sampleText1.txt

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k-anonymity:
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k-anonymity is a property possessed by certain anonymized data. 
The term k-anonymity was first introduced by Pierangela Samarati and Latanya Sweeney in a paper 
published in 1998, although the concept dates to a 1986 paper by Tore Dalenius.

k-anonymity is an attempt to solve the problem "Given person-specific field-structured data, 
produce a release of the data with scientific guarantees that the individuals who are the 
subjects of the data cannot be re-identified while the data remain practically useful.
"[3][4][5] A release of data is said to have the k-anonymity property if the information 
for each person contained in the release cannot be distinguished from at least 
k - 1 individuals whose information also appear in the release. Unfortunately, 
the guarantees provided by k-anonymity are aspirational, not mathematical.

Methods for k-anonymization
To use k-anonymity to process a dataset so that it can be released with privacy protection,
 a data scientist must first examine the dataset and decide whether each attribute (column) 
 is an identifier (identifying), a non-identifier (not-identifying), or a quasi-identifier 
 (somewhat identifying). Identifiers such as names are suppressed, non-identifying values 
 are allowed to remain, and the quasi-identifiers need to be processed so that every distinct 
 combination of quasi-identifiers designates at least k records.

In the example table below presents a fictional nonanonymized database consisting 
of the patient records for a fictitious hospital. The Name column is an identifier, 
Age, Gender, State of domicile, and Religion are quasi-identifiers, and Disease is 
a non-identifying sensitive value. But what about Height and Weight? Are they also 
non-identifying sensitive values, or are they quasi-identifiers?

Patients treated in the study on April 30
Name	Age	Gender	Height	Weight	State of domicile	Religion	Disease
Ramsha	30	Female	165 cm	72 kg	Tamil Nadu	Hindu	Cancer
Yadu	24	Female	162 cm	70 kg	Kerala	Hindu	Viral infection
Salima	28	Female	170 cm	68 kg	Tamil Nadu	Muslim	Tuberculosis
Sunny	27	Male	170 cm	75 kg	Karnataka	Parsi	No illness
Joan	24	Female	165 cm	71 kg	Kerala	Christian	Heart-related
Bahuksana	23	Male	160 cm	69 kg	Karnataka	Buddhist	Tuberculosis
Rambha	19	Male	167 cm	85 kg	Kerala	Hindu	Cancer
Kishor	29	Male	180 cm	81 kg	Karnataka	Hindu	Heart-related
Johnson	17	Male	175 cm	79 kg	Kerala	Christian	Heart-related
John	19	Male	169 cm	82 kg	Kerala	Christian	Viral infection
There are 6 attributes and 10 records in this data. There are two common methods for 
achieving k-anonymity for some value of k:

Suppression. In this method, certain values of the attributes are replaced by an asterisk "*". 
All or some values of a column may be replaced by "*". In the anonymized table below, 
we have replaced all the values in the Name attribute and all the values in the Religion attribute with a "*".
Generalization. In this method, individual values of attributes are replaced with a broader category.
 For example, the value "19" of the attribute 
 Age may be replaced by "≤ 20", the value "23" by "20 < Age ≤ 30", etc.
The next table shows the anonymized database.

Patients treated in the study on April 30
Name	Age	Gender	Height	Weight	State of domicile	Religion	Disease
*	20 < Age ≤ 30	Female	165 cm	72 kg	Tamil Nadu	*	Cancer
*	20 < Age ≤ 30	Female	162 cm	70 kg	Kerala	*	Viral infection
*	20 < Age ≤ 30	Female	170 cm	68 kg	Tamil Nadu	*	Tuberculosis
*	20 < Age ≤ 30	Male	170 cm	75 kg	Karnataka	*	No illness
*	20 < Age ≤ 30	Female	165 cm	71 kg	Kerala	*	Heart-related
*	20 < Age ≤ 30	Male	160 cm	69 kg	Karnataka	*	Tuberculosis
*	Age ≤ 20	Male	167 cm	85 kg	Kerala	*	Cancer
*	20 < Age ≤ 30	Male	180 cm	81 kg	Karnataka	*	Heart-related
*	Age ≤ 20	Male	175 cm	79 kg	Kerala	*	Heart-related
*	Age ≤ 20	Male	169 cm	82 kg	Kerala	*	Viral infection
This data has 2-anonymity with respect to the attributes Age, Gender and State of domicile, 
since for any combination of these attributes found in any row of the table there are always
 at least 2 rows with those exact attributes. The attributes available to an adversary
  are called quasi-identifiers. Each quasi-identifier tuple occurs in at least k records
   for a dataset with k-anonymity.[6]

Critiques of k-anonymity
This examples demonstrates a failing with k-anonymity: there may exist other data records
 that can be linked on the variables that are allegedly non-identifying. For example,
  if an attacker is able to obtain the a log from the person who was taking vital signs as 
  part of the study and learns that Kishor was at the hospital on April 30 and is 180 cm tall, 
  this information can be used to link with the "anonymized" database (which may have been 
  published on the Internet) and learn that Kishor has a heart-related disease. An attacker 
  who knows that Kishor visited the hospital on April 30 may be able to infer this simply
   knowing that Kishor is 180 cm height, roughly 80–82 kg, and comes from Karnataka.

The root of this problem is the core problem with k-anonymity: there is no way to mathematically,
 unambiguously determine whether an attribute is an identifier, a quasi-identifier, or a non-identifying
  sensitive value. In fact, all values are potentially identifying, depending on their prevalence
   in the population and on auxiliary data that the attacker may have. Other privacy mechanisms 
   such as differential privacy do not share this problem.

Meyerson and Williams (2004) demonstrated that optimal k-anonymity is an NP-hard problem, 
however heuristic methods such as k-Optimize as given by Bayardo and Agrawal (2005) often 
yield effective results.[7][8] A practical approximation algorithm that enables solving the
 k-anonymization problem with an approximation guarantee of 
�
(
log
⁡
�
)
O(\log k) was presented by Kenig and Tassa.[9]

Attacks
While k-anonymity is a relatively simple-to-implement approach for de-identifying 
a dataset prior to public release, it is susceptible to many attacks. When background
 knowledge is available to an attacker, such attacks become even more effective. Such attacks include:

Homogeneity Attack: This attack leverages the case where all the values for a sensitive
 value within a set of k records are identical. In such cases, even though the data has
  been k-anonymized, the sensitive value for the set of k records may be exactly predicted.
Background Knowledge Attack: This attack leverages an association between one or more 
quasi-identifier attributes with the sensitive attribute to reduce the set of possible 
values for the sensitive attribute. For example, Machanavajjhala, Kifer, Gehrke, and 
Venkitasubramaniam (2007) showed that knowing that heart attacks occur at a reduced
 rate in Japanese patients could be used to narrow the range of values for 
 a sensitive attribute of a patient's disease.
Downcoding Attack: This attack, introduced in 2022 by Aloni Cohen, takes advantage of 
the way that anonymity algorithms aggregate attributes in separate records. 
Because the aggregation is deterministic, it is possible to reverse-engineer 
the original data image, and in many cases reveal the original data that was 
to be protected. This attack does not require background knowledge, but is 
strengthened by it.[10]

Because k-anonymization does not include any randomization, attackers
 can make reliable, unambiguous inferences about data sets that may harm 
 individuals. For example, if the 19-year-old John from Kerala is known 
 to be in the database above, then it can be reliably said that he has
  either cancer, a heart-related disease, or a viral infection.

K-anonymization is not a good method to anonymize high-dimensional datasets.[11]

It has also been shown that k-anonymity can skew the results of a data set
 if it disproportionately suppresses and generalizes data points with
  unrepresentative characteristics.[12] The suppression and generalization algorithms
   used to k-anonymize datasets can be altered, however, so that they do not have such
    a skewing effect.[13]

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     t-closeness:
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t-closeness is a further refinement of l-diversity group based anonymization that is
 used to preserve privacy in data sets by reducing the granularity of a data representation. 
 This reduction is a trade off that results in some loss of effectiveness of data management or 
 data mining algorithms in order to gain some privacy. The t-closeness model extends the
  l-diversity model by treating the values of an attribute distinctly by taking into 
  account the distribution of data values for that attribute.

Formal definition
Given the existence of data breaches where sensitive attributes may be inferred based 
upon the distribution of values for l-diverse data, the t-closeness method was created
 to further l-diversity by additionally maintaining the distribution of sensitive fields. 
 The original paper[1] by Ninghui Li, Tiancheng Li, and Suresh Venkatasubramanian defines
  t-closeness as:

The t-closeness Principle: An equivalence class is said to have t-closeness if the distance
 between the distribution of a sensitive attribute in this class and the distribution of
  the attribute in the whole table is no more than a threshold t. A table is said to 
  have t-closeness if all equivalence classes have t-closeness.

Charu Aggarwal and Philip S. Yu further state in their book on privacy-preserving data mining[2] 
that with this definition, threshold t gives an upper bound on the difference between the 
distribution of the sensitive attribute values within an anonymized group as compared to
 the global distribution of values. They also state that for numeric attributes, using 
 t-closeness anonymization is more effective than many other privacy-preserving data mining methods.

Data breaches and l-diversity
In real data sets attribute values may be skewed or semantically similar. However, accounting 
for value distributions may cause difficulty in creating feasible l-diverse representations.
 The l-diversity technique is useful in that it may hinder an attacker leveraging the global
  distribution of an attribute's data values in order to infer information about sensitive data values.
   Not every value may exhibit equal sensitivity, for example, a rare positive indicator for
    a disease may provide more information than a common negative indicator. Because of 
    examples like this, l-diversity may be difficult and unnecessary to achieve when 
    protecting against attribute disclosure. Alternatively, sensitive information
     leaks may occur because while l-diversity requirement ensures “diversity” of 
     sensitive values in each group, it does not recognize that values may be 
     semantically close, for example, an attacker could deduce a stomach 
     disease applies to an individual if a sample containing the individual
      only listed three different stomach diseases.

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l-diversity: 
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l-diversity, also written as ℓ-diversity, is a form of group based anonymization that is
 used to preserve privacy in data sets by reducing the granularity of a data representation.
 This reduction is a trade off that results in some loss of effectiveness of data management or 
 mining algorithms in order to gain some privacy. 
 The l-diversity model is an extension of the k-anonymity model which reduces
  the granularity of data representation using techniques including generalization 
  and suppression such that any given record maps onto at least k-1 other records 
  in the data. The l-diversity model handles some of the weaknesses in the k-anonymity
   model where protected identities to the level of k-individuals is not equivalent
    to protecting the corresponding sensitive values that were generalized or
     suppressed, especially when the sensitive values within a group exhibit
      homogeneity. The l-diversity model adds the promotion of intra-group
       diversity for sensitive values in the anonymization mechanism.

Attacks on k-anonymity
See also: k-anonymity § Possible attacks
While k-anonymity is a promising approach to take for group based 
anonymization given its simplicity and wide array of algorithms that 
perform it, it is however susceptible to many attacks. When background 
knowledge is available to an attacker, such attacks become even more 
effective. Such attacks include:

Homogeneity Attack: This attack leverages the case where all 
the values for a sensitive value within a set of k records are identical. 
In such cases, even though the data has been k-anonymized, the sensitive 
value for the set of k records may be exactly predicted.
Background Knowledge Attack: This attack leverages an association
 between one or more quasi-identifier attributes with 
 the sensitive attribute to reduce the set of possible
  values for the sensitive attribute. For example,
   Machanavajjhala, Kifer, Gehrke, and Venkitasubramaniam (2007) 
   showed that knowing that heart attacks occur at a reduced
    rate in Japanese patients could be used to narrow the
     range of values for a sensitive attribute of a
      patient's disease.
Formal definition
Given the existence of such attacks where sensitive 
attributes may be inferred for k-anonymity data, the
 l-diversity method was created to further k-anonymity
 by additionally maintaining the diversity of sensitive fields.
  The book Privacy-Preserving Data Mining – Models and Algorithms
   (2008)[1] defines l-diversity as being:

Let a q*-block be a set of tuples such that its non-sensitive 
values generalize to q*. A q*-block is l-diverse if it contains
 l "well represented" values for the sensitive attribute S. 
 A table is l-diverse, if every q*-block in it is l-diverse.

The paper t-Closeness: Privacy beyond k-anonymity and
 l-diversity (2007)[2] defines l-diversity as being:

The l-diversity Principle – An equivalence class is
 said to have l-diversity if there are at least l “well-represented” 
 values for the sensitive attribute. A table is said to have l-diversity 
 if every equivalence class of the table has l-diversity.

Machanavajjhala et al. (2007)[3] define “well-represented” 
in three possible ways:

Distinct l-diversity – The simplest definition ensures that at
 least l distinct values for the sensitive field in each equivalence class exist.
Entropy l-diversity – The most complex definition defines Entropy of
 an equivalent class E to be the negation of summation of s across the 
 domain of the sensitive attribute of p(E,s)log(p(E,s)) where p(E,s) is
  the fraction of records in E that have the sensitive value s. A table 
  has entropy l-diversity when for every equivalent class E, Entropy(E) ≥ log(l).
Recursive (c-l)-diversity – A compromise definition that ensures the most 
common value does not appear too often while less common values are ensured 
to not appear too infrequently.
Aggarwal and Yu (2008) note that when there is more than one sensitive field the 
l-diversity problem becomes more difficult due to added dimensionalities.