Query, then deidentify

Suppose you have a database of personally identifiable information (PII) and you want to allow someone else to query the data while protecting the privacy of the individuals represented by the data. There are two approaches:

  1. Deidentify, then query
  2. Query, then deidentify

The first approach is to do whatever is necessary to deidentify the data—remove some fields, truncate or randomize others, etc.—and then pose a query to this redacted data.

The second approach is to query the original data, then do whatever is necessary to deidentify the results.

In graphical terms, you can get from raw data to a deidentified result either by following the green arrows or the blue arrows below. In mathematical terms, this diagram does not commute.

The first approach is most common. A company that owns data (a “covered entity” in HIPAA terms) will deidentify it and license it to another company who then queries it. The second approach is becoming more common, where a company will license access to querying their data.

Pros and cons

Which approach is better? If by better you mean more accurate results, it’s always best to query first then deidentify. The order in which you do things matters, and deidentifying as late as possible preserves information.

The situation is analogous to carrying out a sequence of steps on a calculator. If you want your final result to be accurate to two decimal places, you first carry out all your operations to as much precision as you can, then round the final result. If you round your numbers first, you probably will get less accurate results, maybe even useless results.

However, deidentifying data before querying it is better in some non-mathematical ways. Data scientists want the convenience of working with the data with their tools in their environment. They want to possess (a deidentified version of) the data rather than have access to query the (exact) data. They also want the freedom to run ad hoc queries [1].

There are logistical and legal details to work out in order to license access to query data rather than licensing the data. But it is doable, and companies are doing it.

Why query first

When you deidentify data first, you have to guard against every possible use of the data. But when you deidentify data last, you only have to guard against the actual use of the data.

For example, suppose you are considering creating a new clinic and you would like to know how many patients of a certain type live closer to the location you have in mind than the nearest alternative. A data vendor cannot give you exact locations of patients. If they were to release such data, they’d have to obscure the addresses somehow, such as giving you the first three digits of zip codes rather than full addresses. But if you could ask your query of someone holding the full data, they may tell you exactly what you want to know.

Some queries may pose no privacy risk, and the data holder can return exact results. Or they may need to jitter the result a bit in order to protect privacy, for reasons explained here. But it’s better to jitter an exact result than to jitter your data before computing.

How to query first

The query-first approach requires a trusted party to hold the unredacted data. There are a variety of ways the data holder can license access, from simple to sophisticated, and in between.

The simplest approach would be for the data holder to sell reports. Maybe the data holder offers a predetermined set of reports, or maybe they allow requests.

The most sophisticated approach would be to use differential privacy. Clients are allowed to pose any query they wish, and a query manager automatically adds an amount of randomness to the results in proportion to the sensitivity of the query. All this is done automatically according to a mathematical model of privacy with no need for anyone to decide a priori which queries will be allowed.

There are approaches conceptually between pre-determined reports and differential privacy, offering more flexibility than the former and being easier to implement than the latter. There’s a lot of room for creativity in this space.

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[1] Being able to run ad hoc queries with no privacy budget is certainly simpler, in the same way that an all-you-can-eat buffet is simpler than ordering food à la carte. But it also means the price is higher. Deidentifying an entire data set entails more loss of accuracy that deidentifying a set of queries.

What can you learn from a credit card number?

The first 4 to 6 digits of a credit card number are the bank identification number or BIN. The information needed to decode a BIN is publicly available, with some effort, and so anyone could tell from a credit card number what institution issued it, what bank it draws on, whether its a personal or business card, etc.

Suppose your credit card number was exposed in a data breach. Someone makes a suspicious purchase with your card, the issuer contacts you, you cancel the card, and you get a new card from the same source. The number can no longer be used to make purchases on your account, but what information did it leave behind?

The cancelled number might tell someone where you used to bank, which is probably where you still bank. And it may tell them the first few digits of your new card since the new card is issued by the same institution [1]. If the old BIN doesn’t directly reveal your new BIN, it at least narrows down the possibilities.

The information in your BIN, by itself, will not identify you, but it does provide clues that might lead to identifying you when combined with other information.

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[1] According to Andrew in the comments, American Express often changes credit card numbers as little as possible when issuing a replacement, changing only one content digit and the checksum.

First names and Bayes’ theorem

Is the woman in this photograph more likely to be named Esther or Caitlin?

black and white photo of an elderly woman

Yesterday Mark Jason Dominus published wrote about statistics on first names in the US from 1960 to 2021. For each year and state, the data tell how many boys and girls were given each name.

Reading the data “forward” you could ask, for example, how common was it for girls born in 1960 to be named Paula. Reading the data “backward” you could ask how likely it is that a woman named Paula was born in 1960.

We do this intuitively. When you hear a name like Blanche you may think of an elderly woman because the name is uncommon now (in the US) but was more common in the past. Sometimes we get a bimodal distribution. Olivia, for example, has made a comeback. If you hear that a female is named Olivia, she’s probably not middle aged. She’s more likely to be in school or retired than to be a soccer mom.

Bayes’ theorem tells us how to turn probabilities around. We could go through Mark’s data and compute the probabilities in reverse. We could quantify the probability that a woman named Paula was born in the 1960s, for example, by adding up the probabilities that she was born in 1960, 1961, …, 1969.

Bayes theorem says

P(age | name) = P(name | age) P(age) / P(name).

Here the vertical bar separates the thing we want the probability of from the thing we assume. P(age | name), for example, is the probability of a particular age, given a particular name.

There is no bar in the probability in the denominator above. P(name) is the overall probability of a particular name, regardless of age.

People very often get probabilities backward; they need Bayes theorem to turn them around. A particular case of this is the prosecutor’s fallacy. In a court of law, the probability of a bit of evidence given that someone is guilty is irrelevant. What matters is the probability that they are guilty given the evidence.

In a paternity case, we don’t need to know the probability of someone having a particular genetic marker given that a certain man is or is not their father. We want to know the probability that a certain man is the father, given that someone has a particular genetic marker. The former probability is not what we’re after, but it is useful information to stick into Bayes’ theorem.

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Photo by Todd Cravens on Unsplash.

Identifiable to man or machine?

Like the previous post, this post riffs on a photo [1] I stumbled on while looking for something else.

Would it be easier to identify the man in this photo or the man whose photo appeared in the previous post, copied below.

I think it would be easier for a human to recognize the person in the first image. But what about a computer?

We humans identify people most easily by their faces, and especially by their eyes. These features are easier to see in the first photo. But what might we find if we applied some image processing to the two photos? Maybe the green man’s facial features could be exposed by some diligent processing. We see more of the second man’s body. Maybe a computer algorithm could extract more information out of the second image for this reason.

Photographs may, and often do, contain Exif (Exchangeable image file format) metadata, such as the GPS coordinates of the camera at the time the photo was taken. A photo taken when the lens cap on by mistake might contain a good deal of information about the subject even though the photo per se is useless. This information can be useful to the photographer, but it could also pose a privacy risk. Before posting a photo publicly, you might want to strip out the metadata.

As I noted in the previous post, the privacy risk from data depends on context. Suppose the metadata embedded in a photo contains the serial number of the camera. That serial number would not help most people identify a photo(grapher), but it would someone who had access to a database linking serial numbers to the customers who purchased the cameras.

Was the first photo created by actually projecting the red and green lights onto the subject, or were these added in post production? For that matter, was there actually a man who posed for the photo or was the image synthetically generated? A forensic investigation of the photo might be able to answer these questions.

[1] Photo by Sebastian Mark on Unsplash

Privacy and tomography

I ran across the image below [1] when I was searching for something else, and it made me think of a few issues in data privacy.

green grid of light on young man

The green lights cut across the man’s body like tomographic imaging. No one of these green lines would be identifiable, but maybe the combination of the lines is.

We can tell it’s a young man in the image, someone in good shape. But is this image identifiable?

It’s identifiable to the photographer. It’s identifiable to the person in the photo.

If hundreds of men were photographed under similar circumstances, and we knew who those men were, we could probably determine which of them is in this particular photo.

The identifiability of the photo depends on context. The HIPAA Privacy Rule acknowledges that the risk of identification of individuals in a data set depends on who is receiving the data and what information the recipient could reasonably combine the data with. The NSA could probably tell who the person in the photo is; I cannot.

Making photographs like this available is not a good idea if you want to protect privacy, even if its debatable whether the person in the photo can be identified. Other people photographed under the same circumstances might be easier to identify.

Differential privacy takes a more conservative approach. Differential privacy advocates argue that deidentification procedures should not depend on what the recipient knows. We can never be certain what another person does or doesn’t know, or what they might come to know in the future.

Conventional approaches to privacy consider some data more identifiable than other data. Your phone number and your lab test results from a particular time and place are both unique, but the former is readily available public information and the latter is not. Differential privacy purists would say both kinds of data should be treated identically. A Bayesian approach might be to say we need to multiply each risk by a prior probability: the probability of an intruder looking up your phone number is substantially greater than the probability of the intruder accessing your medical records.

Some differential privacy practitioners make compromises, agreeing that not all data is equally sensitive. Purists decry this as irresponsible. But if the only alternatives are pure differential privacy and traditional approaches, many clients will choose the latter, even though an impure approach to differential privacy would have provided better privacy protection.

[1] Photo by Caspian Dahlström on Unsplash

Privacy implications of hashing data

Cryptographic hash functions are also known as one-way functions because given an input x, one can easily compute its hashed value f(x), but it is impractical to recover x from knowing f(x).

However, if we know that x comes from a small universe of possible values, our one-way function can effectively become a two-way function, i.e. it may be possible to start with f(x) and recover x using a rainbow table attack.

It’s possible to defend against a rainbow attack yet still leak information about the probability distribution of values of x given f(x).

For privacy protection, hashing is better than not hashing. Keyed hashing is better than unkeyed hashing. But even keyed hashing can leak information.

Rainbow tables

Suppose a data set contains SHA-256 hashed values of US Social Security Numbers (SSNs). Since SSNs have 10 digits, there are 10 billion possible SSNs. It would be possible to hash all possible SSNs and create a lookup table, known as a rainbow table. There are three things that make the rainbow table attack possible in this example:

  1. The range of possible inputs is known and relatively small.
  2. The hashing algorithm is known.
  3. The hashing algorithm can be computed quickly.

There are a couple ways to thwart a rainbow table attack. Assuming we have no control of (1) above, we can alter (2) or (3).

Keyed hashing

A way to alter (2) is to use a keyed hash algorithm. For example, if we XOR the SSNs with a key before applying SHA-256, an attacker cannot construct a rainbow table without knowing the key. The attacker may know the core hash algorithm we are using, but they do not know the entire algorithm because the key is part of the algorithm.

Expensive hashing

A way to alter (3) is to use hashing algorithms that are expensive to compute, such as Argon2. The idea is that such hash functions can be computed quickly enough for legitimate use cases, but not for brute-force attacks.

The time required to create a rainbow table is the product of the time to compute a single hash and the size of the set of possible inputs. If it took an hour to compute a hash value, but there are only 10 possible values, then an attacker could compute a rainbow table in 10 hours.

Leaking attribute probabilities

Now suppose we’re using a keyed hashing algorithm. Maybe we’re paranoid and use an expensive hashing algorithm on top of that. What can go wrong now?

If we’re hashing values that each appear one time then we’re OK. If we apply a keyed hash to primary keys in a database, such as patient ID, then the hashed ID does not reveal the patient ID. But if we hash attributes associated with that patient ID, things are different.

Frequency analysis

Suppose US state is an attribute in your database, and you hash this value. No matter how secure and how expensive your hash algorithm is, each state will have a unique hash value. If the database contains a geographically representative sample of the US population, then the hashed state value that appears most often is probably the most populous state, i.e. California. The second most common hashed state value probably corresponds to Texas.

Things are fuzzier on the low end. The hashed state value appearing least often may not correspond to Wyoming, but it very likely does not correspond to Florida, for example.

In short, you can infer the state values using the same kind of frequency analysis you’d use to solve a simple substitution cipher in a cryptogram puzzle. The larger the data set, the more closely the empirical order will likely align with the population order.

Maybe this is OK?

Frequency analysis makes it possible to infer (with some uncertainty) the most common values. But the most common values are also the least informative. Knowing someone is from California narrows down their identity less than knowing that they are from Wyoming.

Frequency analysis is less specific for less common values. It might not tell you with much confidence that someone is from Wyoming, but it might tell you with some confidence that they come from a low-population state. However, since there are several low-population states, knowing someone is from such a state, without knowing which particular state, isn’t so informative.

Data privacy depends on context. Knowing what state someone is likely from may or may not be a problem depending on what other information is available.

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“We won’t sell your personal data, but …”

When a company promises not to sell your personal data, this promise alone doesn’t mean much.

“We will not sell your personal data, but …

  • We might get hacked.
  • We might give it to a law enforcement or intelligence agency.
  • We might share or trade your data without technically selling it.
  • We might alter our terms. Pray we do not alter them any further.
  • We might be acquired by a new company that alters the terms.
  • We might go bankrupt and the data be sold as an asset.”


(This post started as a Twitter thread. Thanks to Michael Madden for his contribution to the thread.)

Sharing data without letting it go

Sharing data

Suppose two companies would like to share data, but they’d also each like to retain ownership of their own data. They’d like to enable querying as if each company had given the other all its data, without actually letting go of its data.

Maybe the two companies are competitors who want to collaborate for a particular project. Or maybe the companies each have data that they are not legally allowed to share with the other. Maybe one company is interested in buying (the data of) the other and would like to have some sort of preview of what they may be buying.

Differential privacy makes this possible, and can be useful even if privacy is not an issue. The two companies have data on inanimate widgets, not persons, and yet they have privacy-like concerns. They don’t want to hand over row-level data about their widgets, and yet they both want to be able to pose questions about the combined widget data. The situation is analogous to being concerned about the “privacy” of the widgets.

Both companies would deposit data with a trusted third party, and gain access to this data via an API that implements differential privacy. Such APIs let users pose queries but do not allow either side to request row-level data.

How is this possible? What if one party poses a query that unexpectedly turns out to be asking for row-level data? For example, maybe someone asks for the average net worth of customers in Alaska, assuming there are hundreds of such customers, but the data only contains one customer in Alaska. What was intended to be an aggregate query turns out to be a row-level query.

Differential privacy handles this sort of thing automatically. It adds an amount of random noise to each query in proportion to how sensitive the query is. If you ask for what amounts to data about an individual person (or individual widget) the system will add enough noise to the result to prevent revealing row-level information. (The system may also refuse to answer the query; this is done more often in practice than in theory.) But if you ask a question that reveals very little information about a single database row, the amount of noise added will be negligible.

The degree of collaboration can be limited up front by setting a privacy budget for each company. (Again, we may not necessarily be talking about the privacy of people. We may be looking at analogous protections on units of information about physical things, such as results of destructive testing of expensive hardware.)

Someone could estimate at the start of the collaboration how large the privacy budget would need to be to allow both companies to satisfy their objectives without being so large as to risk giving away intellectual property that the parties do not wish to exchange. This budget would be spent over the course of the project. When the parties exhaust their privacy budgets, they can discuss whether to allow each other more query budget.

This arrangement allows both parties the ability to ask questions of the combined data as if they had exchanged data. However, neither party has given up control of its data. They have given each other some level of information inferred from the combined data, but neither gives a single row of data to the other.

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Conspicuously missing data

I was working on a report for a client this afternoon when I remembered this comic from Spiked Math.

Waitress: Does everyone want a beer? Logician 1: I don't know. Logician 2: I don't know. Logician 3: Yes!

I needed to illustrate the point that revealing information about one person or group can reveal information on other people or other groups. If you give your genetic information to a company, for example, you also give that company (and every entity they share your data with) information about your relatives.

This comic doesn’t illustrate the point I had in mind, but it does illustrate a related point. The third logician didn’t reveal the preferences of the first two, though it looks like that at first. Actually, the first two implicitly reported their own preferences.

If the first logician did not want a beer, he or she could have said “No” to the question “Does everyone want a beer?” Answering this question with “I don’t know” is tantamount to answering the question “Do you want a beer?” with “Yes.” What appears to be a non-committal answer is a definite answer on closer examination.

One of the Safe Harbor provisions under HIPAA is that data may not contain sparsely populated three-digit zip codes. Sometimes databases will replace sparse zip codes with nulls. But if the same database reports a person’s state, and the state only has one sparse zip code, then the data effectively lists all zip codes. Here the suppressed zip code is conspicuous by its absence. The null value itself didn’t reveal the zip code, nor did the state, but the combination did.

A naive approach to removing sensitive data can be about as effective as bleeping out profanity: it’s not hard to infer what was removed.

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Why target ads at pregnant women

I’m listening to a podcast interviewing Neil Richards, the author of Why Privacy Matters. Richards makes a couple interesting points about the infamous example of Target figuring out which women were pregnant based on their purchase history.

First, pregnancy is a point at which women are open to trying new things. So if a company can get a woman to buy a baby stroller at their store, they may be able to get her to remain a customer for years to come. (Richards mentioned going off to college as another such milestone, so a barrage of advertising is aimed at first-year college students.)

Second, women understandably freaked-out over the targeted ads. So Target hid the ads in with irrelevant ads. They might show a woman ads for lawnmowers and baby wipes. That way the baby wipe ads didn’t seem so on-the-nose. The target audience would see the ad without feeling like they’re being targeted.

Just to be clear, I’m not writing this post to offer how-to advice for doing creepy advertising. The info here is presumably common knowledge in the advertising industry, but it’s not common knowledge for the public.