A Relational Algebra for Negative Databases

A negative database is a representation of all elements not contained in a given database. A negative database can enhance the privacy of sensitive information without resorting to encryption. This can be useful in settings where encryption is too expensive, e.g., some sensor networks, or for applications where searches or other operations on stored data are desired. The original negative database framework supported only authentication queries and operations for modifying data, such as insert and delete. This paper extends that work by defining a set of relational operators for negative representations. For each relational operator, the corresponding negative operator is defined such that the result of the negative operator applied to a negative representation is equivalent to the positive version applied to the positive representation. Algorithms for each relational operator are described and compared to its positive counterpart. This work enhances the practicality of negative databases and expands their range of application.