1. © 2004 Ravi Sandhu www.list.gmu.edu The Typed Access Matrix Model (TAM) and Augmented TAM (ATAM) Ravi Sandhu Laboratory for Information Security Technology George Mason University www.list.gmu.edu sandhu@gmu.edu

2. © 2004 Ravi Sandhu www.list.gmu.edu 2 Outline TAM: Typed Access Matrix Model TAM adds types to HRU and preserves strong safety results of SPM/ESPM SO-TAM: Single Object TAM SO-TAM manipulates one column of the access matrix at a time and is equivalent to TAM ATAM: Augmented TAM ATAM adds testing for absence of rights to TAM ATAM is equivalent to TAM in one sense but more expressive in another

3. © 2004 Ravi Sandhu www.list.gmu.edu 3 TAM adds types to HRU

4. © 2004 Ravi Sandhu www.list.gmu.edu 4 TAM adds types to HRU

5. © 2004 Ravi Sandhu www.list.gmu.edu 5 TAM commands

6. © 2004 Ravi Sandhu www.list.gmu.edu 6 TAM primitive operations

7. © 2004 Ravi Sandhu www.list.gmu.edu 7 TAM operations: enter and delete

8. © 2004 Ravi Sandhu www.list.gmu.edu 8 TAM operations: create and destroy

9. © 2004 Ravi Sandhu www.list.gmu.edu 9 TAM operations: create and destroy

10. © 2004 Ravi Sandhu www.list.gmu.edu 10 ORCON in TAM

11. © 2004 Ravi Sandhu www.list.gmu.edu 11 ORCON in TAM

12. © 2004 Ravi Sandhu www.list.gmu.edu 12 ORCON in TAM

13. © 2004 Ravi Sandhu www.list.gmu.edu 13 ORCON in TAM

14. © 2004 Ravi Sandhu www.list.gmu.edu 14 MTAM: Monotonic TAM

15. © 2004 Ravi Sandhu www.list.gmu.edu 15 MTAM Canonical Schemes

16. © 2004 Ravi Sandhu www.list.gmu.edu 16 MTAM Canonical Schemes

17. © 2004 Ravi Sandhu www.list.gmu.edu 17 ORCON as a MTAM Canonical Scheme

18. © 2004 Ravi Sandhu www.list.gmu.edu 18 Acyclic TAM schemes

19. © 2004 Ravi Sandhu www.list.gmu.edu 19 Acyclic TAM unfolded state

20. © 2004 Ravi Sandhu www.list.gmu.edu 20 Acyclic MTAM unfolded state

21. © 2004 Ravi Sandhu www.list.gmu.edu 21 Acyclic MTAM safety

22. © 2004 Ravi Sandhu www.list.gmu.edu 22 Ternary MTAM

23. © 2004 Ravi Sandhu www.list.gmu.edu 23 Ternary MTAM

24. © 2004 Ravi Sandhu www.list.gmu.edu 24 Binary and Unary MTAM Unary MTAM Useless Binary MTAM Single-parent creation or spontaneous double- child creation Less expressive than multi-parent creation

25. © 2004 Ravi Sandhu www.list.gmu.edu 25 SOTAM: single object TAM

26. © 2004 Ravi Sandhu www.list.gmu.edu 26 SOTAM SOTAM is equivalent in expressive power to TAM

27. © 2004 Ravi Sandhu www.list.gmu.edu 27 ATAM: Augmented TAM Allow testing for absence of rights in the conditions of commands ATAM is equivalent in expressive power to TAM in unbounded simulation but most likely not in bounded simulation Most likely not has recently been shown to be provably cannot