Protecting data privacy through hard-to-reverse negative databases

Abstract

A set DB of data elements can be represented in terms of its complement set, known as a negative database. That is, all of the elements not in DB are represented, and DB itself is not explicitly stored. This method of representing data has certain properties that are relevant for privacy enhancing applications.The paper reviews the negative database (N DB) representation scheme for storing a negative image compactly, and it proposes using a collection of N DBs to represent a single DB, that is, one N DB is assigned for each record in DB. This method has the advantage of producing negative databases that are hard to reverse in practice, i.e., from which it is hard to obtain DB. This result is obtained by adapting a technique for generating hard-to-solve 3-SAT formulas. Finally we suggest potential avenues of application.

Attacks on privacy and deFinetti's theorem

“…Informally, we say that a data set has been sanitized if it is impossible or very difficult for an attacker to infer sensitive information from the data. Difficulty could either result from a high average-case computational complexity [18] or from the amount of extra information an attacker needs to collect in order to breach privacy [35,36,10]. Thus it is clear that when designing a method for sanitizing data, one should also reason about attacks available to an attacker.…”

Hiding a Needle in a Haystack Using Negative Databases

“…There are a several algorithms in the literature for creating negative databases [8,12,9]. Moreover, since it was shown in [9] that negative databases are linked by a simple transformation to boolean satisfiability formulas, algorithms for generating formulas can be adapted to generate N DBs.…”

“…First, is the previous work on negative databases: In [11] the negative database representation is introduced; [8] uses a similar algorithm for generating N DBs and introduces some interesting applications, but relies on NP-hardness for its security. In [12] the issue of attaching a code is proposed, albeit it is used with a different purpose, and [7] is concerned with generating N DBs efficiently. Both consider ways of creating secure N DBs.…”

“…Previous work on negative databases relied on the theoretical difficulty of "reversing" a negative database (deciding whether a negative database is empty or not is NP-complete) and on finding suitably hard instances for its security [12]. Our current proposal does not lean on this property, as it may very well be easy to find entries not included in the negative database; its security relies on the number of superfluous entries included alongside the data and on the infeasibility of retrieving only the valid items.…”

Password Security through Negative Filtering

“…As the profile consists of invalid entities, it is called a complement profile or negative profile. This complement profile represents the negative abstraction of valid credentials and actually is the problem specific realization of the negative database described in [12]. The use of negative authentication for a system login application was first examined in [10].…”