Smart Meter Privacy by sankar, Rajgopalan, Mohajer, Vincent CSE 898AB Privacy Enhancing Technologies Dr. Murtaza Jadliwala Presented by Viswa Chaitanya Kanakam

 Definition  Recent news on Smart Meter  Previous Work  Proposed Work  Related Work  Author's Contribution  Notations  Model  Utility and Privacy Metric  Privacy Preserving Mapping  Utility-Privacy Trade-off  Privacy Preserving Spectral water filling  Illustrations  Conclusion  Remark  Future Work Presentation Outline

Smart Grid Smart Meter Load Signature Libraries :- Unique consumption pattern intrinsic to each individual electrical appliance. Definitions

 2012 FBI warns smart meter Hacking may cost Utility companies $400 Million a year.  US power grid being hit with increasing Hacking Attacks as Smart Meter Deployment continues  Stuxnet-style attack on US smart grid could cost government $1 trillion Recent news about Smart Meter

 Attack is considered to be the possibility of inferring appliance usage from load data with the help of load signature libraries.  Solution :- Energy Storage Devices  Flaws :-  Is detection of usage pattern the only loss  what extent proposed solution withstand  Only assurance but no guarantees Previous Work

 Goal :- To provide a framework to accommodate both Privacy and Utility  Work:- To decouple the collected data from the personal actions of consumer.  Model :- A formal framework is designed for smart meter time-series data and metrics for utility and privacy of data. A hidden Markov model is proposed on that describing states of appliances which is in turn modelled as real valued correlated Gaussian random Variables Proposed Work

 Trusted escrow Service  Neighbourhood-level aggregation  Differential Privacy over aggregate queries  NILL to mask NALM Related Work

 Notations:-  H k,j – Random Variables.  h k,j – Random Variable realizations (observed values).  X n – n-length vector.  X – Matrix (I - Identity matrix).  N(µ n, ∑) – n variable real Gaussian distribution with mean µ n and covariance ∑.  (x) + -- max(x,0)  I(.;.) – Mutual Information  h(.) – Differential Entropy Author's Work

 M be the total number of appliances in the residency  Each device has two states (On/Off), so 2 M state appliance are possible at a time instant.  S(K) = { 0,1, ….., 2 M-1 } is state variable at k th time instant  X(k) is the meter measurement variable at k th time instant. Model

A Hidden Markov Model(HMM) is observed between the state and measurement X k-1 – S(k) – X(k) forms a Markov chain S(k) – S(k-1) – S k-1 forms a Markov chain HMM is characterized by the following parameters  Initial state distribution  State transition matrix  Conditional distribution

Observations of HMM in this model reveal that:- State S remains unchanged for a continuous period of time In that time, each appliance that is in ON state generates a sequence of random measurement characteristic of appliance Author assumes that when an appliance is in the ONstate, its power consumption pattern is approximately Gaussian.

State S can have both continuous and intermittent appliance S = (S i, S c ) G n c (S c ) and G n i (S i ) denote the length n Gaussian distributed time sequence for states S c and S i respectively which are independent of each other. Length n is chosen such that the memory effects of each state are contained within the sequence.

Measurements in Vector Notation as:- X n (S)= G n c (S c ) + G n i (S i )+ Z n Z n is a Gaussian noise vector The covariance matrix R x of X n (S) is a Toeplitz matrix with autocorrelation entries. {E} n j,k=1 = [R x (|j-k| mod n)] j,k=1 n which is non zero for all k<=m<n This circular n-block correlated sequence is decomposed into n independent Gaussian measurements subject to same distortion and leakage constraints using Discrete Fourier Transform (T is a DFT matrix)

 Data is captured as a sequence of n load measurements and compressed to transmit over finite channel  Compressed data should be perturbed in such a way it still holds desired level of fidelity  Utility metric proposed is an average distance distortion function between original and perturbed data.  Privacy metric measures the difficulty of inferring private information leaked by the appliance state via meter measurements  The privacy loss is quantified as a result of revealing perturbed data via the mutual information between the two data sequences Utility and Privacy Metrics

 Hard to transmit the measured data over the limited bandwidth hence mapping is done into a quantized sequence  Privacy-preserving mapping also needs to ensure that a minimal amount of information can be inferred about the personal habits of consumer.  Encoding :- F E : x n (s) → M = {1,2, ….., 2 n,R }  Decoding :- F D : M → x^ n  Distortion Leakage Privacy Preserving Mapping

 Utility-privacy trade-off region T is set of all pairs (D,L) to which a coding scheme satisfying the distortion and leakage functions.  The classical rate-distortion theory, constraint is on the number M of encoded sequences such that the rate I bits per entry of the sequence is bounded as M ≤ 2 n(R+€).  The aim then is to determine the infimum R(D) of all rates that are achievable for a desired distortion D.  Minimize the number of correlated sequence leaked from the revealed sequence X ^n  This paper focus on leakage constraint and not the rate constraint due to tractability Utility-Privacy Trade-off Region

If an additional constraint on minimizing the encoding rate is included, the minimal achievable rate for a desired distortion is The revealed measurements leak information about the appliance state which in turn can lead to a significant set of inferences, model focus directly on problem of minimizing the leakage of specific states via the revealed data.

 Suppressing specific appliance signatures requires detection of the appliance states in the meter by using an external algorithm.  Intermittent signals are the once that can be the source for revealing personal data, thus aim is to minimize the leakage. Privacy Preserving Spectral Water- filling

The first term in min function is for the non-negative leakage and the second term is a result of optimization, is lagrangian variable satisfying distortion constraint, it Is viewed as a waterlevel such that only that portion of the spectrum is revealed which is strictly above than this. The minimal Leakage is given as

Where

Illustrations  It models the continues and intermittent appliance load sequences in Gauss-Markov processes with an auto-correlation function given by The power spectral density of this process is

 The framework proposed allows to quantify the utility –privacy trade-off in smart meter.  This model captures dynamic nature of appliance states and smooth continual nature of the measurements via a hidden markov model and Gaussian measures.  The distortion acts as a filter in suppressing the intermittent appliance signal i.e. signals which are less than certain threshold Conclusion

 This model focus on only data loss through intermittent appliance signals but did not provide the data loss through power consumption variability by non-intermittent appliances Remark

 Applying the model on measured data to validate whether filter eliminates signatures of intermittent devices to desired degree,  Apply and demonstrate the power of these concepts in a practical context  Develop a appliance-agnostic privacy-guarantees based on detecting changes in energy patterns that are characteristic of personal habits Future Work

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