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A Secure Protocol for Computing Dot-products in Clustered and Distributed Environments. Ioannis Ioannidis, Ananth Grama and Mikhail Atallah Purdue University. Acknowledgements: National Science Foundation. The Problem. Dot-products are the basis of many important applications

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A Secure Protocol for Computing Dot-products in Clustered and Distributed Environments


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a secure protocol for computing dot products in clustered and distributed environments

A Secure Protocol for Computing Dot-products in Clustered and Distributed Environments

Ioannis Ioannidis, Ananth Grama and Mikhail Atallah

Purdue University.

Acknowledgements: National Science Foundation.

the problem
The Problem
  • Dot-products are the basis of many important applications
      • Scientific computations
      • Data mining
      • Transaction processing
      • Biometrics
  • Use of distributed environments creates security issues
      • Data too valuable to expose
      • Untrusted links or hosts
      • Spoofing is very easy
the problem1
The Problem
  • Each party is honest-but-curious
    • They play by the rules, but if they can find out more, they will.
  • Only one of the parties is interested in the result.
  • We have a random number generator, which generates a uniformly distributed random integer, cast into a real.
candidate solution
Candidate Solution
  • Use conventional cryptography
    • Secure tunneling can protect the links
    • More complex protocols offer protection against untrusted hosts
  • Unfortunately, public-key crypto has a high complexity
    • Modular exponentiation computations can have a crippling effect on the overall performance
security vs efficiency
Security vs. Efficiency
  • Ideally, no information should leak about the participating vectors during a secure dot-product protocol
  • However, in the context of the given problem, in a clustered environment, security need not be so tight
    • Dot-products inherently leak data in the solution
    • Some leakage may be acceptable, since the same dot-product will not be computed multiple times
    • Small compromises in security can lead to large gains in efficiency
an efficient alternative
An Efficient Alternative
  • Use linear algebraic properties to achieve a sufficient level of security
    • Hide a vector inside a matrix
    • Scramble the matrix
    • Multiply the matrix by the other vector
    • Retrieve the dot-product
    • A large part of the computation can be reused
    • Both parties must share a secret – a number – before the protocol
an efficient alternative1
An Efficient Alternative
  • Security is not perfect
    • A small number of equations will leak
    • Statistics can reveal information
  • But is sufficient for a real-world setting
    • If you don’t need to execute the same instance many times, leaking a few equations is not a problem
    • Statistical attacks demand larges amounts of information
    • Not so easy to gather them in clustered environments
algorithmic considerations
Algorithmic Considerations
  • Time overhead
    • How much more computation needs to be performed?
    • Public-key cryptography adds an unacceptable amount of overhead.
    • But it is the only solution if perfect secrecy is the goal.
  • Communication overhead
    • Network latency prevails in larger networks.
    • Bit count is the decisive factor in tightly coupled networks.
stability considerations
Stability Considerations
  • Algebraic manipulations of the data can introduce numerical errors in scientific computation data.
  • Any protocol applied to real-valued vectors must be numerically stable to be of practical importance.
experimental results
Experimental Results
  • The protocol was executed on two PIII/450Mhz machines connected on a Gigabit Ethernet network
  • Data was randomly generated vectors of length 106
  • We measured the total overhead (computation and communication)
    • Communication overhead is expected to be a factor of 4
experimental results1
Experimental Results
  • Measured overhead showed a factor of 4.69 overhead
    • Communication overhead is the dominating factor, even on a fast network
  • Average numerical error was measured to 4.5 x 10-9
conclusions and ongoing research
Conclusions and Ongoing Research
  • It is possible to execute multiparty, real-valued dot-product computations efficiently and with satisfactory security
  • Binary dot-products pose a different problem due to the sparsity of the vectors
    • Number theoretic techniques introduce large time and communication overheads