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Plan today
• An introduction to differential privacy

What to do?
“The future of privacy is lying” – (April 10 2013, , )

A Simple Example
• Negative data survey – ask people to lie, and then make inferences based on the aggregate answers

Warm up

Negative data surveys
• Participants select a choice that does not fit their situation
• Providing more choices provides more privacy
• May be challenging to design appropriate questions
• Reliance on honesty of the respondents
• This is an example of a local type of privacy, each person responsible for adding noise to their data

Differential privacy: Local and global
•
•
•
Global: We have a sensitive dataset, a trusted data owner Alice and a researcher Bob. Alice does analysis on the raw data, adds noise to the answers, and reports the (noisy) answers to : Each person is responsible for adding noise to their own data. Classic survey example each person has to answer question “Do you use drugs?”
• They flip a coin in secret and answer “Yes” if it comes up heads, but tell the truth otherwise.
• Plausible deniability about a “Yes” answer
We will next be looking further at the global case (global systems generally more accurate,
and less noise is needed)

Differential privacy: Where?
• Since its introduction in 2006:
– US Census Bureau in 2012: On The Map project
• Where people are employed and where they live
– Apple in 2016: iOS 10
• User data collection, e.g. for emoji suggestions
• https://images.apple.com/privacy/docs/Differential_Privac y_Overview.pdf
– NSW Department of Transport open release of 2016 Opal ticketing system data
• https://opendata.transport.nsw.gov.au/sites/default/files/r esources/Open%20Opal%20Data%20Documentation%2 0170728.pdf

Global differential privacy: Our focus
k-anonymity l-diversity
Privatizing
Public
Differential privacy
Privatized Analysis
Public
Original Data
Anonymous Data
Original Data
Results

What is being protected?
• Imagine a survey is asking you: – Are you a smoker?
• Result: Number of smokers will be reported Would you take part in it?
ID
Age
Sex
Smoker
sdhj5vbg
20
Male
False
wu234u4
25
Female
True
hi384yrh
17
Female
False
po92okwj
50
Male
False

What is being protected?
I would feel safe submitting the survey if:
I know the chance that the privatized result would be 𝑹 is nearly the same, whether or not I take part in the survey.
• Does this mean that an individual’s answer has no impact on the released result?

Overview of the process: Global differential privacy
Original Data
Privatized Analysis
Public
Results
• The privatized analysis comprises two steps:
– Querythedataandobtaintherealresult,e.g.,howmany female students are in the survey?
– Add random noise to hide the presence/absence of any individual. Release noisy result to the user.
Query
Doriginal
Rreal
Noise
Rreleased

The released results will be different each time (different amount of noised added)
• Query: How many females in the dataset? (true result = 32)
• Generate some random values, according to a distribution with
mean value 0: {1,2,-2,-1,0,-3,1,0}, add to true result and release
– 1st query: Released result=33 (32+1)
– 2nd query: Released result=34 (32+2)
– 3rd query:
– 4th query:
– 5th query:
– 6th query:
– 7th query:
– 8th query: –…
Released result=30 (32-2) Released result=31 (32-1) Released result=32 (32+0) Released result=29 (32-3) Released result=33 (32+1) Released result=32 (32,0)
• On average, the released result will be 32, but observing a single released result doesn’t give the adversary exact knowledge

Emoji scenario and use of differential privacy
• A developer wants to understand which emoji’s are popular, in ordertomakebetterrecommendations. Thereisadatabase like
• Query from developer: How many times was 🥺used today?
• System will release a noisy result to developer, to protect customer privacy
User
Emoji used today
Bob
😀
Alice
🥺
Sarah
🥺
Rudolph
😫
Cameron
🥺

The promise of differential privacy
• The chance that the noisy released result will be 𝑅is nearly the same, whether or not an individual participates in the dataset.
R
A=Probability that result is R
B=Probability that result is R
Possible world where I Possible world where I
participate do not participate
• If we can guarantee A≅B (A is very close to B), then no one can guess which possible world resulted in R.

The promise of differential privacy
• Does this mean that the attacker cannot learn anything sensitive about individuals from the released results?

Differential privacy: How?
• How much noise should we add to the result? This depends on – Privacy loss budget: How private we want the result to be
(how hard for the attacker to guess the true result)
– Globalsensitivity:Howmuchdifferencethepresenceor absence of an individual could make to the result.

Global sensitivity
• Global sensitivity of a query Q is the maximum difference in answers that adding or removing any individual from the dataset can cause (maximum effect of an individual)
• Intuitively, we want to consider the worst case scenario
• If asking multiple queries, global sensitivity is equal to the sum of the differences

Global sensitivity
• QUERY: How many people in the dataset are female? Global sensitivity = 1
X+1 people are female
X people are female
Possible world where I Possible world where I
participate do not participate

Global sensitivity
• QUERY: How many people in the dataset are smokers? Global sensitivity = 1
X+1 people are smokers
X people are smokers
Possible world where I Possible world where I
participate do not participate

Global sensitivity
• QUERY: How many people in the dataset are female? And how many people are smokers?
Global sensitivity = 1+1=2
X+1 people are smokers M+1 males and F females OR
M males and F+1 females
X people are smokers M males and F females
Possible world where I Possible world where I
participate do not participate

Privacy loss budget = k
• We want that the presence or absence of a user in the dataset does not have a considerable effect on the released result
R
A=Probability that result is R
Possible world where I
participate
Privacy loss budget = k (k ≥ 0) ChoosektoguaranteethatA≤2k× B
B=Probability that result is R
Possible world where I
do not participate

Privacy loss budget = k
A=Probability that result is R
Possible world where I
participate
B=Probability that result is R
Privacy loss budget=k (k ≥0) ChoosektoguaranteethatA≤2k× B
• k=0: No privacy loss (A=B), low utility
• k=high: Larger privacy loss, higher utility
• k=low: Low privacy loss, lower utility
R
Possible world where I
do not participate

Differential privacy: How?
• How much noise should we add to the result? This depends on
– Privacy loss budget (k): How private we want the result to be (how hard for the attacker to guess the true result)
– Globalsensitivity(G):Howmuchdifferencethepresence of absence of an individual could make to the result.
• Strategy: Add noise to the result according to
– Releasedresult=Trueresult+noise
• Where noise is a number randomly sampled from a distribution having
– averagevalue=0(μ)
– standarddeviation(spread)=G/k(b)
• Details about the distribution are beyond the scope of our study (it is called the Laplace distribution)

Example Code

Example

Summary
• Differential privacy guarantees that the presence or absence of a user cannot be revealed after releasing the query result
– It does not prevent attackers from drawing conclusions about individuals from the aggregate results over the population
• We need to determine the budget and global sensitivity to know what is the scale of the noise to be added

Summary
• Differential privacy guarantees that the presence or absence of a user cannot be revealed after releasing the query result
– It does not prevent attackers from drawing conclusions about individuals from the aggregate results over the population
• We need to determine the budget and global sensitivity to know what is the scale of the noise to be added