Cryptanalysis of DiscreteSequence Spread Spectrum Watermarks

1
Cryptanalysis of Discrete-Sequence Spread
Spectrum Watermarks

• M. Kivanc Mihcak kivancm_at_microsoft.com
• Ramarathnam Venkatesan venkie_at_microsoft.com
• Microsoft Research, Crypto Group
• Mustafa Kesal kesal_at_ifp.uiuc.edu
• University of Illinois, Urbana-Champaign

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Executive Summary

• Goal To provide a refined mathematical model of
  attacking by re-modulation
• X ? XW Y ? W ? Y a W X
• and comparing this model to some experimental
  results.

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Outline

• Short overview of literature on attack
  approaches
• A brief description of targeted WM algorithm
• Proposed attack description
• Toy example and experimental simulation
  results
• Further refinements in the attack
• Discussion

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Attack Methods - Overview

• Standard benchmark attacks Stirmark
  Checkmark
• Independent of the particular targeted WM
  algorithm
• Analogous to randomness checks in cryptography

• Generic vs. Specialized?
• Business model for attacker
• Partial success could be dangerous for attacker
• Goal Specialized attack that is almost always
  successful

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Background
Considered a DSSS (Discrete Sequence Spread
Spectrum) WM scheme

• s host (un-watermarked signal)
• m watermark
• x s m watermarked signal
• m , s independent

• Correlation detector (suboptimal in general in P
  e sense, simple)
• y received signal

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A State-of-the-art DSSS-WM Algorithm
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Redundancy vs. Robustness
Fundamental relationship between redundancy and
robustness to geometric and malicious attacks
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Basics of Proposed Attack

• Specialized to Kirovski-Malvar-IHW01
• Use estimation techniques to estimate the
  embedded WM
• Attack performed via subtracting scaled estimate

Remarks

• 1. Estimation accuracy (and hence attack success
  probability) depends on
• code redundancy and source correlations
• Approach similar to (but specialized and refined
  version of) estimation
• attack of Checkmark Voloshynovskiy et.al.

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Contributions

• Provided a cryptanalysis of the proposed attack
• Use locally approximately i. i. d. Gaussian
  models for the source
• Considered several codes of interest at
  embedding layer
• Perform approximate ML estimation of the WM
  accordingly
• Quantified Pe (probability of error) in
  estimation
• Quantified the distortion induced by the attack
• Quantified the increase in Pe of the correlation
  detector after attack
• Used tools from detection-estimation theory
• Applied successfully to a state-of-the-art audio
  WM technology

See paper for details and mathematical analysis
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Toy Example
Single random variable setup x s w w e
D,-D s N (0,s2)
Induced distortion E (y-s)2 D2 1 a2 2a
2Q(D/s) 1
Pe of correlation detector after attack
Discrete nature of Pe due to discrete nature of
WM embedding
Generalizable to more complex codes and better
stochastic models
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Toy Example
D
0
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Toy Example
Single random variable setup x s w w e
D,-D s N (0,s2)
Induced distortion E (y-s)2 D2 1 a2 2a
2Q(D/s) 1
Pe of correlation detector after attack
Discrete nature of Pe due to discrete nature of
WM embedding
Generalizable to more complex codes and better
stochastic models
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Toy Example
D
aD
0
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Toy Example
Single random variable setup x s w w e
D,-D s N (0,s2)
Induced distortion E (y-s)2 D2 1 a2 2a
2Q(D/s) 1
Pe of correlation detector after attack
Discrete nature of Pe due to discrete nature of
WM embedding
Generalizable to more complex codes and better
stochastic models
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Toy Example
D
aD
0
t
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A Simulation Result
Locally i. i. d. Gaussian source block
repetition code on WM
Lower bound on Pe at detector
Normalized induced distortion (expected
MSE/sample)
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Real-Life Experimental Results

• Applied variants of proposed attack on
  Kirovski-Malvar DSSS audio WM scheme
• Kirovski-Malvar robust to all reasonable
  geometric distortions
• WM detector failed after applying proposed
  attacks
• Recovered more than 90 of secret WM chips
  almost always

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Further Refinements in the Attack

• Can incorporate correlations in the source to
  raise estimation accuracy
• Possibly perform joint estimation of unmarked
  host and WM iteratively

Watermarked data
Estimated host
Host Estimation
Estimated watermark
Watermark Estimation
Estimated watermark
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Discussion

• Designed a specialized successful attack on
  Kirovski-Malvar audio-WM scheme
• Provided a cryptanalysis using tools from
  detection-estimation theory
• Quantified the distortion induced by the attack
  and degradation in probability of error at the
  detector
• Fundamental trade-off between robustness to
  geometric attacks and malicious attacks
• Necessary to introduce enough randomness in
  future WM algorithms

Acknowledgements Thanks to Darko Kirovski, Rico
Malvar and Yacov Yacobi
for various discussions.