An Ad Omnia Approach to Defining and Achieving Private Data ...

An Ad Omnia Approach to Defining and Achieving Private Data ...

Defining and Achieving Differential Privacy Cynthia Dwork, Microsoft Meaningful Privacy Guarantees Statistical databases Medical Government Agency Social Science Searching / click stream Learn non-trivial trends while protecting privacy of individuals and fine-grained

structure Linkage Attacks Using innocuous data in one dataset to identify a record in a different dataset containing both innocuous and sensitive data At the heart of the voluminous research on hiding small cell counts in tabular data The Netflix Prize Netflix Recommends Movies to its Subscribers Offers $1,000,000 for 10% improvement in its

recommendation system Not concerned here with how this is measured Publishes training data Nearly 500,000 records, 18,000 movie titles The ratings are on a scale from 1 to 5 (integral) stars. To protect customer privacy, all personal information identifying individual customers has been removed and all customer ids have been replaced by randomlyassigned ids. The date of each rating and the title and year of release for each movie are provided. Some ratings not sensitive, some may be sensitive

OK for Netflix to know, not OK for public to know A Publicly Available Set of Movie Rankings International Movie Database (IMDb) Individuals may register for an account and rate movies Need not be anonymous Visible material includes ratings, dates, comments By definition, these ratings not sensitive The Fiction of Non-PII

Narayanan & Shmatikov 2006 Movie ratings and dates are PII With 8 movie ratings (of which we allow 2 to be completely wrong) and dates that may have a 3-day error, 96% of Netflix subscribers whose records have been released can be uniquely identified in the dataset. Linkage attack prosecuted using the IMDb. Link ratings in IMDb to (non-sensitive) ratings in Netflix, revealing sensitive ratings in Netflix

NS draw conclusions about user. May be wrong, may be right. User harmed either way. What Went Wrong? What is Personally Identifiable Information? Typically syntactic, not semantic Suppressing PII doesnt rule out linkage attacks Eg, genome sequence not considered PII ??

Famously observed by Sweeney, circa 1998 AOL debacle Need a more semantic approach to privacy Semantic Security Against an Eavesdropper Goldwasser &Micali 1982 Vocabulary Plaintext: the message to be transmitted Ciphertext: the encryption of the plaintext Auxiliary information: anything else known to attacker The ciphertext leaks no information about the

plaintext. Formalization Compare the ability of someone seeing aux and ciphertext to guess (anything about) the plaintext, to the ability of someone seeing only aux to do the same thing. Difference should be tiny. Semantic Security for Statistical Databases? Dalenius, 1977 Anything that can be learned about a respondent from the statistical database can be learned without access to the database An ad omnia guarantee

Happily, Formalizes to Semantic Security Recall: Anything about the plaintext that can be learned from the ciphertext can be learned without the ciphertext Popular Intuition: prior and posterior views about an individual shouldnt change too much. Clearly Silly My (incorrect) prior is that everyone has 2 left feet. Very popular in literature nevertheless Definitional awkwardness even when used correctly 10 Semantic Security for Statistical Databases?

Unhappily, Unachievable Cant achieve cryptographically small levels of tiny Intuition: (adversarial) user is supposed to learn unpredictable things about the DB; translates to learning more than a cryptographically tiny amount about a respondent Relax tiny? 11 Relaxed Semantic Security for Statistical Databases? Relaxing Tininess Doesnt Help

Dwork & Naor 2006 Database teaches average heights of population subgroups Terry Gross is two inches shorter than avg Lithuanian Access to DB teaches Terrys height Terrys height learnable from the DB, not learnable otherwise Formal proof extends to essentially any notion of privacy compromise, uses extracted randomness from the SDB as a one-time pad. Bad news for k-,l-,m- etc. Attack Works Even if Terry Not in DB! Suggests new notion of privacy: risk incurred by joining DB

Differential Privacy Privacy, when existence of DB is stipulated Before/After interacting vs Risk when in/notin DB Differential Privacy K gives -differential privacy if for all values of DB and Me and all transcripts t: Pr[ K (DB - Me) = t] Pr[ K (DB + Me) = t] e 1 Pr [t] 13

Differential Privacy is an Ad Omnia Guarantee No perceptible risk is incurred by joining DB. Anything adversary can do to me, it could do without Me (my data). Pr [response] Bad Responses: X X X 14 An Interactive Sanitizer: K Dwork, McSherry, Nissim, Smith 2006

f + noise ? K f: DB R K (f, DB) = f(DB) + Noise Eg, Count(P, DB) = # rows in DB with Property P 15 Sensitivity of a Function f How Much Can f(DB + Me) Exceed f(DB - Me)? Recall: K (f, DB) = f(DB) + noise Question Asks: What difference must noise obscure? f = maxDB, Me |f(DB+Me) f(DB-Me)| eg, Count = 1

16 Calibrate Noise to Sensitivity f = maxDB, Me |f(DB+Me) f(DB-Me)| Theorem: To achieve -differential privacy, use scaled symmetric noise Lap(|x|/R) with R = f/ -4R -3R -2R -R 0 R 2R 3R

4R 5R Pr[x] proportional to exp(-|x|/R) Increasing R flattens curve; more privacy Noise depends on f and not on the database 17 Calibrate Noise to Sensitivity f = maxDB, Me |f(DB+Me) f(DB-Me)| Theorem: To achieve -differential privacy, use scaled symmetric noise Lap(|x|/R) with R = f/ -4R -3R -2R -R

Pr[ K (f, DB - Me) = t] Pr[ K (f, DB + Me) = t] 0 R 2R 3R 4R 5R = exp(-(|t- f-|-|t- f+|)/R) exp(-f/R)

18 Multiple Queries For query sequence f1, , fd -privacy achieved with noise generation parameter Ri = fi/for each response. Can sometimes do better. Noise must increase with the sensitivity of the query sequence. Naively, more queries means noisier answers Dinur and Nissim 2003 et sequelae Speaks to the Non-Interactive Setting Any non-interactive solution permitting too accurate answers to too many questions is vulnerable to attack. Privacy mechanism is at an even greater disadvantage than in the interactive case; can be exploited 19 Future Work

Investigate Techniques from Robust Statistics Area of statistics devoted to coping with What are the utility questions of interest? Definitional and Algorithmic Work for Other Settings

Problem: the statistical setting makes strong assumptions about existence and nature of an underlying distribution Differential Privacy for Social Networks, Graphs Small amounts of wild data entry errors Rounding errors Limited dependence among samples Differential approach more broadly useful Several results discussed in next few hours Porous Boundary Between Inside and Outside? Outsourcing, bug reporting, combating D-DoS attacks and terror Privacy is a natural resource.

Its non-renewable, and its not yours. Conserve it.

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