Private Keyword Search on Streaming Data

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Private Keyword Search on Streaming Data

Rafail Ostrovsky William
Skeith UCLA
(patent pending)
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Motivating Example

• The intelligence community collects data from
  multiple sources that might potentially be
  useful for future analysis.
• Network traffic
• Chat rooms
• Web sites, etc
• However, what is useful is often classified.

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Current Practice

• Continuously transfer all data to a secure
  environment.
• After data is transferred, filter in the
  classified environment, keep only small fraction
  of documents.

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• Classified Environment

Filter
Storage
! D(1,3)! D(1,2)! D(1,1)!
D(3,1)
D(1,1)
D(1,2)
D(2,2)
D(2,3)
D(3,2)
D(2,1)
D(1,3)
D(3,3)
! D(2,3)! D(2,2)! D(2,1)!
Filter rules are written by an analyst and are
classified!
! D(3,3)! D(3,2)! D(3,1)!
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Current Practice

• Drawbacks
• Communication
• Processing

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How to improve performance?

• Distribute work to many locations on a network
• Seemingly ideal solution, but
• Major problem
• Not clear how to maintain privacy, which is the
  focus of this talk

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• Classified Environment

Storage E (D(1,2)) E (D(1,3))
Filter
! D(1,3)! D(1,2)! D(1,1)!
Decrypt
Storage E (D(2,2))
Filter
! D(2,3)! D(2,2)! D(2,1)!
Storage D(1,2) D(1,3) D(2,2)
Storage
Filter
! D(3,3)! D(3,2)! D(3,1)!
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• Example Filter
• Look for all documents that contain special
  classified keywords, selected by an analyst
• Perhaps an alias of a dangerous criminal
• Privacy
• Must hide what words are used to create the
  filter
• Output must be encrypted

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More generally

• We define the notion of Public Key Program
  Obfuscation
• Encrypted version of a program
• Performs same functionality as un-obfuscated
  program, but
• Produces encrypted output
• Impossible to reverse engineer
• A little more formally

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Public Key Program Obfuscation
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Privacy
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Related Notions

• PIR (Private Information Retrieval)
  CGKS,KO,CMS
• Keyword PIR KO,CGN,FIPR
• Program Obfuscation BGIRSVY
• Here output is identical to un-obfuscated
  program, but in our case it is encrypted.
• Public Key Program Obfuscation
• A more general notion than PIR, with lots of
  applications

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What we want
Filter
Storage
! D(1,3)! D(1,2)! D(1,1)!
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This is matching document 2

This is a Non-matching document
This is matching document 1
This is matching document 3


This is a Non-matching document
This is a Non-matching document




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How to accomplish this?
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Several Solutions based on Homomorphic Encryptions

• For this talk Paillier Encryption
• Properties
• Plaintext set Zn
• Ciphertext set Zn2
• Homomorphic, i.e., E(x)E(y) E(xy)

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Simplifying Assumptions for this Talk

• All keywords come from some poly-size dictionary
• Truncate documents beyond a certain length

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D
Dictionary
. . .
(g,gD)



Output Buffer
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Heres another matching document

• Collisions cause two problems
• Good documents are destroyed
• 2. Non-existent documents could be fabricated

This is matching document 1
This is matching document3

This is matching document 2
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• Well make use of two combinatorial lemmas

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(No Transcript)
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How to detect collisions?

• Append a highly structured, (yet random) k-bit
  string to the message
• The sum of two or more such strings will be
  another such string with negligible probability
  in k
• Specifically, partition k bits into triples of
  bits, and set exactly one bit from each triple to
  1

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• 100001100010010100001010010

010001010001100001100001010
010100100100010001010001010

100100010111100100111010010
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Detecting Overflow gt m

• Double buffer size from m to 2m
• If m lt documents lt 2m, output overflow
• If documents gt 2m, then expected number of
  collisions is large, thus output overflow in
  this case as well.
• Not yet in eprint version, will appear soon, as
  well as some other extensions.

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More from the paper that we dont have time to
discuss

• Reducing program size below dictionary size
  (using ? Hiding from CMS)
• Queries containing AND (using BGN machinery)
• Eliminating negligible error (using perfect
  hashing)
• Scheme based on arbitrary homomorphic encryption

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Conclusions

• Private searching on streaming data
• Public key program obfuscation, more general than
  PIR
• Practical, efficient protocols
• Many open problems

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Thanks For Listening!?