician who contributed to statistical privacy through his 1977 paper that revealed a key point about statistical databases, which was that databases should not reveal information about an individual that is not otherwise accessible. He also defined a typology for statistical disclosures. In 1979, Dorothy Denning , Peter J. Denning and Mayer D. Schwartz formalized the concept of

3481-456: Was implied by previous work. The general phenomenon is known as the Fundamental Law of Information Recovery , and its key insight, namely that in the most general case, privacy cannot be protected without injecting some amount of noise, led to development of differential privacy. In 2006, Cynthia Dwork , Frank McSherry , Kobbi Nissim and Adam D. Smith published an article formalizing

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