UT-ORNL 15 March 2005 CSIIR Workshop 1 Trusted Computing Amidst Untrustworthy Intermediaries Mike Langston Department of Computer Science University of Tennessee currently on leave to Computer Science and Mathematics Division Oak Ridge National Laboratory USA

UT-ORNL 15 March 2005 CSIIR Workshop 2 Overview Programs Data Highly Parallel Scalable Network Variable Topology Internet Like But Untrusted!

UT-ORNL 15 March 2005 CSIIR Workshop 3 Possible Solutions Accept faulty results. Uh, no thanks. Authenticate/verify by central authority. Unrealistic, does not scale. Exploit complexity and checkability. Problems in NP can be hard to solve -- but they are always easy to check! No need for centralized control, ownership, or verification.

UT-ORNL 15 March 2005 CSIIR Workshop 4 A Little Complexity Theory The Classic View: P NP PSPACE Σ 2 P …… “easy”

UT-ORNL 15 March 2005 CSIIR Workshop 5 A Little Complexity Theory The Classic View: P NP PSPACE Σ 2 P …… “easy” “hard” NP-complete

UT-ORNL 15 March 2005 CSIIR Workshop 6 A Little Complexity Theory The Classic View: P NP PSPACE Σ 2 P …… “easy” “hard” “fuggettaboutit”

UT-ORNL 15 March 2005 CSIIR Workshop 7 Parameter Sensitivity: Instance(n,k) Suppose our problem is, say, NP-complete. Consider an algorithm with a time bound such as O(2 k+n ). And now one with a time bound more like O(2 k +n).

UT-ORNL 15 March 2005 CSIIR Workshop 8 Parameter Sensitivity: Instance(n,k) Suppose our problem is, say, NP-complete. Consider an algorithm with a time bound such as O(2 k+n ). And now one with a time bound more like O(2 k +n). Both are exponential in parameter value(s).

UT-ORNL 15 March 2005 CSIIR Workshop 9 Parameter Sensitivity: Instance(n,k) Suppose our problem is, say, NP-complete. Consider an algorithm with a time bound such as O(2 k+n ). And now one with a time bound more like O(2 k +n). Both are exponential in parameter value(s). But what happens when k is fixed?

UT-ORNL 15 March 2005 CSIIR Workshop 10 Parameter Sensitivity: Instance(n,k) Suppose our problem is, say, NP-complete. Consider an algorithm with a time bound such as O(2 k+n ). And now one with a time bound more like O(2 k +n). Both are exponential in parameter value(s). But what happens when k is fixed? Fixed Parameter Tractability: confines superpolynomial behavior to the parameter.

UT-ORNL 15 March 2005 CSIIR Workshop 11 Complexity Theory, Revised Hence, the Parameterized View: FPT … … W[1] W[2]XP “solvable (even if NP-complete)”

UT-ORNL 15 March 2005 CSIIR Workshop 12 Complexity Theory, Revised The Parameterized View: FPT … … W[1] W[2]XP “solvable (even if NP-hard!)” “heuristics only”

UT-ORNL 15 March 2005 CSIIR Workshop 13 Complexity Theory, Revised The Parameterized View: FPT … … W[1] W[2]XP “solvable (even if NP-hard!)” “heuristics only” “ I said fuggettaboutit! ”

UT-ORNL 15 March 2005 CSIIR Workshop 14 Target Problems Not membership in P (assuming P≠NP)  hard to compute

UT-ORNL 15 March 2005 CSIIR Workshop 15 Target Problems Not membership in P (assuming P≠NP)  hard to compute Membership in NP  easy to check

UT-ORNL 15 March 2005 CSIIR Workshop 16 Target Problems NP-complete FPT Not membership in P (assuming P≠NP)  hard to compute Membership in NP  easy to check Fixed Parameter Tractable  use kernelization and branching

UT-ORNL 15 March 2005 CSIIR Workshop 17 Kernelization Consider Clique and Vertex Cover High Degree Rule(s) Low Degree Rule(s) LP, Crown Reductions –kernel of linear size, and extreme density –the “hard part” of the problem instance

UT-ORNL 15 March 2005 CSIIR Workshop 18 Branching Let’s stay with Clique and Vertex Cover Bounded tree search Depth at most k With this technique, we can now solve vertex cover in O(1.28 k +n) time Easily parallelizable No processor sees another’s work, nor the original graph

UT-ORNL 15 March 2005 CSIIR Workshop Untrusted intermediaries cannot deduce data Data decomposition Nor can they spoof answers Answer check (NP certificate). Branching as A Form of Cyber Security

UT-ORNL 15 March 2005 CSIIR Workshop 20 Overall Appeal Verifiability –easy to check answers: a faulty or malicious processor cannot invalidate or subvert computations

UT-ORNL 15 March 2005 CSIIR Workshop 21 Overall Appeal Verifiability –easy to check answers: a faulty or malicious processor cannot invalidate or subvert computations Security –damage from intrusion contained: strong concealment of the total problem is a natural part of this method

UT-ORNL 15 March 2005 CSIIR Workshop 22 Overall Appeal Verifiability –easy to check answers: a faulty or malicious processor cannot invalidate or subvert computations Security –damage from intrusion contained: strong concealment of the total problem is a natural part of this method Scalability –branching translates into partitioning: no a priori bounds on the degree of parallelism

UT-ORNL 15 March 2005 CSIIR Workshop 23 Overall Appeal Verifiability –easy to check answers: a faulty or malicious processor cannot invalidate or subvert computations Security –damage from intrusion contained: strong concealment of the total problem is a natural part of this method Scalability –branching translates into partitioning: no a priori bounds on the degree of parallelism Robustness –subtrees are compartmentalized: processes can be reassigned at will

UT-ORNL 15 March 2005 CSIIR Workshop 24 Research Thrusts Range of amenable problems? –FPT –non FPT Ubiquity of untrustworthy processors? –grid computing –unbrokered resource sharing Relationship to traditional forms of security? –internet-style lightweight security –no heavyweight authentication needed