Trusted Computing Amidst Untrustworthy Intermediaries

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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
2
Overview
Highly Parallel Scalable Network Variable
Topology Internet Like But Untrusted!
Programs
Data
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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.

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A Little Complexity Theory
The Classic View
easy
P


NP
S
P
PSPACE
2
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A Little Complexity Theory

• The Classic View

easy
NP-complete
P


NP
S
P
PSPACE
2
hard
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A Little Complexity Theory

• The Classic View

fuggettaboutit
easy
P


NP
S
P
PSPACE
2
hard
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Parameter Sensitivity Instance(n,k)

• Suppose our problem is, say, NP-complete.
• Consider an algorithm with a time bound such as
  O(2kn).
• And now one with a time bound more like O(2kn).

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Parameter Sensitivity Instance(n,k)

• Suppose our problem is, say, NP-complete.
• Consider an algorithm with a time bound such as
  O(2kn).
• And now one with a time bound more like O(2kn).
• Both are exponential in parameter value(s).

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Parameter Sensitivity Instance(n,k)

• Suppose our problem is, say, NP-complete.
• Consider an algorithm with a time bound such as
  O(2kn).
• And now one with a time bound more like O(2kn).
• Both are exponential in parameter value(s).
• But what happens when k is fixed?

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Parameter Sensitivity Instance(n,k)

• Suppose our problem is, say, NP-complete.
• Consider an algorithm with a time bound such as
  O(2kn).
• And now one with a time bound more like O(2kn).
• Both are exponential in parameter value(s).
• But what happens when k is fixed?
• Fixed Parameter Tractability confines
  superpolynomial behavior to the parameter.

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Complexity Theory, Revised
Hence, the Parameterized View
solvable (even if NP-complete)


W1
W2
XP
FPT
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Complexity Theory, Revised
The Parameterized View
solvable (even if NP-hard!)


W1
W2
XP
FPT
heuristics only
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Complexity Theory, Revised
The Parameterized View
I said fuggettaboutit!
solvable (even if NP-hard!)


W1
W2
XP
FPT
heuristics only
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Target Problems

• Not membership in P (assuming P?NP)
• hard to compute

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Target Problems

• Not membership in P (assuming P?NP)
• hard to compute
• Membership in NP
• easy to check

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Target Problems

• Not membership in P (assuming P?NP)
• hard to compute
• Membership in NP
• easy to check
• Fixed Parameter Tractable
• use kernelization and branching

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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

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Branching

• Lets stay with Clique and Vertex Cover
• Bounded tree search
• Depth at most k
• With this technique, we can now solve vertex
  cover in O(1.28kn) time
• Easily parallelizable
• No processor sees anothers work, nor the
  original graph

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Branching as A Form of Cyber Security
Data decomposition
Answer check (NP certificate)
.
Untrusted intermediaries cannot deduce data
Nor can they spoof answers
. . . . . .
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Overall Appeal

• Verifiability
• easy to check answers a faulty or malicious
  processor cannot invalidate or subvert
  computations

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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

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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

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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

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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