Open Access Open Access  Restricted Access Subscription or Fee Access

Algebraic Analysis of Akl and Taylor Key Assignment Scheme

(*) Corresponding author

Authors' affiliations



Key assignment schemes are used to distribute keys to users to enable them decrypt and view information. Usually users, based on their authority, are represented as a hierarchy such that a user can derive the keys of all users that have less authority. Several methods are exist in the literature to assign keys to users. However, some of them are not correct orvulnerable to collusion attacks such that two users can cooperate together to compute the key of a user at a higher level. One of the pioneer methods in key assignment is Akl and Taylor technique [1]. Several papers are introduced later based on their technique. In this paper, we analyze Akl and Taylor technique and its variations algebraically in terms of their correctness and the possibility of collusion attack. Furthermore, we introduce a new technique that is secure in a more restrictive assumption of collusion attack. We show that the proposed technique is more efficient than the existing ones.
Copyright © 2014 Praise Worthy Prize - All rights reserved.


Key Assignment Schemes; Key Algebraic Structure; Collusion Attack

Full Text:



S. Akl and P. Taylor, Cryptographic solution to a problem of access control in a hierarchy, ACM Transaction on Computer Systems, Vol. 1, n. 3, pp. 239-248, 1983.

S. Zhong and T. Lin, A comment on the chen-chung scheme for hierarchical access control, Computers & Security, Vol. 22, n. 5, pp. 450-452, June 2003.

X. Yi, Y. Ye, Security of Tzeng’s Time-Bound Key Assignment Scheme for Access Control in a Hierarchy, IEEE Transactions on Knowledge and Data Engineering, Vol. 15, n. 4, pp. 1054-1055, 2003.

X. Yi, Security of Chien’s Efficient Time-Bound Hierarchical Key Assignment Scheme, IEEE Transactions on Knowledge and Data Engineering, Vol. 17, n. 9, 2005.

J. Crampton, K. Martin, and P. Wild, On key assignment for hierarchical access control, In Proceedings of the 19th IEEE workshop on Computer Security Foundations (CSFW '06), IEEE Computer Society, pp. 98-111, 2006.

K. Sabri and R. Khedri, A Generic Algebraic Model for the Analysis of Cryptographic-Key Assignment Schemes, In Proceedings of the 5th international conference on Foundations and Practice of Security (FPS'12), Joaquin Garcia-Alfaro, Frédéric Cuppens, Nora Cuppens-Boulahia, Ali Miri, and Nadia Tawbi (Eds.). Springer-Verlag, Berlin, Heidelberg, pp. 62-77, 2012.

S. MacKinnon, P. Taylor, H. Meijer, and S. Akl, An Optimal Algorithm for Assigning Cryptographic Keys to Control Access in a Hierarchy, IEEE Transactions on Computers, Vol. 34, n. 9, pp.797-802, 1985.

K. Sabri, Algebraic Analysis of Object-Based Key Assignment Schemes, Journal of Software, Vol. 9, n. 8, pp. 2033-2042, August 2014.

K. Sabri and R. Khedri, Algebraic framework for the specification and analysis of cryptographic-key distribution, Fundamenta Informaticae, Vol. 112, n. 4, pp. 305-335, 2011.

H. Liaw, S. Wang, and C. Lei, A dynamic cryptographic key assignment scheme in a tree structure, Computers & Mathematics with Applications, Vol. 25, n. 6, pp.109-114, March 1993.

R. Sandhu. On some cryptographic solutions for access control in a tree Hierarchy, In ACM '87: Proceedings of the 1987 Fall Joint Computer Conference on Exploring technology: today and tomorrow, Los Alamitos, CA, USA, IEEE Computer Society Press., pp. 405-410, 1987.

L. Harn and H. Lin, A cryptographic key generation scheme for multilevel data security, Computer Security, Vol. 9, n. 6, pp. 539-546, 1990.

Kayem, S. Akl, and P. Martin, An Independent Set Approach to Solving the Collaborative Attack Problem, International Conference on Parallel and Distributed Computing Systems, Phoenix, AZ, USA, pp. 594-599, 2005.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize