Skip to main content
SpringerLink
Log in

Protecting data privacy through hard-to-reverse negative databases

  • Special Issue Paper
  • Published:
International Journal of Information Security Aims and scope Submit manuscript

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 (NDB) representation scheme for storing a negative image compactly, and proposes using a collection of NDBs to represent a single DB, that is, one NDB 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

s, y, v::

Binary strings

l::

The number of positions in a string

DB::

A set of binary strings, referred to as a positive database

NDB::

A set of strings over {0,1,*}, referred to as a negative database

NDB (s)::

A negative database for the string s. When a specific string is alluded to, its numeric decimal value is used in its place

NDB A ::

A negative database belonging to agent A

\(\Upsilon\) ::

A set of integers indicating bit positions in a string

m::

The number of records in a negative database

r::

The ratio of records to string length in a negative database

k::

Number of specified positions (non “*” symbols) in a string

c::

The number of bits appended to a string. The code length

References

  1. Achlioptas, D., Beame, M.: A sharp threshold in proof complexity. In: STOC: ACM Symposium on Theory of Computing (STOC) (2001)

  2. Achlioptas, D., Gomes, C., Kautz, H., Selman, B.: Generating satisfiable problem instances. In: Proceedings of AAAI-00 and IAAI-00, pp. 256–261. AAAI Press, Menlo Park (2000)

  3. Achlioptas, D., Peres, Y.: The threshold for random k-SAT is 2k log 2–O(k). JAMS: J. Am. Math. Soc. 17 (2004)

  4. Adam N.R. and Wortman J.C. (1989). Security-control methods for statistical databases. ACM Comput. Surv. 21(4): 515–556

    Article  Google Scholar 

  5. Agrawal, D., Aggarwal, C.C.: On the design and quantification of privacy preserving data mining algorithms. In: Symposium on Principles of Database Systems, pp. 247–255 (2001)

  6. Agrawal, R., Evfimievski, A., Srikant, R.: Information sharing aoss private databases. In: SIGMODIC: ACM SIGMOD Interantional Conference on Management of Data (2003)

  7. Agrawal, R., Srikant, R.: Privacy-preserving data mining. In: Proceedings of the ACM SIGMOD Conference on Management of Data, pp. 439–450. ACM Press, New York (2000)

  8. Benaloh, J.C., de Mare, M.: One-way accumulators: a decentralized alternative to digital signatures. In: Advances in cryptology— EUROYPT ’93, pp. 274–285 (1994)

  9. Blakley, G.R., Meadows, C.: A database enyption scheme which allows the computation of statistics using enypted data. In: Proceedings of the IEEE Symposium on Research in Security and Privacy, pp. 116–122. IEEE CS Press (1985)

  10. Blum, M., Goldwasser, S.: An efficient probabilistic public-key enyption scheme which hides all partial information. In: Blakely, G.R., Chaum, D. (eds.) Advances in cryptology: proceedings of CRYPTO 84, Lecture Notes in Computer Science, vol. 196, pp. 289–302. Springer, Berlin, Germany/Heidelberg, Germany/London, UK/etc. (1985)

  11. Camenisch, J., Lysyanskaya, A.: Dynamic accumulators and application to efficient revocation of anonymous edentials. In: Yung, M. (ed.) Advances in cryptology—CRYPTO’ 2002, Lecture Notes in Computer Science, vol. 2442, pp. 61–76. International Association for cryptologic Research, Springer, Berlin (2002)

  12. Chin F. (1986). Security problems on inference control for sum, max and min queries. J. ACM 33(3): 451–464

    Article  MathSciNet  Google Scholar 

  13. Cook, S.A., Mitchell, D.G.: Finding hard instances of the satisfiability problem: a survey. In: Du, D., Gu, J., Pardalos, P.M. (eds.) Satisfiability Problem: Theory and Applications, Dimacs Series in Disete Mathematics and Theoretical Computer Science, vol. 35, pp. 1–17. American Mathematical Society (1997)

  14. Denning D. (1982). Cryptography and Data Security. Addison-Wesley, Reading

    MATH  Google Scholar 

  15. Denning D. and Schlorer J. (1983). Inference controls for statistical databases. Computer 16(7): 69–82

    Article  Google Scholar 

  16. Denning D.E., Denning P.J. and Schwartz M.D. (1979). The tracker: a threat to statistical database security. ACM Trans. Database Syst. 4(1): 76–96

    Article  Google Scholar 

  17. Denning D.E. and Schlorer J. (1980). A fast procedure for finding a tracker in a statistical database. ACM Trans. Database Syst. 5(1): 88–102

    Article  Google Scholar 

  18. Dobkin D., Jones A. and Lipton R. (1979). Secure databases: Protection against user influence. ACM Trans. Database Syst. 4(1): 97–106

    Article  Google Scholar 

  19. Esponda, F.: Negative representations of information. Ph.D. thesis, University of New Mexico (2005)

  20. Esponda, F., Ackley, E.S., Forrest, S., Helman, P.: On-line negative databases. In: Proceedings of ICARIS (2004)

  21. Esponda F., Ackley E.S., Forrest S. and Helman P. (2005). On-line negative databases (with experimental results). Int. J. Unconv. Comput. 1(3): 201–220

    Google Scholar 

  22. Esponda, F., Forrest, S., Helman, P.: Enhancing privacy through negative representations of data. University of New Mexico, Technical report (2004)

  23. Esponda, F., Forrest, S., Helman, P.: Negative representations of information. Int. J. Inform. Secur. (2004) (Submitted)

  24. Even, S., Yacobi, Y.: Cryptography and np-completeness. In: Proceedings 7th Colloq. Automata, Languages, and Programming. Lecture Notes in Computer Science, vol. 85, pp. 195–207. Springer-Verlag (1980)

  25. Feigenbaum, J., Grosse, E., Reeds, J.A.: Cryptographic protection of membership lists 9(1), 16–20 (1992)

    Google Scholar 

  26. Feigenbaum, J., Liberman, M.Y., Wright, R.N.: Cryptographic protection of databases and software. In: Distributed Computing and cryptography, pp. 161–172. American Mathematical Society (1991)

  27. Fiorini C., Martinelli E. and Massacci F. (2003). How to fake an RSA signature by encoding modular root finding as a SAT problem. Disete Appl. Math. 130(2): 101–127

    Article  MATH  MathSciNet  Google Scholar 

  28. Gent, I.P., Walsh, T.: The SAT phase transition. In: Proceedings of the Eleventh European Conference on Artificial Intelligence (ECAI’94), pp. 105–109 (1994)

  29. Goldreich O. (2000). Foundations of cryptography: Basic Tools. Cambridge University Press, Cambridge

    Google Scholar 

  30. Goldwasser S. and Micali S. (1984). Probabilistic enyption. J. Comput. Syst. Sci. 28(2): 270–299

    Article  MATH  MathSciNet  Google Scholar 

  31. Impagliazzo, R., Levin, L.A., Luby, M.: Pseudo-random generation from one-way functions. In: Proceedings of the twenty-first annual ACM symposium on Theory of computing, pp. 12–24. ACM, New York (1989)

  32. Impagliazzo, R., Naor, M.: Efficient cryptographic schemes provably as secure as subset sum. In: IEEE (ed.) 30th annual Symposium on Foundations of Computer Science, October 30–November 1, 1989, Research Triangle Park, NC, pp. 236–241. IEEE Computer Society Press, 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA (1989)

  33. Jia, H., Moore, C., Strain, D.: Generating hard satisfiable formulas by hiding solutions deceptively. In: AAAI (2005)

  34. Kautz, H.A., Ruan, Y., Achlioptas, D., Gomes, C., Selman, B., Stickel, M.E.: Balance and filtering in structured satisfiable problems. In: IJCAI, pp. 351–358 (2001)

  35. Li Y., Tygar J. and Hellerstein J. (2005). Private matching. In: Lee, D., Shieh, S., and Tygar, J. (eds) Computer Security in the 21st Century., pp 25–50. Springer, Berlin

    Chapter  Google Scholar 

  36. Freedman, M., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Advances in cryptology—Euroypt ’2004 Proceedings, LNCS 3027, pp. 1–19. Springer (2004)

  37. Matloff, N.S.: Inference control via query restriction vs. data modification: a perspective. In: on Database Security: Status and Prospects, pp. 159–166. North-Holland, Amsterdam (1988)

  38. Merkle, R.C., Hellman, M.E.: Hiding information and signatures in trapdoor knapsacks. vol. IT-24, pp. 525–530 (1978)

  39. Micali, S., Rabin, M., Kilian, J.: Zero-knowledge sets. In: Proceedings FOCS 2003, p. 80 (2003)

  40. Mitchell, D., Selman, B., Levesque, H.: Problem solving: hardness and easiness—hard and easy distributions of SAT problems. In: Proceeding of (AAAI-92), pp. 459–465. AAAI Press, Menlo Park (1992)

  41. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference (DAC’01) (2001)

  42. Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing: Seattle, Washington, May 15–17, 1989, pp. 33–43. ACM, New York (1989)

  43. Odlyzko, A.M.: The rise and fall of knapsack cryptosystems. In: Pomerance, C., Goldwasser, S. (eds.) cryptology and Computational Number Theory, Proceedings of symposia in applied mathematics. AMS short course lecture notes, vol. 42, pp. 75–88. pub-AMS (1990)

  44. Ostrovsky, R., Rackoff, C., Smith, A.: Efficient consistency proofs for generalized queries on a committed database. In: ICALP: Annual International Colloquium on Automata, Languages and Programming, pp. 1041—1053 (2004)

  45. Princeton: zChaff. http://ee.princeton.edu/˜chaff/zchaff.php (2004)

  46. Selman, B., Kautz, H.A., Cohen, B.: Local search strategies for satisfiability testing. In: Trick, M., Johnson, D.S. (eds.) Proceedings of the Second DIMACS Challange on Cliques, Coloring, and Satisfiability. Providence (1993)

  47. Shaw, P., Stergiou, K., Walsh, T.: Arc consistency and quasigroup completion. In: Proceedings of ECAI98 Workshop on Non-binary Constraints (1998)

  48. Tendick, P., Matloff, N.: A modified random perturbation method for database security. ACM Trans. Database Syst. 19(1), 47–63 (1994). DOI http://doi.acm.org/10.1145/174638.174641

    Google Scholar 

  49. Wayner, P.: Translucent databases. Flyzone Press (2002)

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Yale University, New Haven, CT, 06520-8285, USA

    Fernando Esponda

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

    Elena S. Ackley, Paul Helman, Haixia Jia & Stephanie Forrest

Authors
  1. Fernando Esponda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elena S. Ackley
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paul Helman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haixia Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Stephanie Forrest
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fernando Esponda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Esponda, F., Ackley, E.S., Helman, P. et al. Protecting data privacy through hard-to-reverse negative databases. Int. J. Inf. Secur. 6, 403–415 (2007). https://doi.org/10.1007/s10207-007-0030-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10207-007-0030-1

Keywords

Search

Navigation