Skip to main content

Matrix Powers Algorithms for Trust Evaluation in Public-Key Infrastructures

  • Conference paper
Security and Trust Management (STM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7783))

Included in the following conference series:

Abstract

This paper deals with the evaluation of trust in public-key infrastructures. Different trust models have been proposed to interconnect the various PKI components in order to propagate the trust between them. In this paper we provide a new polynomial algorithm using linear algebra to assess trust relationships in a network using different trust evaluation schemes. The advantages are twofold: first the use of matrix computations instead of graph algorithms provides an optimized computational solution; second, our algorithm can be used for generic graphs, even in the presence of cycles. Our algorithm is designed to evaluate the trust using all existing (finite) trust paths between entities as a preliminary to any exchanges between PKIs. This can give a precise evaluation of trust, and accelerate for instance cross-certificate validation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adkins, H.: An update on attempted man-in-the-middle attacks. Technical report, Google Online Security Blog (August 2011), http://googleonlinesecurity.blogspot.com/2011/08/update-on-attempted-man-in-middle.html

  2. Albert, R., Jeong, H., Barabasi, A.-L.: Diameter of the world-wide web. Nature 401, 130–131 (1999)

    Article  Google Scholar 

  3. Dolev, S., Gilboa, N., Kopeetsky, M.: Computing multi-party trust privately: in O(n) time units sending one (possibly large) message at a time. In: Proceedings of the ACM Symposium on Applied Computing, SAC 2010, pp. 1460–1465. ACM, New York (2010)

    Google Scholar 

  4. Ellison, C., Schneier, B.: Ten risks of PKI: What you’re not being told about Public Key Infrastructure. Computer Security Journal 16(1), 1–7 (2000), http://www.counterpane.com/pki-risks.pdf

    Google Scholar 

  5. Estrada, E., Hatano, N.: Communicability graph and community structures in complex networks. Applied Mathematics and Computation 214(2), 500–511 (2009)

    Article  MATH  Google Scholar 

  6. Foley, S.N., Adams, W.M., O’Sullivan, B.: Aggregating trust using triangular norms in the keyNote trust management system. In: Cuellar, J., Lopez, J., Barthe, G., Pretschner, A. (eds.) STM 2010. LNCS, vol. 6710, pp. 100–115. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Goldberg, G., Okunev, P., Neumann, M., Schneider, H.: Distribution of subdominant eigenvalues of random matrices. Methodology and Computing in Applied Probability 2, 137–151 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gomes, F.: Security alert: Fraudulent digital certificates. Technical report, SANS Institute InfoSec Reading Room (June 2001), http://www.sans.org/reading_room/whitepapers/certificates/security-alert-fraudulent-digital-certificates_679

  9. Goto, K., van de Geijn, R.A.: High-performance implementation of the level-3 BLAS. ACM Transactions on Mathematical Software 35(1), 4:1–4:14 (2008)

    Google Scholar 

  10. Govindan, K., Mohapatra, P.: Trust computations and trust dynamics in mobile adhoc networks: A survey. IEEE Communications Surveys and Tutorials 14(2), 279–298 (2012)

    Article  Google Scholar 

  11. Guha, R., Kumar, R., Raghavan, P., Tomkins, A.: Propagation of trust and distrust. In: Proceedings of the 13th International Conference on World Wide Web, WWW 2004, pp. 403–412. ACM, New York (2004)

    Google Scholar 

  12. Huang, J., Nicol, D.: A calculus of trust and its application to PKI and identity management. In: Proceedings of the 8th Symposium on Identity and Trust on the Internet, IDTRUST 2009, pp. 23–37. ACM, New York (2009)

    Chapter  Google Scholar 

  13. Huang, J., Nicol, D.: A formal-semantics-based calculus of trust. IEEE Internet Computing 14, 38–46 (2010)

    Article  Google Scholar 

  14. Jøsang, A.: Trust extortion on the internet. In: Meadows, C., Fernandez-Gago, C. (eds.) STM 2011. LNCS, vol. 7170, pp. 6–21. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  15. Jøsang, A.: Probabilistic logic under uncertainty. In: Proceedings of Computing: The Australian Theory Symposium (CATS 2007) (January 2007)

    Google Scholar 

  16. Orman, L.V.: Transitivity and aggregation in trust networks. In: Proc. of the 21st Workshop on Information Technologies and Systems (WITS 2010) (December 2010)

    Google Scholar 

  17. Pala, M.: A proposal for collaborative internet-scale trust infrastructures deployment: the public key system (pks). In: Proceedings of the 9th Symposium on Identity and Trust on the Internet, IDTRUST 2010, pp. 108–116. ACM, New York (2010)

    Google Scholar 

  18. Pala, M., Smith, S.W.: Peaches and peers. In: Mjølsnes, S.F., Mauw, S., Katsikas, S.K. (eds.) EuroPKI 2008. LNCS, vol. 5057, pp. 223–238. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Reiter, M.K., Stubblebine, S.G.: Resilient authentication using path independence. IEEE Trans. Comput. 47, 1351–1362 (1998)

    Article  MathSciNet  Google Scholar 

  20. Rifà-Pous, H., Herrera-Joancomartí, J.: An interdomain PKI model based on trust lists. In: López, J., Samarati, P., Ferrer, J.L. (eds.) EuroPKI 2007. LNCS, vol. 4582, pp. 49–64. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  21. Schiffner, S., Clauß, S., Steinbrecher, S.: Privacy and liveliness for reputation systems. In: Martinelli, F., Preneel, B. (eds.) EuroPKI 2009. LNCS, vol. 6391, pp. 209–224. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Schnettler, S.: A structured overview of 50 years of small-world research. Social Networks 31(3), 165–178 (2009)

    Article  Google Scholar 

  23. Whaley, R.C., Petitet, A., Dongarra, J.J.: Automated empirical optimizations of software and the ATLAS project. Parallel Computing 27(1–2), 3–35 (2001), http://www.netlib.org/utk/people/JackDongarra/PAPERS/atlas_pub.pdf

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dumas, JG., Hossayni, H. (2013). Matrix Powers Algorithms for Trust Evaluation in Public-Key Infrastructures. In: Jøsang, A., Samarati, P., Petrocchi, M. (eds) Security and Trust Management. STM 2012. Lecture Notes in Computer Science, vol 7783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38004-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38004-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38003-7

  • Online ISBN: 978-3-642-38004-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics