Lowen and I just received word of acceptance of our recent work to ISIT. This papers asks whether you can build a universal fuzzy extractor for all high fuzzy min-entropy distributions. That is, can we have one construction that always just works. Unfortunately, the answer is negative. It is possible to artificially construct families of distributions that are impossible to simultaneously secure. This paper shares a lot of techniques with prior work of myself, Reyzin, and Smith. Excited to talk about these techniques more with the information theory community!

# key derivation

# FPGA Implementation of a Cryptographically-Secure PUF Based on Learning Parity with Noise

Published in MDPI Cryptography

Joint Work with Chenglu, Charles, Ling, Ha, Srini, and Marten.

Abstract: Herder et al. (IEEE Transactions on Dependable and Secure Computing, 2017) designed a new computational fuzzy extractor and physical unclonable function (PUF) challenge-response protocol based on the Learning Parity with Noise (LPN) problem. The protocol requires no irreversible state updates on the PUFs for security, like burning irreversible fuses, and can correct for significant measurement noise when compared to PUFs using a conventional (information theoretical secure) fuzzy extractor. However, Herder et al. did not implement their protocol. In this paper, we give the first implementation of a challenge response protocol based on computational fuzzy extractors. Our main insight is that “confidence information” does not need to be kept private, if the noise vector is independent of the confidence information, e.g., the bits generated by ring oscillator pairs which are physically placed close to each other. This leads to a construction which is a simplified version of the design of Herder et al. (also building on a ring oscillator PUF). Our simplifications allow for a dramatic reduction in area by making a mild security assumption on ring oscillator physical obfuscated key output bits.

# Reusable Authentication from the Iris

I’m super excited to put out my first paper written solely with UConn students. James and Sailesh have put a ton of work into this. We build a full key derivation system from the human iris by integrating image processing and the crypto described in our previous paper. I’m particularly excited because I started working on this problem in graduate school and it felt like we’d never get to an actual implementation.

Abstract: Mobile platforms use biometrics for authentication. Unfortunately, biometrics exhibit noise between repeated readings. Due to the noise, biometrics are stored in plaintext, so device compromise completely reveals the user’s biometric value.

To limit privacy violations, one can use fuzzy extractors to derive a stable cryptographic key from biometrics (Dodis et al., Eurocrypt 2004). Unfortunately, fuzzy extractors have not seen wide deployment due to insufficient security guarantees. Current fuzzy extractors provide no security for real biometric sources and no security if a user enrolls the same biometric with multiple devices or providers.

Previous work claims key derivation systems from the iris but only under weak adversary models. In particular, no known construction securely handles the case of multiple enrollments. Canetti et al. (Eurocrypt 2016) proposed a new fuzzy extractor called sample-then-lock.

We construct biometric key derivation for the iris starting from sample-then-lock. Achieving satisfactory parameters requires modifying and coupling of the image processing and the cryptography. Our construction is implemented in Python and being open-sourced. Our system has the following novel features:

— 45 bits of security. This bound is pessimistic, assuming the adversary can sample strings distributed according to the iris in constant time. Such an algorithm is not known.

— Secure enrollment with multiple services.

— Natural incorporation of a password, enabling multifactor authentication. The structure of the construction allows the overall security to be sum of the security of each factor (increasing security to 79 bits).

# Presentation at Asiacrypt 2016

I just presented our paper “When are Fuzzy Extractors Possible?” with Leonid Reyzin and Adam Smith at Asiacrypt 2016. The talk video is available here: https://youtu.be/eiKqok3pNIs?t=13906 and the slides are here: fuzzy-extractors-when-possible-asiacrypt

# When are Fuzzy Extractors Possible?

*Benjamin Fuller*, Leonid Reyzin, and Adam Smith. When are Fuzzy Extractors Possible? Asiacrypt 2016.

### Abstract

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a high-entropy secret into the same uniformly distributed key. A minimum condition for the security of the key is the hardness of guessing a value that is similar to the secret, because the fuzzy extractor converts such a guess to the key.

We define fuzzy min-entropy to quantify this property of a noisy source of secrets. Fuzzy min-entropy measures the success of the adversary when provided with only the functionality of the fuzzy extractor, that is, the \emph{ideal} security possible from a noisy distribution. High fuzzy min-entropy is necessary for the existence of a fuzzy extractor.

We ask: is high fuzzy min-entropy a sufficient condition for key extraction from noisy sources? If only computational security is required, recent progress on program obfuscation gives evidence that fuzzy min-entropy is indeed sufficient. In contrast, information-theoretic fuzzy extractors are not known for many practically relevant sources of high fuzzy min-entropy.

In this paper, we show that fuzzy min-entropy is also sufficient for information-theoretically secure fuzzy extraction. For every source distribution W for which security is possible we give a secure fuzzy extractor.

Our construction relies on the fuzzy extractor knowing the precise distribution of the source W. A more ambitious goal is to design a single extractor that works for all possible sources. We show that this more ambitious goal is impossible: we give a family of sources with high fuzzy min-entropy for which no single fuzzy extractor is secure. This result emphasizes the importance of accurate models of high entropy sources.

# Reusable Fuzzy Extractors for Low-Entropy Distributions

Ran Canetti, *Benjamin Fuller*, Omer Paneth, Leonid Reyzin, and Adam Smith. Reusable Fuzzy Extractors for Low-Entropy Distributions. Eurocrypt 2016.

Previous titles were “Reusable Fuzzy Extractors via Digital Lockers” and “Key Derivation From Noisy Sources With More Errors Than Entropy.”

### Abstract

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, CCS 2004) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations).

We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated (the only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient and tolerates near-linear error rates.

Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates–lower than those supported by prior (nonreusable) constructions–assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. We show that such structural assumptions are necessary to support low entropy rates.

We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, providing a computationally secure and an information-theoretically secure construction for large-alphabet sources.

# Iris Biometric Security Challenges and Possible Solutions

Gene Itkis, Venkat Chandar, Benjamin Fuller, Joseph Campbell, Robert Cunningham. Iris Biometric Security Challenges and Possible Solutions: For your eyes only? Using the iris as a key. IEEE Signal Processing Magazine, 2015.

### Abstract

Biometrics were originally developed for identification, such as for criminal investigations. More recently, biometrics have been also utilized for authentication. Most biometric authentication systems today match a user?s biometric reading against a stored reference template generated during enrollment. If the reading and the template are sufficiently close, the authentication is considered successful and the user is authorized to access protected resources. This binary matching approach has major inherent vulnerabilities.

# Key Derivation from Noisy Sources with More Errors Than Entropy

Our work will appear with about proceedings at Allerton 2014. This work was subsequently published in Reusable Fuzzy Extractors for Low-Entropy Distributions.

# Computational Fuzzy Extractors

*Benjamin Fuller*, Xianrui Meng, and Leonid Reyzin. Computational Fuzzy Extractors. Asiacrypt 2013.

### Abstract

Fuzzy extractors derive strong keys from noisy sources. Their security is defined information- theoretically, which limits the length of the derived key, sometimes making it too short to be useful. We ask whether it is possible to obtain longer keys by considering computational security, and show the following.

-Negative Result: Noise tolerance in fuzzy extractors is usually achieved using an information reconciliation component called a “secure sketch.” The security of this component, which directly affects the length of the resulting key, is subject to lower bounds from coding theory. We show that, even when defined computationally, secure sketches are still subject to lower bounds from coding theory. Specifically, we consider two computational relaxations of the information-theoretic security requirement of secure sketches, using conditional HILL entropy and unpredictability entropy. For both cases we show that computational secure sketches cannot outperform the best information-theoretic secure sketches in the case of high-entropy Hamming metric sources.

-Positive Result: We show that the negative result can be overcome by analyzing computational fuzzy extractors directly. Namely, we show how to build a computational fuzzy extractor whose output key length equals the entropy of the source (this is impossible in the information-theoretic setting). Our construction is based on the hardness of the Learning with Errors (LWE) problem, and is secure when the noisy source is uniform or symbol-fixing (that is, each dimension is either uniform or fixed). As part of the security proof, we show a result of independent interest, namely that the decision version of LWE is secure even when a small number of dimensions has no error.