International Journal of Information Security

, Volume 8, Issue 5, pp 331–345

Negative representations of information

Regular Contribution

DOI: 10.1007/s10207-009-0078-1

Cite this article as:
Esponda, F., Forrest, S. & Helman, P. Int. J. Inf. Secur. (2009) 8: 331. doi:10.1007/s10207-009-0078-1


In a negative representation, a set of elements (the positive representation) is depicted by its complement set. That is, the elements in the positive representation are not explicitly stored, and those in the negative representation are. The concept, feasibility, and properties of negative representations are explored in the paper; in particular, its potential to address privacy concerns. It is shown that a positive representation consisting of n l-bit strings can be represented negatively using only O(ln) strings, through the use of an additional symbol. It is also shown that membership queries for the positive representation can be processed against the negative representation in time no worse than linear in its size, while reconstructing the original positive set from its negative representation is an \({\mathcal{NP}}\) -hard problem. The paper introduces algorithms for constructing negative representations as well as operations for updating and maintaining them.


Negative databases Immune-inspired algorithms Privacy information hiding Data representations 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Fernando Esponda
    • 1
    • 2
  • Stephanie Forrest
    • 3
  • Paul Helman
    • 1
  1. 1.Department of Computer ScienceUniversity of New MexicoAlbuquerqueUSA
  2. 2.Department of Computer ScienceInstituto Tecnológico Autónomo de MéxicoMexico, D.F.Mexico
  3. 3.Santa Fe InstituteSanta FeUSA