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Privacy beyond confjdentiality
- Common belief: “if I encrypt my data, then the data is
private”
- Encryption works and gets more and more effjcient!
- But does not hide all data
- Origin and destination
- Timing
- Frequency
- Location
- …
You cannot hide for long: De-anonymization of real-world dynamic - - PowerPoint PPT Presentation
You cannot hide for long: De-anonymization of real-world dynamic - - PowerPoint PPT Presentation
You cannot hide for long: De-anonymization of real-world dynamic behaviour George Danezis (University College London) Carmela Troncoso (Gradiant) Privacy beyond confjdentiality Common belief: if I encrypt my data, then the data is
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Anonymization
- Decouple user identity from actions
- Enabler for privacy-preserving technologies
- Anonymous credentials
- eVoting
- Privacy-preserving statistics computation
Anonymizer Anonymizer
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Anonymity in reality
- Diffjcult to guarantee perfect anonymity due to constraints
- Observations allow for inferences (e.g., behavioral profjles)
Anonymizer behaviour Prior info on users Alice Bob Alice is speaking to Bob with probability X
State of the art limitation: static behavior
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A model for dynamic behaviour
- Users
- Anonymizer
- Divided in batches (n batches per epoch)
- Perfect anonymity
t t
Sends messages to at rate λAB Sends messages to at rate λAO Send messages to at rate λOB Send messages to at rate λOO Dynamism: Epochs t of stationary behaviour Profjle evolution probability VA VO VB VO’
) ( Pois ) ( Pois ) ( Pois ) ( Pois
' OO AO O OB AB B OO OB O AO AB A
V V V V λ λ λ λ λ λ λ λ + ← + ← + ← + ←
Visible Hidde n Given observation… What is λAB?
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Sequential Monte Carlo aka. Particle Filters
- Inferring hidden parameters of sequential models
- Our case: modeling λAB at t depends on λAB at t-1
- Core idea:
- Particles representing sample hidden states (λAB , λOB)
- Distributed following posterior distribution given
evidence (VX)
- From Bayes theorem
Allow for statistic computation (mean, std, …) of hidden variables
)] , Pr[( ) | ( ) | ( ] | ) , Pr[(
1 1 1 * * * − − −
∝
t t t t t t
OB AB AB AB OB AB
E V L V λ λ λ λ λ λ λ
Prob at epoch t Likelihood of obs. given hidden state Prob evolving to current λAB Prior (epoch t-1)
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T
- y example
t-1 t
t t
VA VO VB VO’
λt λt λt λt λt-1 λt-1 λt-1 λt-1
- 1. Propose new
particles
- 2. Likelihood
given Obs and previous state
Weight particles: i. Likelihood
- ii. Evolution
- iii. Proposal
- 3. Re-sample
] | ) , Pr[(
*
V
t t
OB AB λ
λ
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In pseudocode
Take obs in all epochs Initialize particles Propose current state given
- bservation
Likelihood of
- bservation given
current and previous state Reweighting of proposal likelihood given proposal distributions Resampling to obtain new particles according to posterior All types of samples
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- How likely is an observation V* given sending
rates λ*
) ( Pois ) ( Pois ) ( Pois ) ( Pois
' OO AO O OB AB B OO OB O AO AB A
V V V V λ λ λ λ λ λ λ λ + ← + ← + ← + ←
The likelihood function
t t
VA VO VB VO’ Visible Hidde n
) | (
* * λ
V L
Prob of total volume in epoch given λ* (just Poisson) Prob of each of the rounds pab is just the probability A sent to B pab=(λAB/ λAB+ λOB) Binomial
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- Probability of λAB at t given λAB at t-1
- T
wo stages 1) Probability transitions silent-communication 2) Probability of given difgerence: mixture with heavy tails
The profjle evolution probability
) | (
1 − t AB t AB
E λ λ
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- Three datasets:
- eMail: Enron dataset ~0.5M emails, 150 users.
- Mailing list: Indymedia ~300K posts from 28237 senders to
693 lists
- Location: Gowala dataset ~6.5M checkins from ~200K users
- Parameters empirically inferred using EM
- T
wo sets
- Communication
- Silent
- Anonymity system
- 1 day delay (anonymity vs delay trade-ofg given 1 week
epochs)
- Thresholds: eMail/Mailing ~100 Location ~15K
Evaluation
Prio r silen t Transitions Stop talking Stay silent Mixtur e evoluti
- n
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- State of the art: Statistical Disclosure Attack
- Background traffjc:
- Use background to estimate volume in her rounds
- Assumes static behaviour: short and long term
Evaluation - an example trace (Avg(Batch)= 244)
messages to
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Evaluation – estimation accuracy as Squared error
Epoch Trace
MSEComm =12 84 13 3.7 K 20 83 K 0.7 2.8 0.8 1.2 2.3 K 36 MSESilent
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Evaluation – communication detection
Are Alice and Bob communicating? Base rate fallacy! Use particles distribution Use rate directly
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Conclusions
- Structured model for traffjc analysis based on known
Bayesian inference techniques
- easy to extend
- allow assessment of inference quality
- avoid base rate fallacy
- Attacks on real world traces
- can be efgective for rather low action rates
- can be efgective over a much shorter period of time than
previously thought
- can be efgective for secure confjgurations of the anonymity
system
- Rethink current evaluations and fjgures of merit
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