k-anonymity

k-anonymity is a property possessed by certain anonymized data. The concept of k-anonymity was first formulated by Latanya Sweeney in a paper published in 2002 as 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."^[1][2] 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. The various procedures and programs for generating anonymised data providing k-anonymity protection have been patented in the United States (Patent 7,269,578).^[3]

Methods for k-anonymization

In the context of k-anonymization problems, a database is a table with n rows and m columns. Each row of the table represents a record relating to a specific member of a population and the entries in the various rows need not be unique. The values in the various columns are the values of attributes associated with the members of the population. The following table is a nonanonymized database consisting of the patient records of some fictitious hospital in Kochi.

Name	Age	Gender	State of domicile	Religion	Disease
Ramsha	29	Female	Tamil Nadu	Hindu	Cancer
Yadu	24	Female	Kerala	Hindu	Viral infection
Salima	28	Female	Tamil Nadu	Muslim	TB
sunny	27	Male	Karnataka	Parsi	No illness
Joan	24	Female	Kerala	Christian	Heart-related
Bahuksana	23	Male	Karnataka	Buddhist	TB
Rambha	19	Male	Kerala	Hindu	Cancer
Kishor	29	Male	Karnataka	Hindu	Heart-related
Johnson	17	Male	Kerala	Christian	Heart-related
John	19	Male	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.

1. 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below, we have replaced all the values in the 'Name' attribute and all the values in the 'Religion' attribute have been replaced by a '*'.
2. Generalization: In this method, individual values of attributes are replaced by 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.

Name	Age	Gender	State of domicile	Religion	Disease
*	20 < Age ≤ 30	Female	Tamil Nadu	*	Cancer
*	20 < Age ≤ 30	Female	Kerala	*	Viral infection
*	20 < Age ≤ 30	Female	Tamil Nadu	*	TB
*	20 < Age ≤ 30	Male	Karnataka	*	No illness
*	20 < Age ≤ 30	Female	Kerala	*	Heart-related
*	20 < Age ≤ 30	Male	Karnataka	*	TB
*	Age ≤ 20	Male	Kerala	*	Cancer
*	20 < Age ≤ 30	Male	Karnataka	*	Heart-related
*	Age ≤ 20	Male	Kerala	*	Heart-related
*	Age ≤ 20	Male	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.^[4]

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 yields effective results.^[5][6]

Caveats

Because k-anonymization does not include any randomization, attackers can still make 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.^[7] For example, researchers showed that, given 4 points, the unicity of mobile phone datasets ($\mathcal{E}_4$, k-anonymity when $k=1$) can be as high as 95%.^[8]

See also

• t-closeness
• l-diversity
• Differential privacy

References

1. L. Sweeney. "Database Security: k-anonymity". Retrieved 19 January 2014.
2. L. Sweeney. k-anonymity: a model for protecting privacy. International Journal on Uncertainty, Fuzziness and Knowledge-based Systems, 10 (5), 2002; 557-570.
3. "Systems and methods for de-identifying entries in a data source". United States Patents and Trademarks Office. Retrieved 19 January 2014.
4. Narayanan, Arvind; Shmatikov, Vitaly. "Robust De-anonymization of Large Sparse Datasets" (PDF).
5. Roberto J. Bayardo; Rakesh Agrawal (2005). "Data Privacy through Optimal k-anonymization" (PDF). ICDE '05 Proceedings of the 21st International Conference on Data Engineering: 217–28. doi:10.1109/ICDE.2005.42. ISBN 0-7695-2285-8. ISSN 1084-4627. Data de-identification reconciles the demand for release of data for research purposes and the demand for privacy from individuals. This paper proposes and evaluates an optimization algorithm for the powerful de-identification procedure known as k-anonymization. A k-anonymized dataset has the property that each record is indistinguishable from at least k - 1 others. Even simple restrictions of optimized k-anonymity are NP-hard, leading to significant computational challenges. We present a new approach to exploring the space of possible anonymizations that tames the combinatorics of the problem, and develop data-management strategies to reduce reliance on expensive operations such as sorting. Through experiments on real census data, we show the resulting algorithm can find optimal k-anonymizations under two representative cost measures and a wide range of k. We also show that the algorithm can produce good anonymizations in circumstances where the input data or input parameters preclude finding an optimal solution in reasonable time. Finally, we use the algorithm to explore the effects of different coding approaches and problem variations on anonymization quality and performance. To our knowledge, this is the first result demonstrating optimal k-anonymization of a nontrivial dataset under a general model of the problem.
6. Adam Meyerson; Ryan Williams (2004). "On the Complexity of Optimal K-Anonymity" (PDF). PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems (New York, NY: ACM): 223–8. doi:10.1145/1055558.1055591. ISBN 158113858X. The technique of k-anonymization has been proposed in the literature as an alternative way to release public information, while ensuring both data privacy and data integrity. We prove that two general versions of optimal k-anonymization of relations are NP-hard, including the suppression version which amounts to choosing a minimum number of entries to delete from the relation. We also present a polynomial time algorithm for optimal k-anonymity that achieves an approximation ratio independent of the size of the database, when k is constant. In particular, it is a O(k log k)-approximation where the constant in the big-O is no more than 4. However, the runtime of the algorithm is exponential in k. A slightly more clever algorithm removes this condition, but is a O(k logm)-approximation, where m is the degree of the relation. We believe this algorithm could potentially be quite fast in practice.
7. Aggarwal, Charu C. "On k-Anonymity and the Curse of Dimensionality" (PDF).
8. de Montjoye, Yves-Alexandre; César A. Hidalgo; Michel Verleysen; Vincent D. Blondel (March 25, 2013). "Unique in the Crowd: The privacy bounds of human mobility". Nature srep. doi:10.1038/srep01376.