Information-Theoretical Analysis of Private Content Identification

Transcription

1 Information-Theoretical Analysis of Private Content Identification S. Voloshynovskiy, O. Koval, F. Beekhof, F. Farhadzadeh, T. Holotyak Stochastic Information Processing Group, University of Geneva, Switzerland ITW200 Dublin, Ireland

2 2 Outline Introduction 2 Identification setup 3 Error events 4 Identification capacity and privacy leak 5 Complexity of fingerprint-based identification 6 Conclusions

3 Introduction Physical Objects Humans Digital Content Images Videos Audios Text docs 3 watches Online sharing services packaging Physical objects Biometrics Main concerns Identification: identity, authenticity, origin, ownership, Tracking and tracing Automatic tagging

4 Introduction Physical Objects Humans Digital Content Images Videos Audios Text docs 4 watches Online sharing services packaging Physical objects Biometrics A solution Digital fingerprinting (a.k.a. robust perceptual hashing) is a technique for computing a compact robust, secure and private binary representation of physical or digital content.

5 Introduction Physical Objects Humans Digital Content Images Videos Audios Text docs 5 watches Online sharing services packaging Physical objects Biometrics Objectives Performance analysis (probability of error, achievable rate); Privacy leak evaluation; Complexity for large-scale applications. Related works: F. Willems, T. Kalker, J. Goseling, and J.-P. Linnartz, ISIT2003 Westover and O Sullivan, ISIT2004, IEEE IT2008 and Tuncel IEEE IT2009

6 Identification Setup () 6 Enrollment Digital Fingerprint Extraction Codebook/Database 2 M Key Identification Decoder Digital Fingerprint Extraction Codebook cardinality: with being the rate. - dim. reduction (sensing matrix) - binarization - privacy amplification

7 Identification Setup (2) 7 Identification Proposition 2as composite hypothesis testing 0 Enrollment 0 0 Identification 0 Equivalent 0 Equivalent Channel 0 Binary fingerprinting - enrollment bit error probability - identification bit error probability

8 Identification Setup (3) 8 Forney s Proposition erasure/list 2 decoder [Forney 68] - binary entropy. Binary fingerprinting Bounded Distance Decoder (BDD) List decoding Unique decoding with Erasure decoding

9 Identification Setup (4) 9 Properties Correct acceptance Correct rejection Hypothesis testing Binomial distribution Binomial distribution

10 Identification Setup (5) 0

11 Error events () Proposition The optimal threshold rule should satisfy error. Proof: for unique content identification under Forney s erasure to guarantee a minimum of overall identification - probability of false acceptance - probability of incorrect decoding - divergence

12 Error events (2) 2 that is minimized by: Forney s threshold vs For large, for the identification rates. Remark For the identification rate satisfying, the above optimal threshold yields. PL b b y

13 Identification capacity and privacy leak () 3 Proposition 2 For and if there exist codes with rate and error probability such that: As soon as is arbitrarily close to, the rate is achievable, and it is referred to as: private identification capacity: privacy leak: Remark 2 /result coincides with F. Willems et al ISIT2003/ If privacy amplification is not applied, i.e., and, one is interested in the maximization of the identification capacity that yields:

14 Identification capacity and privacy leak (2) 4 Remark P b =0.0 P b =0. P b =0.2 P b =0.3 P b =

15 Complexity of fingerprint based identification () 5 Decoding Proposition algorithms 2 Exhaustive implementation of BDD Hamming sphere decoding Reliability-based decoding

16 Complexity of fingerprint based identification (2) 6 Exhaustive implementation of BDD Given: codewords, with Compute: Complexity: exponential Identification = exhaustive computation Codebook/Database Fingerprint 2 M Remark 3 Complexity does not depend on data quality (both privacy amplification and acquisition).

17 Complexity of fingerprint based identification (3) 7 Hamming sphere decoding Observation: the most likely codewords radius around. are within a Hamming sphere with Identification = codeword presence verification Data user Fingerprint Hamming sphere PL b b y query Server Y/N Codebook/Database 2 M

18 Complexity of fingerprint based identification (4) 8 Hamming sphere decoding Proposition 3 The cardinality of the list of candidates contained in the sphere of radius, is:, where Asymptotically: For unique decoding : Remark 4 Complexity depends on data quality. Remark 5 Analogy: binary fingerprint = computer memory address with flag.

19 Complexity of fingerprint based identification (5) 9 Reliability based decoding Observation: the reliability of bits of within Hamming sphere can be estimated based on the fingerprint magnitude. Random projections: impact of distortions Concept of random projection bit reliability (sign-magnitude decomp.) Sort

20 Complexity of fingerprint based identification (6) 20 Identification = soft decoding or soft verification Data user Hamming sphere Server Codebook/Database Fingerprint PL b b y query Y/N 2 M b u ( m) m M Two-channel splitting: Good channel with Bad channel with 2 3 Multi-channel splitting, randomization and decoding [Voloshynovskiy et al, IEEE WIFS200]

21 Complexity Introduction Identification setup Error events Capacity-Privacy Complexity Conclusions Complexity of fingerprint based identification (7) 2 Comparison of decoding strategies Exhaustive search Hamming sphere decoding Reliability based decoding Fixed 0 2 ES Hamming Reliability ES 0 8 Hamming Reliability Database size Remark 6 Reference performance: [F. Willems, ISIT2009]

22 22 Conclusions Remark 5 Content identification = coding problem with random codes. We have analyzed the performance-privacy trade-off of content identification framework. We have investigated the complexity of three decoding strategies based on the BDD. The obtained results can be of interest for security and content-based retrieval system analysis as well as low-complexity approximate search implementations. Extensions Compression (memory storage) Identification Rate Privacy Complexity List decoding vs unique decoding Performance under soft decoding.