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# Introduction to Statistical Database Security

Statistical databases are used mainly to produce statistics about various populations.

Introduction to Statistical Database Security

Statistical databases are used mainly to produce statistics about various populations. The database may contain confidential data about individuals, which should be protected from user access. However, users are permitted to retrieve statistical information about the populations, such as averages, sums, counts, maximums, minimums, and standard deviations. The techniques that have been developed to protect the privacy of individual information are beyond the scope of this book. We will illustrate the problem with a very simple example, which refers to the relation shown in Figure 24.3. This is a PERSON relation with the attributes Name, SsnIncome, Address, City, State, Zip, Sex, and Last_degree.

A population is a set of tuples of a relation (table) that satisfy some selection condition. Hence, each selection condition on the PERSON relation will specify a particular population of PERSON tuples. For example, the condition Sex = ‘M’ specifies the male population; the condition ((Sex = ‘F’) AND (Last_degree = ‘M.S.’ OR Last_degree = ‘Ph.D.’)) specifies the female population that has an M.S. or Ph.D. degree as their highest degree; and the condition City = ‘Houston’ specifies the population that lives in Houston.

Statistical queries involve applying statistical functions to a population of tuples. For example, we may want to retrieve the number of individuals in a population or the average income in the population. However, statistical users are not allowed to retrieve individual data, such as the income of a specific person. Statistical database security techniques must prohibit the retrieval of individual data. This can be achieved by prohibiting queries that retrieve attribute values and by allowing only queries that involve statistical aggregate functions such as COUNT, SUM, MIN, MAX, AVERAGE, and STANDARD DEVIATION. Such queries are sometimes called statistical queries.

It is the responsibility of a database management system to ensure the confidentiality of information about individuals, while still providing useful statistical summaries of data about those individuals to users. Provision of privacy protection of users in a statistical database is paramount; its violation is illustrated in the following example.

In some cases it is possible to infer the values of individual tuples from a sequence of statistical queries. This is particularly true when the conditions result in a

population consisting of a small number of tuples. As an illustration, consider the following statistical queries:

Q1: SELECT COUNT (*) FROM PERSON

WHERE <condition>;

Q2: SELECT AVG (Income) FROM PERSON

WHERE <condition>;

Now suppose that we are interested in finding the Salary of Jane Smith, and we know that she has a Ph.D. degree and that she lives in the city of Bellaire, Texas. We issue the statistical query Q1 with the following condition:

(Last_degree=‘Ph.D.’ AND Sex=‘F’ AND City=‘Bellaire’ AND State=‘Texas’)

If we get a result of 1 for this query, we can issue Q2 with the same condition and find the Salary of Jane Smith. Even if the result of Q1 on the preceding condition is not 1 but is a small number—say 2 or 3—we can issue statistical queries using the functions MAX, MIN, and AVERAGE to identify the possible range of values for the Salary of Jane Smith.

The possibility of inferring individual information from statistical queries is reduced if no statistical queries are permitted whenever the number of tuples in the population specified by the selection condition falls below some threshold. Another technique for prohibiting retrieval of individual information is to prohibit sequences of queries that refer repeatedly to the same population of tuples. It is also possible to introduce slight inaccuracies or noise into the results of statistical queries deliberately, to make it difficult to deduce individual information from the results. Another technique is partitioning of the database. Partitioning implies that records are stored in groups of some minimum size; queries can refer to any complete group or set of groups, but never to subsets of records within a group. The interested reader is referred to the bibliography at the end of this chapter for a discussion of these techniques.

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