Managing key hierarchies for access control enforcement: Heuristic approaches

1. Managing key hierarchies for access control enforcement: Heuristic approaches Author:Carlo Blundo, Stelvio Cimato, Sabrina De Capitani di Vimercati, Alfredo De Santis, Sara Foresti, Stefano Paraboschi, Pierangela Samarati Source: Computers & Security, vol.29, 2010, pp. 533-547 Presenter: Tsuei-Hung Sun Date: 2010/7/6

2. Outline • Introduction • Motivation • Scheme • Advantage vs. weakness • Conclusion

3. Introduction • Data outsourcing promises higher availability and more effective disaster protection than in-house operations. • It need to protect the privacy of the data from the so called honest-but-curious servers.

4. Introduction • Prim's algorithm Image source: Prim's algorithm, 清華大學資訊工程所 劉炯朗 教授http://nthucad.cs.nthu.edu.tw/~yyliu/personal/nou/04ds/prim.html

5. Motivation • Existing approaches do not address the problem of supporting different access authorizations for different users. • Enforcing the authorization policy by heuristic and minimizing the number of keys to be maintained by the system and distributed to users.

6. Scheme • Basic concept Fig. Access matrix Fig. User tree acl(r):access control list of r, users that can access r. Ex. acl(r2) = {A, C} cap(u):capability list of u, resources that u can access. Ex. cap(C) = {r2 , r4 , r6} v.acl: set of users represented by vertex v. v.key: key associated with v.

7. Scheme • Integer Linear Programming (ILP) minimum user tree Fig. ILP minimum weight user tree Fig. General minimum weight user tree

8. Scheme • ILP minimum user tree problem is formulated as follows

9. Scheme • Three families of heuristics • sibling-based (S) • leaf-based (L) • mixed (M) • Three preference criteria • rnd: at random. • max: |vi.acl| + |vj.acl| is maximum, ties are broken randomly. • min: |vi.acl| + |vj.acl| is minimum, ties are broken randomly.

10. Sibling-based heuristic

11. Sibling-based heuristic

12. Leaves-based heuristic

13. Leaves-based heuristic

14. Mixed heuristics

15. Experimental result • Compare three heuristics with Damiani’s approach. Fig. sibling-based heuristic with different preference criteria.

16. Experimental result • Compare three heuristics adopting the min preference criterion with Damiani’s approach. Fig. Percentage of times each heuristic returns a solution at distance d from the lowest weight solution computed.

17. Advantage vs. weakness • Advantage • Three families of heuristics preference better than Damiani’s heuristics. • Integer linear programming formulation of the minimization problem. • Weakness • Execution time of the mixed heuristic is higher than the time requested by the other heuristics. • High variability of the time necessary to solve the ILP problem.

18. Conclusion • Protect the resource confidentiality from both unauthorized users and ‘‘honest-but-curious’’ servers. • Most of the existing efforts focus on the techniques for the evaluation of queries on encrypted outsourced data. • Integrating access control and encryption and by exploiting key derivation methods as a way for minimizing the number of keys distributed to users.

19. References • Prim's algorithm http://en.wikipedia.org/wiki/Prim%27s_algorithm (2010/7/7) • 普林演算法(Prim's algorithm) http://nthucad.cs.nthu.edu.tw/~yyliu/personal/nou/04ds/prim.html (2010/7/8) • Graph (mathematics) http://en.wikipedia.org/wiki/Undirected_graph (2010/7/7) • Minimum spanning tree http://en.wikipedia.org/wiki/Minimum_spanning_tree (2010/7/7) • Regular graph http://en.wikipedia.org/wiki/Regular_graph (2010/7/8) • Graph factorization http://en.wikipedia.org/wiki/Graph_factorization (2010/7/8) • Directed acyclic graph http://en.wikipedia.org/wiki/Directed_acyclic_graph (2010/7/8) • Linear programming http://en.wikipedia.org/wiki/Linear_programming (2010/7/9)

20. Thank you