MaskIt: Privately Releasing User Context Streams for Personalized Mobile Applications SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data

Background  Not just location.  More sensors means more privacy can be detected.

Background  User’s contexts have correlation with former context.  Some contexts are not sensitive.

Solution  System Model  x 1, x 2,…, x t o 1, o 2,…, o t  To compute o t, MASKIT employs a check deciding whether to release or suppress the current context.

Solution  Propose MASKIT: a system that decide whether to release or to suppress the current state of the use.  Probabilistic check: flips for each context a coin is chosen suitably to guarantee privacy.  Simulatable check: makes the decision only based on the released contexts so far and completely ignores the current context.  Explain how to select the better check.

Problem Statement  Utility Goal  Release as many states as possible, while satisfying the privacy goal.  The MASKIT System

Problem  What is privacy?  To preserve privacy:  When context should be suppressed?  What context should be suppressed?  How to ensure utility?

Privacy  Privacy  DEFINITION 1: We say that a system A preserves -privacy against an adversary if for all possible inputs sampled from the Markov chain M with non-zero probability, for all possible outputs, for all times t and all sensitive contexts

Utility  Measure utility as the expected number of released context: for state c i at time t’ a suppression probability

Probabilistic Privacy Check

 Prior belief:  suppression probability p i t at time t for state c i, the prior belief is 1- p i t  Posterior belief:  HMM Forward procedure Backward procedure

Probabilistic Privacy Check  Utility ：  For vectors passing the check we can compute their utility  Return the one with the maximum utility  Efficiency  Use algorithms to speeding up IsPrivate & SearchAlgorithm

Simulatable Privacy Check  Only based on information available to the adversary:  The Markov chain M  Output sequence  Posterior belief  t1: last time before or at t at which a context was released  t2: earliest time after t at which a context was released  t2: end state if t2 does not exist

Simulatable Privacy Check

 Privacy :

Simulatable Privacy Check  Utility:  The simulatable check is locally optimal in the sense that if the next state is published despite the indication of the privacy check to suppress it (improving the utility) then there is a chance that future states will inevitably breach privacy.  Efficiency  Speeding up okayToRelease

Comparative Analysis Weakness of the simulatable check: It makes the suppression decision without looking at the current state. Weakness of the probabilistic check: Its decision ignores the previously released states.

Comparative Analysis  Hybrid Privacy Check:  Probabilistic check  Simulatable check Using supp i (t) we can compute recursively the expected number of suppressions following the release of X t = c i utility Simulatable (M) = T - expected number

Limited Background Knowledge  Weak adversary:  Knowing the Frequency of sensitive contexts  Knowing a Set-Labeled chain

Experiment  Continuous data on daily activities of 100 students and staff at MIT.  For each user, we train a Markov chain on the first half of his trace; the remaining half is used to for evaluation.  This paper only use location data.

Experiment  Efficiency

Experiments  Compare MASKIT using:  The simulatable check  The probabilistic check (with a granularity of d = 10)  The hybrid check with the naive approach, called MaskSensitive

Experiments

Thank you!

Problem Statement  User Model  User’s behaves like a sample from a Markov chain M  The states in M are labeled with contexts {c 1,…,c n }  Each day, the user starts at the “start” state in M and ends T steps later in the “end” state  X 1,…,X T : random variables generated from M, each taking on the value of some context c i  The independence property of Markov chains states that

Problem Statement  Adversary Model  Strong Adversary: know the Markov chain M of a user.  Week Adversary: have less knowledge about M,but they can learn more about M over time.  can access the full output sequence generated by a general suppression system A, and we assume the adversaries also know A.  adversaries have a prior belief about the user being in context ci at time t.

Problem Statement  Preliminaries: Markov chains  Markovian process with transition matrices A (1),…, A (T+1) :  PROPOSITION 1: The prior belief of an adversary about the user being in a sensitive context s at time t is equal to  The joint probability of a sequence of states is:  The probability of transitioning from state c i at time t 1 to state c j at time t 2 e i is the unit vector that is 1 at position i and 0 otherwise

Problem Statement  Preliminaries: Hidden Markov Models  Hidden Markov models help us understand how adversaries make inference about suppressed states.  Each state has a distribution over possible outputs from a set K = {k 1,…,k m }.  Define emission matrices B(t) as:  For a given output sequence, we compute the conditional probability that at tine t the hidden state was c i :

Problem Statement  Preliminaries: Hidden Markov Models  Use the forward procedure and the backward procedure to compute this ratio efficiently :  Initialize  Initialize, put everything together: