k-anonymity

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.

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 with a '*'.
2. 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.

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.[14]

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.[15][16] A practical approximation algorithm that enables solving the k-anonymization problem with an approximation guarantee of ${\displaystyle O(\log k)}$ was presented by Kenig and Tassa.[17]

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.

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.[18] For example, researchers showed that, given 4 locations, the unicity of mobile phone timestamp-location datasets (${\displaystyle {\mathcal {E}}_{4}}$, k-anonymity when ${\displaystyle k=1}$) can be as high as 95%.[19]

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.[20] The suppression and generalization algorithms used to k-anonymize datasets can be altered, however, so that they do not have such a skewing effect.[21]

Hash-based k-Anonymity has been largely developed by Junade Ali, initially for preventing Compromised Credential Checking[22][23][24] and later for real-time anonymisation of MAC addresses.[25]

This approach works by taking a cryptographic hash of one dimensional data and truncating the hash such that there are at least ${\displaystyle k-1}$ hash collisions. This approach allows for efficient anonymised searching of large datasets, such as breached passwords.[26] This approach can further be used to provide a formally demonstrable level of anonymity to privacy-sensitive data, allowing a precise trade-off to be made between information leakage and functionality (such as for MAC address anonymization).[27][28]

• t-closeness
• l-diversity
• Differential privacy