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Negative representations of information

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Abstract

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.

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Author notes

  1. Fernando Esponda

    Present address: Department of Computer Science, Instituto Tecnológico Autónomo de México, Mexico, D.F., Mexico

Authors and Affiliations

  1. Department of Computer Science, University of New Mexico, Albuquerque, NM, 87131-1386, USA

    Fernando Esponda & Paul Helman

  2. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

    Stephanie Forrest

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  1. Fernando Esponda
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Correspondence to Fernando Esponda.

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Esponda, F., Forrest, S. & Helman, P. Negative representations of information. Int. J. Inf. Secur. 8, 331–345 (2009). https://doi.org/10.1007/s10207-009-0078-1

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