Differentially Private Oblivious RAM Sameer Wagh , Paul Cuff , - - PowerPoint PPT Presentation

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Differentially Private Oblivious RAM Sameer Wagh , Paul Cuff , Prateek Mittal July 24, 2019 Princeton University, Renaissance Technologies Introduction: Oblivious RAM Access data privately from private database. 1

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Differentially Private Oblivious RAM

Sameer Wagh∗, Paul Cuff†, Prateek Mittal∗ July 24, 2019

∗Princeton University, †Renaissance Technologies

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Introduction: Oblivious RAM

Access data privately from private database.

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Introduction: Oblivious RAM

User receives record R

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Introduction: Oblivious RAM

Obliviousness: Adversary should not know R

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ORAM Application I

Client-server environments

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ORAM Application II

Trusted Execution Environments such as SGX-based enclaves

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The Problem?

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The Problem?

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The Problem: Overhead

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Overheads

  • Logarithmic bandwidth overhead (≥ 100×)
  • Logarithmic storage overhead
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Key Insight

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Overheads

  • Logarithmic bandwidth overhead (≥ 100×)
  • Logarithmic storage overhead

Key Insight

Can we improve performance by relaxing privacy?

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Key Insight: Improve Performance by Relaxing Privacy

  • Statistically private ORAM

◮ Better performance at the cost of privacy loss ◮ Challenge: Can we provide rigorous guarantees?

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Key Insight: Improve Performance by Relaxing Privacy

  • Statistically private ORAM

◮ Better performance at the cost of privacy loss ◮ Challenge: Can we provide rigorous guarantees?

  • Efficiency

◮ Reduce performance overheads – bandwidth, local storage ◮ Achieve privacy proportional to application resources

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Key Insight: Improve Performance by Relaxing Privacy

  • Statistically private ORAM

◮ Better performance at the cost of privacy loss ◮ Challenge: Can we provide rigorous guarantees?

  • Efficiency

◮ Reduce performance overheads – bandwidth, local storage ◮ Achieve privacy proportional to application resources

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Differential Privacy

  • Formalize Differentially Private ORAM
  • Introduce Root ORAM
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Key Insight: Improve Performance by Relaxing Privacy

  • Statistically private ORAM

◮ Better performance at the cost of privacy loss ◮ Challenge: Can we provide rigorous guarantees?

  • Efficiency

◮ Reduce performance overheads – bandwidth, local storage ◮ Achieve privacy proportional to application resources

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Differential Privacy

  • Formalize Differentially Private ORAM
  • Introduce Root ORAM

Root ORAM

  • Theoretical Results
  • Empirical Results
  • Private Information Retrieval
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Differentially Private Oblivious RAM

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DP-ORAM Intuition

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DP-ORAM Intuition

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DP-ORAM Intuition

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Statistical closeness - Differential Privacy

Pr[ORAM(a1) ∈ S] ≤ eǫPr[ORAM(a2) ∈ S] + δ

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Protocol Construction

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Root ORAM: Storage

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Root ORAM: Invariant

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Root ORAM: Updated mapping

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Root ORAM: Updated mapping

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Root ORAM: Updated mapping

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Key Insight

  • Uniform mapping ⇒ Conventional Security
  • Non-uniform mapping ⇒ DP-ORAM Security
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Root ORAM: Updated mapping

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Key Insight

  • Uniform mapping ⇒ Conventional Security
  • Non-uniform mapping ⇒ DP-ORAM Security
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Root ORAM: Updated mapping

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Root ORAM: Non-Uniform mapping

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Impact

  • Lower average placement ⇒ Improved performance
  • Privacy loss
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Root ORAM: Write back

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Root ORAM: Lowest Common Intersection

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Root ORAM: Lowest Common Intersection

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Root ORAM: Lowest Common Intersection

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Database view before access

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Database view after access

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Results

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Security Result: Root ORAM is DP-ORAM

Differentially Private ORAM Protocol The Root ORAM protocol with parameters k, p is (ǫ, δ)-differentially private for the following choice of ǫ and δ ǫ = 2 log 1 + (2k − 1) · p 1 − (1 − δk0)p

  • δ = M ·

1 + (2k − 1) · p N M (1) where δk0 is the Kronecker delta, M is the size of the access sequence and M > total stash size.

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Performance Improvements

Improvement in stash usage for (L, k, Z) = (15, 1, 4)

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Performance Improvements

Improvement in stash usage for (L, k, Z) = (15, 1, 4)

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Key takeaway

DP-ORAM can enhance performance at the cost of privacy

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Application: Private Information Retrieval

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Private Information Retrieval (PIR)

Access data privately from public database.

[46] Mittal, Prateek, Femi G. Olumofin, Carmela Troncoso, Nikita Borisov, and Ian

  • Goldberg. ”PIR-Tor: Scalable Anonymous Communication Using Private Information

Retrieval.” In USENIX Security Symposium, p. 31. 2011.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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ORAM based PIR

  • ORAM has been used previously for PIR [7, 59]

[7] Michael Backes, Aniket Kate, Matteo Maffei, and Kim Pecina. ObliviAd: Provably secure and practical online behavioral advertising. In IEEE Symposium on Security and Privacy (S&P), 2012. [59] Peter Williams and Radu Sion. Usable PIR. In Symposium on Network and Distributed System Security (NDSS), 2008.

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DP-PIR Bandwidth Comparison

Security-Bandwidth trade-offs for DP-PIR protocols (Toledo et.al. [54], Path-PIR [42], and Path ORAM [53]).

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DP-PIR Bandwidth Comparison

Security-Bandwidth trade-offs for DP-PIR protocols (Toledo et.al. [54], Path-PIR [42], and Path ORAM [53]).

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DP-ORAMs provide significant performance benefits for DP-PIR

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Conclusion

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Summary

  • Formalized Differentially Private ORAMs
  • Introduced a family of DP-ORAM protocols
  • Analyzed security, performance
  • Showcased utility for Private Information Retrieval

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Summary

  • Formalized Differentially Private ORAMs
  • Introduced a family of DP-ORAM protocols
  • Analyzed security, performance
  • Showcased utility for Private Information Retrieval
  • Possible to enhance performance by relaxing privacy

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Summary

  • Formalized Differentially Private ORAMs
  • Introduced a family of DP-ORAM protocols
  • Analyzed security, performance
  • Showcased utility for Private Information Retrieval
  • Possible to enhance performance by relaxing privacy

Source code is available at https://github.com/inspire-group/Root-ORAM

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Thank you!

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Thank you!

Questions?

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