Posts tagged ‘fingerprinting’

Printer Dots, Pervasive Tracking and the Transparent Society

So far in the fingerprinting series, we’ve seen how a variety of objects and physical devices [1234], often even supposedly identical ones, can be uniquely fingerprinted. This article is non-technical; it is an opinion on some philosophical questions about tracking and surveillance.

Here’s a fascinating example of tracking that’s all around you but that you’re probably unaware of:

Color laser printers and photocopiers print small yellow dots on every page for tracking purposes.

My source for this is the EFF’s Seth Schoen, who has made his presentation on the subject available.

The dots are not normally visible, but can be seen by a variety of methods such as shining a blue LED flashlight, magnification under a microscope or scanning the document with a commodity scanner. The pattern of dots typically encodes the device serial number and a timestamp; some parts of the code are yet unidentified. There are interesting differences between the codes used by different manufacturers. [1] Some examples are shown in the pictures. There’s a lot more information in the presentation.

Pattern of dots from three different printers: Epson, HP LaserJet and Canon.

Schoen says the dots could have been the result of the Secret Service pressuring printer manufacturers to cooperate, going back as far as the 1980s. The EFF’s Freedom of Information Act request on the matter from 2005 has been “mired in bureaucracy.”

The EFF as well as the Seeing Yellow project would like to see these dots gone. The EFF has consistently argued against pervasive tracking. In this article on biometric surveillance, they say:

EFF believes that perfect tracking is inimical to a free society. A society in which everyone’s actions are tracked is not, in principle, free. It may be a livable society, but would not be our society.

Eloquently stated. You don’t have to be a privacy advocate to see that there are problems with mass surveillance, especially by the State. But I’d like to ask the question: can we really hope to stave off a surveillance society forever, or are efforts like the Seeing Yellow project just buying time?

My opinion is that it impossible to put the genie back into the bottle — the cost of tracking every person, object and activity will continue to drop exponentially. I hope the present series of articles has convinced you that even if privacy advocates are successful in preventing the deployment of explicit tracking mechanisms, just about everything around you is inherently trackable. [2]

And even if we can prevent the State from setting up a surveillance infrastructure, there are undeniable commercial benefits in tracking everything that’s trackable, which means that private actors will deploy this infrastructure, as they’ve done with online tracking. If history is any indication, most people will happily allow themselves to be tracked in exchange for free or discounted services. From there it’s a simple step for the government to obtain the records of any person of interest.

If we accept that we cannot stop the invention and use of tracking technologies, what are our choices? Our best hope, I believe, is a world in which the ability to conduct tracking and surveillance is symmetrically distributed, a society in which ordinary citizens can and do turn the spotlight on those in power, keeping that power in check. On the other hand, a world in which only the government, large corporations and the rich are able to utilize these technologies, but themselves hide under a veil of secrecy, would be a true dystopia.

Another important principle is for those who do conduct tracking to be required to be transparent about it, to have social and legal processes in place to determine what uses are acceptable, and to allow opting out in contexts where that makes sense. Because ultimately what matters in terms of societal freedom is not surveillance itself, but how surveillance affects the balance of power. To be sure, the society I describe — pervasive but transparent tracking, accessible to everyone, and with limited opt-outs — would be different from ours, and would take some adjusting to, but that doesn’t make it worse than ours.

I am hardly the first to make this argument. A similar position was first prominently articulated by David Brin his 1999 book Transparent Society. What the last decade has shown is just how inevitable pervasive tracking is. For example, Brin focused too much on cameras and assumed that tracking people indoors would always be infeasible. That view seems almost quaint today.

Let me be clear: I have absolutely no beef with efforts to oppose pervasive tracking. Even if being watched all of the time is our eventual destiny, society won’t be ready for it any time soon — these changes take decades if not generations. The pace at which the industry wants us to make us switch to “living in public” is far faster than we’re capable of. Buying time is therefore extremely valuable.

That said, embracing the Transparent Society view has important consequences for civil libertarians. It suggests working toward an achievable if sub-optimal goal instead of an ideal but impossible one. It also suggests that the “democratization of surveillance” should be encouraged rather than feared.

Here are some currently hot privacy and civil-liberties issues that I think will have a significant impact on the distribution of power in a ubiquitous-surveillance society: the right to videotape on-duty police officers and other public officials, transparent government initiatives including FOIA requests, and closer to my own interests, the Do Not Track opt-out mechanism, and tools like FourthParty which have helped illuminate the dark world of online tracking.

Let me close by calling out one battle in particular. Throughout this series, we’ve seen that fingerprinting techniques have security-enhancing applications (such as forensics), as well as privacy-infringing ones, but that most research papers on fingerprinting consider only the former question. I believe the primary reason is that funding is for the most part available only for the former type of research and not for the latter. However, we need a culture of research into privacy-infringing technologies, whether funded by federal grants or otherwise, in order to achieve the goals of symmetry and transparency in tracking.

[1] Note that this is just an encoding and not encryption. The current system allows anyone to read the dots; public-key encryption would allow at least nominally restricting the decoding ability to only law-enforcement personnel, but there is no evidence that this is being done.

[2] This is analogous to the cookies-vs-fingerprinting issue in online tracking, and why cookie-blocking alone is not sufficient to escape tracking.

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October 18, 2011 at 11:35 am 5 comments

Everything Has a Fingerprint — Don’t Forget Scanners and Printers

Previous articles in this series looked at fingerprinting of blank paperdigital cameras and RFID chips. This article will discuss scanners and printers, rounding out the topic of physical-device fingerprinting.

To readers who’ve followed the series so far, it should come as no surprise that scanners can be fingerprinted, and this can be used to match an image to the device that scanned it. Scanners capture images via a process similar to digital cameras, so the underlying principle used in fingerprinting is the same: characteristic ‘pattern noise’ in the sensor array as well as idiosyncracies of the algorithms used in the post-processing pipeline. The former is device-specific whereas the latter is make/model specific.

There are two important differences, however, that make scanner fingerprinting more difficult: first, scanner sensor arrays are one-dimensional (the sensor moves along the length of the device to generate the image), which means that there is much less entropy available from sensor imperfections. Second, the paper may not be placed in the same part of the scanner bed each time, which rules out a straightforward pixel-wise comparison.

group at Purdue has been very active in this area, as well as in printer identification, which I will discuss later in this article. These two papers are very relevant for our purposes. The application they have in mind is forensics; in this context, it can be assumed that the investigator has physical possession of the scanner to generate a fingerprint against which a scanned image of unknown or uncertain origin can be tested.

To extract 1-dimensional noise from a 2-dimensional scanned image, the authors first extract 2-dimensional noise, in a process similar to what is used in camera fingerprinting, and then they collapse each noise pattern into a single row, which is the average of all the rows. Simple enough.

Dealing with the other problem, the lack of synchronicity, is trickier. There are broadly two approaches: 1. try to synchronize the image by trying various alignments 2. extract fingerprints using statistical features of the image that are robust against desynchronization. The authors use the latter approach, mainly moment-based features of the noise vector.

Here are the results. At the native resolution of scanners, 1200–4800 dpi, they were able to distinguish between 4 scanners with an average accuracy of 96%, including a pair with identical make and model. In subsequent work, they improved the feature extraction to be able to handle images that are reduced to 200 dpi, which is typically the resolution used for saving and emailing images. While they achieved 99.9% accuracy in classifying 10 scanners, they can no longer distinguish devices of identical make and model.

The authors claim that a correlation based approach — searching for the right alignment between two images, and then directly comparing the noise vectors — won’t work. I am skeptical about this claim. The fact that it hasn’t worked so far doesn’t mean it can’t be made to work. If it does work, it is likely to give far higher accuracies and be able to distinguish between a much larger number of devices.

The privacy implications of scanner fingerprinting are of an analogous nature to digital camera fingerprinting: a whistleblower exposing scanned documents may be deanonymized. However, I would judge the risk to be much lower: scanners usually aren’t personal devices, and a labeled corpus of images scanned by a particular device is typically not available to outsiders.

The Purdue group have also worked on printer identification, both laser and inkjet. In laser printers, one prominent type of observable signature arising from printer artifacts is banding — alternating light and dark horizontal bands. The bands are subtle and not noticeable to the human eye. But they are easily algorithmically detectable, constituting a 1–2% deviation from average intensity.

Fourier Transform of greyscale amplitudes of a background fill (printed with an HP LaserJet)

Banding can be demonstrated by printing a constant grey background image, scanning it, measuring the row-wise average intensities and taking the Fourier Transform of the resulting 1-dimensional vector. One such plot is shown here: the two peaks (132 and 150 cycles/inch) constitute the signature of the printer. The amount of entropy here is small — the two peak frequencies — and unsurprisingly the authors believe that the technique is good enough to distinguish between printer models but not individual printers.

Detecting banding in printed text is difficult because the power of the signal dominates the power of the noise. Instead the authors classify individual letters. By extracting a set of statistical features and applying an SVM classifier, they show that instances of the letter ‘e’ from 10 different printers can be correctly classified with an accuracy of over 90%.

Needless to say, by combining the classification results from all the ‘e’s in a typical document, they were able to match documents to printers 100% of the time in their tests. Presumably the same method would apply for all other characters, but wasn’t tested due to the additional manual effort required for different shapes.

Vertical lines printed by three different inkjet printers

Inkjet printers seem to be even more variable than laser printers; an example is shown in the picture taken from this paper. I found it a bit hard to discern exactly what the state of the art is, but I’m guessing that if it isn’t already possible to detect different printer models with essentially perfect accuracy, it will soon be.

The privacy implications of printer identification, in the context of a whistleblower who wishes to print and mail some documents anonymously, would seem to be minimal. If you’re printing from the office, printer logs (that record a history of print jobs along with user information) would probably be a more realistic threat. If you’re using a home printer, there is typically no known set of documents that came from your printer to compare against, unless law enforcement has physical possession of your printer.

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October 11, 2011 at 10:02 am 1 comment

Fingerprinting of RFID Tags and High-Tech Stalking

Previous articles in this series looked at fingerprinting of blank paper and digital cameras. This article is about fingerprinting of RFID, a domain where research has directly investigated the privacy threat, namely tracking people in public.

The principle behind RFID fingerprinting is the same as with digital cameras:

Microscopic physical irregularities due to natural structure and/or manufacturing defects cause observable, albeit tiny, behavioral differences.

The basics. First let’s get the obvious question out of the way: why are we talking about devious methods of identifying RFID chips, when the primary raison d’être of RFID is to enable unique identification? Why not just use them in the normal way?

The answer is that fingerprinting, which exploits the physical properties of RFID chips rather than their logical behavior, allows identifying them in unintended ways and in unintended contexts, and this is powerful. RFID applications, for example in e-passports or smart cards, can often be cloned at the logical level, either because there is no authentication or because authentication is broken. Fingerprinting can make the system (more) secure, since fingerprints arise from microscopic randomness and there is no known way to create a tag with a given fingerprint.

If sensor patterns in digital cameras are a relatively clean example of fingerprinting, RF (and anything to do with the electromagnetic spectrum in general) is the opposite. First, the data is an arbitrary waveform instead of an fixed-size sequence of bits. This means that a simple point-by-point comparison won’t work for fingerprint verification; the task is conceptually more similar to algorithmically comparing two faces. Second, the probe signal itself is variable. RFID chips are passive: they respond to the signal produced by the reader (and draw power from it).[1] This means that the fingerprinting system is in full control of what kind of signal to interrogate the chip with. It’s a bit like being given a blank canvas to paint on.

Techniques. A group at ETH Zurich has done some impressive work in this area. In their 2009 paper, they report being able to compare an RFID card with a stored fingerprint and determine if they are the same, with an error rate of 2.5%–4.5% depending on settings.[2] They use two types of signals to probe the chip with — “burst” and “sweep” — and extract features from the response based on the spectrum.

Chip response to different signals. Fingerprints are extracted from characteristic features of these responses.

Other papers have demonstrated different ways to generate signals/extract features. A University of Arkansas team exploited the minimum power required to get a response from the tag at various frequencies. The authors achieved a 94% true-positive rate using 50 identical tags, with only a 0.1% false-positive rate. (About 6% of the time, the algorithm didn’t produce an output.)

Yet other techniques, namely the energy and Q factor of higher harmonics were studied in a couple of papers out of NIST. In the latter work, they experimented with 20 cards which consisted of 4 batches of 5 ‘identical’ cards in each. The overall identification accuracy was 96%.

It seems safe to say that RFID fingerprinting techniques are still in their infancy, and there is much room for improvement by considering new categories of features, by combining different types of features, or by using different classification algorithms on the extracted features.

Privacy. RF fingerprinting, like other types of fingerprinting, shows a duality between security-enhancing and privacy-infringing applications, but in a less direct way.  There are two types of RFID systems: “near-field” based on inductive coupling, used in contactless smartcards and the like, and “far field” based on backscatter, used in vehicle identification, inventory control, etc. The papers discussed so far pertain to near-field systems. There are no real privacy-infringing applications of near-field RF fingerprinting, because you can’t get close enough to extract a fingerprint without the owner of the tag knowing about it. Far-field systems, to which we will now turn, are ideally suited to high-tech stalking.

Fingerprinting provides the ability to enhance the security of near-field RFID systems and to infringe privacy in the context of far-field RFID chips.

In a recent paper, the Zurich team mentioned earlier investigated the possibility of tracking a people in a shopping mall based on strategically placed sensors, assuming that shoppers have several (far-field) RFID tags on them. The point is that it is possible to design chips that prevent tracking at the logical level by authenticating the reader, but this is impossible at the physical level.

Why would people have RFID tags on them? Tags used for inventory control in stores, and not deactivated at the point-of-sale are one increasingly common possibility — they would end up in shopping bags (or even on clothes being worn, although that’s less likely). RFID tags in wallets and medical devices are another source; these are tags that the user wants to be present and functional.

What makes the tracking device the authors built powerful is that it is low-cost and can be operated surreptitiously at some distance from the victim: up to 2.75 meters, or 9 feet. They show that 5.4 bits of entropy can be extracted from a single tag, which means that 5 tags on a person gives 22 bits, easily enough to distinguish everyone who might be in a particular mall.

To assess the practical privacy risk, technological feasibility is only one dimension. We also need to ask who the adversary is and what the incentives are. Tracking people, especially shoppers, in physical space has the strongest incentive of all: selling products. While online tracking is pervasive, the majority of shopping dollars are still spent offline, and there’s still no good way to automatically identify people when they are in the vicinity in order to target offers to them. Facial recognition technology is highly error-prone and creeps people out, and that’s where RF fingerprinting comes in.

That said, RF fingerprinting is only one of the many ways of passively tracking people en masse in physical space — unintentional leaks of identifiers from smartphones and logical-layer identification of RFID tags seem more likely — but it’s probably the hardest to defend against. It is possible to disable RFID tags, but this is usually irreversible and it’s difficult to be sure you haven’t missed any. RFID jammers are another option but they are far from easy to use and are probably illegal in the U.S. One of the ETH Zurich researchers suggests tinfoil wrapping when going out shopping :-)

[1] Active RFID chips exist but most commercial systems use passive ones, and that’s what the fingerprinting research has focused on.

[2] They used a population of 50 tags, but this number is largely irrelevant since the experiment was one of binary classification rather than 1-out-of-n identification.


Thanks to Vincent Toubiana for comments on a draft.

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October 4, 2011 at 1:20 pm Leave a comment

No Two Digital Cameras Are the Same: Fingerprinting Via Sensor Noise

The previous article looked at how pieces of blank paper can be uniquely identified. This article continues the fingerprinting theme to another domain, digital cameras, and ends by speculating on the possibility of applying the technique on an Internet-wide scale.

For various kinds of devices like digital cameras and RFID chips, even supposedly identical units that come out of a manufacturing plant behave slightly differently in characteristic ways, and can therefore be distinguished based on their output or behavior. How could this be? The unifying principle is this:

Microscopic physical irregularities due to natural structure and/or manufacturing defects cause observable, albeit tiny, behavioral differences.

Digital camera identification belongs to a class of techniques that exploits ‘pattern noise’ in the ‘sensor arrays’ that capture images. The same techniques can be used to fingerprint a scanner by analyzing pixel-level patterns in the images scanned by it, but that’ll be the focus of a later article.

A long-exposure dark frame [source]. Click image to see full size. Three ‘hot pixels’ and some other sensor noise can be seen.

A photo taken in the absence of any light doesn’t look completely black; a variety of factors introduce noise. There is random noise that varies in every image, but there is also ‘pattern noise’ due to inherent structural defects or irregularities in the physical sensor array. The key property of the latter kind of noise is that it manifests the same way every image taken by the camera.[1] Thus, the total noise vector produced by a camera is not identical between images, nor is it completely independent.

The pixel-level noise components in images taken by the same camera are correlated with each other.

Nevertheless, separating the pattern noise from random noise and the image itself — after all, a good camera will seek to minimize the strength or ‘power’ of the noise in relation to the image — is a very difficult task, and is the primary technical challenge that camera fingerprinting techniques must address.

Security vs. privacy. A quick note about the applications of camera fingerprinting. We saw in the previous article that there are security-enhancing and privacy-infringing applications of document fingerprinting. In fact, this is almost always the case with fingerprinting techniques. [2]

Camera fingerprinting can be used on the one hand for detecting forgeries (e.g., photoshopped images), and to aid criminal investigations by determining who (or rather, which camera) might have taken a picture. On the other hand, it could potentially also be used for unmasking individuals who wish to disseminate photos anonymously online.

Sadly, most papers studying fingerprinting study only the former type of application, which is why we’ll have to speculate a bit on the privacy impact, even though the underlying math of fingerprinting is the same.

Most fingerprinting techniques have both security-enhancing and privacy-infringing applications. The underlying principles are the same but they are applied slightly differently.

Another point to note is that because of the focus on forensics, most of the work in this area so far has studied distinguishing different camera models. But there are some preliminary results on distinguishing ‘identical’ cameras, and it appears that the same techniques will work.

In more detail. Let’s look at what I think is the most well-known paper on sensor pattern noise fingerprinting, by Binghamton University researchers Jan Lukáš, Jessica Fridrich, and Miroslav Golja. [3] Here’s how it works: the first step is to build a reference pattern of a camera from multiple known images taken from it, so that later an unsourced image can be compared against these reference patterns. The authors suggest using at least 50, but for good measure, they use 320 in their experiments. In the forensics context, the investigator probably has physical possession of the camera and therefore can generate an unlimited number of images. We’ll discuss what this requirement means in the privacy-breach context later.

There are two steps to build the reference pattern. First, for each image, a denoising filter is applied, and the denoised image is subtracted from the original to leave only the noise. Next, the noise is averaged across all the reference images — this way the random noise cancels out and leaves the pattern noise.

Comparing a new image to a reference pattern, to test if it came from that camera, is easy: extract the noise from the test image, and compare this noise pixel-by-pixel with the reference noise. The noise from the test image includes random noise, so the match won’t be close to perfect, but nevertheless the correlation between the two noise patterns will be roughly equal to the contribution of pattern noise towards the total noise in the test image. On the other hand, if the test image didn’t come from the same camera, the correlation will be close to zero.

The authors experimented with nine cameras, of which two were from the same brand and model (Olympus Camedia C765). In addition, two other cameras had the same type of sensor. There was not a single error in their 2,700 tests, including those involving the two ‘identical’ cameras — in each case, the algorithm correctly identified which of the nine cameras a given image came from. By extrapolating the correlation curves, they conservatively estimate that for a False Accept Rate of 10-3, their method achieves a False Reject Rate of anywhere between 10-2 to 10-10 or even less depending on the camera model and camera settings.

The takeaway from this seems to be that distinguishing between cameras of different models can be performed with essentially perfect accuracy. Distinguishing between cameras of the same model also seems to have very high accuracy, but it is hard to generalize because of the small sample size.

Improvements. Impressive as the above numbers are, there are at least two major ways in which this result can, and has been improved. First, the Binghamton paper is focused on a specific signal, sensor noise. But there are several stages in image acquisition and processing pipeline in the camera, each of which could leave idiosyncratic effects on the image. This paper out of Turkey incorporates many such effects by considering all patterns of certain types that occur in the lower order (least significant) bits of the image, which seems like a rather powerful technique.

The effects other than sensor noise seem to help more with identifying the camera model than the specific device, but to the extent that the former is a component of the latter, it is useful. They achieve a 97.5% accuracy among 16 test cameras — but with cellphone cameras with pictures at a resolution of just 640×480.

Second is the effect of the scene itself on the noise. Denoising transformations are not perfect — sharp boundaries look like noise. The Binghamton researchers picked their denoising filter (a wavelet transform) to minimize this problem, but a recent paper by Chang-Tsun Li claims to do it better, and shows even better numerical results: with 6 cameras (all different models), accurate (over 99%) identification for image fragments cropped to just 256 x 512.

What does this mean for privacy? I said earlier that there is a duality between security and privacy, but let’s examine the relationship in more detail. In privacy-infringing applications like mass surveillance, the algorithm need not always produce an answer, and it can occasionally be wrong when it does. The penalty for errors is much lower. On the other hand, the matching algorithm in surveillance-like applications needs to handle a far larger number of candidate cameras. The key point is:

The parameters of fingerprinting algorithms can usually be tweaked to handle a larger number of classes (i.e., devices) at the expense of accuracy.

My intuition is that state-of-the-art techniques, configured slightly differently, should allow probabilistic deanonymization from among tens of thousands of different cameras. A Flickr or Picasa profile with a few dozen images should suffice to fingerprint a camera.[4] Combined with metadata such as location, this puts us within striking distance of Internet-scale source-camera identification from anonymous images. I really hope there will be some serious research on this question.

Finally, a word defenses. If you find yourself in a position where you wish to anonymously publicize a sensitive photograph you took, but your camera is publicly tied to your identity because you’ve previously shared pictures on social networks (and who hasn’t), how do you protect yourself?

Compressing the image is one possibility, because that destroys the ‘lower-order’ bits that fingerprinting crucially depends on. However, it would have to be way more aggressive than most camera defaults (JPEG quality factor ~60% according to one of the studies, whereas defaults are ~95%). A different strategy is rotating the image slightly in order to ‘desynchronize’ it, throwing off the fingerprint matching. An attack that defeats this will have to be much more sophisticated and will have a far higher error rate.

The deanonymization threat here is analogous to writing-style fingerprinting: there are simple defenses, albeit not foolproof, but sadly most users are unaware of the problem, let alone solutions.

[1] That was a bit simplified; mathematically, there is an additive component (dark signal nonuniformity) and a multiplicative component (photoresponse nonuniformity). The former is easy to correct for, and higher-end cameras do, but the latter isn’t.

[2] Much has been said about the tension between security and privacy at a social/legal/political level, but I’m making a relatively uncontroversial technical statement here.

[3] Fridrich is incidentally one of the pioneers of speedcubing i.e., speed-solving the Rubik’s cube.

[4] The Binghamton paper uses 320 images per camera for building a fingerprint (and recommends at least 50); the Turkey paper uses 100, and Li’s paper 50. I suspect that if more than one image taken from the unknown camera is available, then the number of reference images can be brought down by a corresponding factor.

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September 19, 2011 at 9:25 am 5 comments

Everything Has a Fingerprint: The Case of Blank Paper

This article is the first in a series that looks at “fingerprinting” techniques and the implications for privacy.

Unique-identification techniques similar to fingerprints have been applied in an astonishing variety of contexts in recent decades. Biometrics like iris and DNA profiling are well known, but there are lesser known methods like hand geometry, as well as “behavioral biometrics” like voice, handwriting, typing patterns, and even gait analysis. Many techniques for deanonymization, the principal topic of this blog, work by “fingerprinting” people’s preferences, habits, or style.

But this article is not about biometrics, nor is it about fingerprinting of content or complex systems such as a web browser in conjunction with the OS and the user.[1] I will instead discuss one of the most surprising domains of fingerprinting — blank paper.

This is what paper looks like up close — far from being smooth, it has a rich natural structure. Even considering this, the state-of-the-art study on fingerprinting of physical documents, by Will Clarkson and colleagues at Princeton, achieves something remarkable: they show how to extract fingerprints from paper using just commodity scanners, and no microscopic technology. The fingerprint survives when the document/paper is printed on, written or scribbled on, or even soaked in water.

A small (10mm tall) region of paper scanned from two different angles — top-to-bottom and left-to-right

The image above, taken from the Princeton paper, shows what the output of a scanner looks like. Not quite the resolution of the microscopic image, but a lot of structure is still visible. The key technique is: by scanning the paper at different orientations and comparing the images, the height at each point is estimated from which a 3-D map of the not-so-flat surface of the paper is constructed.

These 3-D maps can be used as fingerprints, but for efficiency they look at the maps of only about 100 randomly picked small “patches” on the paper. To further compress the extracted information, they do a “dimensionality reduction,” resulting in a 400 byte “feature vector” for each piece of paper, which is the fingerprint.

To verify or compare an observed fingerprint against a stored one, they simply look at the Hamming distance between the two bit-vectors. Why does this simple comparison technique succeed? Comparison of two human fingerprints is a lot more difficult, after all. It’s because a rectangular piece of paper has a nice property that human skin doesn’t: when the objects being fingerprinted have a precise, fixed geometry, fingerprint verification is easy — it is just a pointwise comparison of the corresponding features.

The result of such comparisons is this: two fingerprints from different pieces of paper match in roughly 50% of the bits, almost always in the 45%–55% range. Two fingerprints from the same piece of paper, on the other hand, differ in less than 5% of the bits, and occasionally up to 20% of bits if it has been handled particularly badly, such as by soaking. Therefore it is straightforward to infer whether or not two fingerprints came from the same piece of paper.

Readers familiar with the “33 bits of entropy” concept might notice that the fingerprint here is 400 bytes long, or 3200 bits, which is ridiculously high. There are surely less than 250 pieces of paper in the world — that’s a million for every person — which means that these fingerprints should easily be able to uniquely identify every piece of paper in the world. [2] The authors estimate that the chance of an error is no more than 1 in 10148. In other words, they achieve perfect accuracy.

What are the implications? As the authors point out, document identification “has a wide range of applications, including detecting forged currency and tickets, authenticating passports, and halting counterfeit goods.” On the negative side, it “could also be applied maliciously to de-anonymize printed surveys and to compromise the secrecy of paper ballots.”

[1] This is often referred to as device fingerprinting, but I find that a poor choice of terminology and will use reserve that term for a different concept in this series.

[2] It is hard to estimate entropy exactly in cases like this, but the feature vector is obtained via Principal Component Analysis, which makes it likely that the entropy is close to the maximum value of 3200 bits.

Thanks to Will Clarkson for reviewing a draft of this post.

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September 13, 2011 at 10:41 am 1 comment


I’m an associate professor of computer science at Princeton. I research (and teach) information privacy and security, and moonlight in technology policy.

This is a blog about my research on breaking data anonymization, and more broadly about information privacy, law and policy.

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