BIT Numerical Mathematics

, Volume 33, Issue 1, pp 46–56 | Cite as

An optimal algorithm to assign cryptographic keys in a tree structure for access control

  • Horng-Twu Liaw
  • Chin-Laung Lei
Part I Computer Science


In a computer communication system, there exists a possibility of two or more users collaborating to derive a key to which they are not entitled. Therefore, a method for ensuring the system is necessary. In this paper, we propose an efficient heuristic algorithm for assigning cryptographic keys among a group of users organized in a tree structure. Comparing with the existing assignment schemes, our scheme always produces economic cryptographic keys, which are smaller than the keys generated by the previous work in a tree structure.

CR Categories



Cryptographic key tree structure access control 


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  1. 1.
    Akl, S. G., and Taylor, P. D.,Cryptographic solutions to a problem of access control in a hierarchy. ACM Transactions on Computer Systems. Vol. 1, No. 3. pp. 239–247. August 1983.Google Scholar
  2. 2.
    Chang, C. C.,On the design of a key-lock-pair mechanism in information protection systems, BIT, Vol. 26, pp. 410–417, 1986.Google Scholar
  3. 3.
    Chang, C. C.,An information protection system scheme based upon number theory. The Computer Journal, Vol. 30, No. 3, pp. 249–253, 1987.Google Scholar
  4. 4.
    Chang, C. C.,On the implementation of user hierarchy structure in information systems. Proceedings of International Conference on Computer Software and Applications, IEEE, pp. 412–415, Tokyo, Japan, October 1987.Google Scholar
  5. 5.
    Conway, R. W., Maxwell, W. L. and Morgan, H. L.,On the implementation of security measures in information systems, Communication of ACM, Vol. 15, No. 4, pp. 211–220, 1972.Google Scholar
  6. 6.
    Harn, L., and Lin, H. Y.,A cryptographic key generation scheme for multilevel data security, Computers & Security. Vol. 9, pp. 539–546, 1990.Google Scholar
  7. 7.
    Graham, G. S. and Denning, P. L.,Protection-principles and practices, proc. Spring Jt. Computer Conference, Vol. 40, pp. 417–429, AFIPS Press, Montvale, N. J., 1972.Google Scholar
  8. 8.
    Gudes, E.,The design of a cryptography-based secure file system, IEEE Transactions on Software Engineering, SE-6, No. 5, pp. 411–419, September 1980.Google Scholar
  9. 9.
    Horowitz, E. and Sanni, S.,Fundamentals of Data Structures, Computer Science Press, Rockville, MD.Google Scholar
  10. 10.
    Jan, J. K.,A single-key access control scheme in information protection systems, Information Sciences, Vol. 51, pp. 1–11, 1990.Google Scholar
  11. 11.
    Jan, J. K., Chang, C. C., and Wang, S. J.,A dynamic key-lock-pair access control scheme, Computers & Security, Vol. 10, No. 2, pp. 129–139, 1991.Google Scholar
  12. 12.
    Lin, C. H., Lee, R. C. T., and Chang, C. C.,A dynamic access control mechanism in information protection systems, Journal of Information Science and Engineering, Vol. 6, pp. 25–35, 1990.Google Scholar
  13. 13.
    Mackinon, S. T., Taylor, P. D., Meijer, H., and Akl, S. G.,An optimal algorithm for assigning cryptographic keys to control access in a hierarchy, IEEE Transactions on Computers, Vol. C-34, No. 9, pp. 797–802, September 1985.Google Scholar
  14. 14.
    Saltzer, J. H. and Schroeder, M. D.,The protection of information in computer systems, Proc. IEEE, Vol. 63, pp. 1278–1308, September 1975.Google Scholar
  15. 15.
    Wu, M. L. and Hwang, T. Y.,Access control with single-key-lock, IEEE Transactions On Software Engineering, Vol. SE-10, No. 2, pp. 185–191, March 1984.Google Scholar

Copyright information

© BIT Foundations 1993

Authors and Affiliations

  • Horng-Twu Liaw
    • 1
  • Chin-Laung Lei
    • 1
  1. 1.Department of Electrical EngineeringNational Taiwan UniversityTaipeiTaiwan 106, R.O.C.

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