Methods of Secure Computation and Data Integration

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Methods of Secure Computation and Data Integration

• Jerome Reiter, Duke University
• Alan Karr, NISS
• Xiaodong Lin, University of Cincinnati
• Ashish Sanil, Bristol Myers Squibb

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General setting

• Multiple agencies seek to improve analyses by
  pooling their data.
• Do not want to reveal individual data values
  unknown to other agencies.
• Want accurate results from pooling procedures.

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Pooling situations

• Horizontally PartitionedAgencies have different
  records but same variables.
• Purely Vertically PartitionedAgencies have same
  records but different variables.
• Partially Overlapping, Vertically
  PartitionedAgencies have different records and
  different variables, with some common records and
  variables.

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Horizontal partitioningKarr, Lin, Sanil, Reiter
(JCGS, 2005)

• Secure data integration-- shares data but
  protects sources.-- allows any analysis to be
  done.
• Secure summation-- shares sums without sharing
  data -- allows regressions, association rules,
  classifications, clustering

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Secure summation

• Obtain without sharing individual
  values
• Agency A passes (x R) to 2nd agency.
• Agency B adds its x to this value and passes sum
  to Agency C.
• Process continues until all agencies have added
  their x.
• Agency A subtracts R from the sum.

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Purely vertical partitioning

• Secure dot/matrix product-- shares dot/matrix
  products without sharing data.-- allows
  regressions, association rules, classification,
  clustering.-- assumes semi-honest.
• Synthetic data approaches-- share synthetic
  copies of data across agencies.-- allows any
  analysis when distributions used to generate
  data are accurate.-- generates public use data
  file.

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Secure dot/matrix productsKarr, Lin, Reiter,
Sanil (NISS tech. report)

• Compute not revealing individual
  values
• Agency A passes where
  for all i,j to Agency B.
• Agency B sends to Agency A.
• Agency A computes

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Purely vertical partitioning

• Secure dot/matrix product-- share dot/matrix
  products without sharing data.-- allows
  regressions, association rules, classification,
  clustering.-- assumes semi-honest.
• Synthetic data approaches-- share synthetic
  copies of data across agencies.-- allows any
  analysis when distributions used to generate
  data are accurate.-- generates public use data
  file.

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Synthetic data approachKohnen (PhD thesis, 2005)

• Assume X not sensitive.
• Pass real X to Agency B.
• Agency B simulates multiple copies of Y for from
  f(YX) estimated using the dataset from Agency A.
  Pass the copies to Agency A.

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Synthetic data approachKohnen (PhD thesis, 2005)

• Agency A uses partially synthetic data methods
  (Reiter, Surv. Meth., 2003) for inferences based
  on YX.
• Agency A can release fully synthetic data to
  public.

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Synthetic data approachesKohnen (PhD thesis,
2005)

1. Agency A simulates disguiser X that look like the
   genuine values of X, ideally from distribution
   close to f(XY). Pass real X and disguisers to
   Agency B.
2. Agency B simulates multiple copies of Y for each
   f(YX) estimated using the datasets from Agency
   A. Pass the copies to Agency A.

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Synthetic data approachesKohnen (PhD thesis,
2005)

• Agency A discards disguisers and uses partially
  synthetic data methods (Reiter, Surv. Meth.,
  2003) to obtain inferences using the real X.
• Agency A can release fully synthetic data to
  public.

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Partially overlapping, vertical partitioning

• Secure EM algorithm-- uses secure dot
  products-- continuous data estimate
  covariance matrix for multivariate normal
  data-- categorical data estimate parameters
  of log-linear models

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Limitations of methodsDefining a research agenda

• Secure computation methods- How to specify
  models without viewing data?- What if
  sophisticated models needed?- How to do
  posterior simulation?
• Synthetic data methods- How to generate good
  disguisers?
• All methods- How to incorporate matching
  errors, differences in data quality and
  definitions?- How to account for disclosure
  risks from models that fit too well?