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1. Impossibility of efficient information-theoretic fuzzy extraction

   https://doi.org/10.1007/s10623-024-01376-z  

   Fuller, Benjamin (March 2024, Designs, Codes and Cryptography)

   Fuzzy extractors convert noisy signals from the physical world into reliable cryptographic keys. Fuzzy min-entropy measures the limit of the length of key that a fuzzy extractor can derive from a distribution (Fuller et al. in IEEE Trans Inf Theory 66(8):5282–5298, 2020). In general, fuzzy min-entropy that is superlogarithmic in the security parameter is required for a noisy distribution to be suitable for key derivation. There is a wide gap between what is possible with respect to computational and information-theoretic adversaries. Under the assumption of general-purpose obfuscation, keys can be securely derived from all distributions with superlogarithmic entropy. Against information-theoretic adversaries, however, it is impossible to build a single fuzzy extractor that works for all distributions (Fuller et al. 2020). A weaker information-theoretic goal is building a fuzzy extractor for each probability distribution. This is the approach taken by Woodage et al. (in: Advances in Cryptology—CRYPTO, Springer, pp 682–710, 2017). Prior approaches use the full description of the probability mass function and are inefficient. We show this is inherent: for a quarter of distributions with fuzzy min-entropy and $2^k$ points there is no secure fuzzy extractor that uses less $$2^{\Theta(k)}$$ bits of information about the distribution. We show an analogous result with stronger parameters for information-theoretic secure sketches. Secure sketches are frequently used to construct fuzzy extractors. 

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2. Nonmalleable Digital Lockers and Robust Fuzzy Extractors in the Plain Model

   https://doi.org/10.1007/978-3-031-22972-5_13  

   Apon, Daniel; Cachet, Chloe; Fuller, Benjamin; Hall, Peter; Liu, Feng-Hao (January 2023, Advances in Cryptology - Asiacrypt)

   We give the first constructions in the plain model of 1) nonmalleable digital lockers (Canetti and Varia, TCC 2009) and 2) robust fuzzy extractors (Boyen et al., Eurocrypt 2005) that secure sources with entropy below 1/2 of their length. Constructions were previously only known for both primitives assuming random oracles or a common reference string (CRS). Along the way, we define a new primitive called a nonmalleable point function obfuscation with associated data. The associated data is public but protected from all tampering. We use the same paradigm to then extend this to digital lockers. Our constructions achieve nonmalleability over the output point by placing a CRS into the associated data and using an appropriate non-interactive zero-knowledge proof. Tampering is protected against the input point over low-degree polynomials and over any tampering to the output point and associated data. Our constructions achieve virtual black box security. These constructions are then used to create robust fuzzy extractors that can support low-entropy sources in the plain model. By using the geometric structure of a syndrome secure sketch (Dodis et al., SIAM Journal on Computing 2008), the adversary’s tampering function can always be expressed as a low-degree polynomial; thus, the protection provided by the constructed nonmalleable objects suffices. 

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3. Code Offset in the Exponent

   https://doi.org/10.4230/LIPIcs.ITC.2021.15  

   Demarest, Luke; Fuller, Benjamin; Russell, Alexander (July 2021, 2nd Conference on Information-Theoretic Cryptography (ITC 2021))

   null (Ed.)

   Fuzzy extractors derive stable keys from noisy sources. They are a fundamental tool for key derivation from biometric sources. This work introduces a new construction, code offset in the exponent. This construction is the first reusable fuzzy extractor that simultaneously supports structured, low entropy distributions with correlated symbols and confidence information. These properties are specifically motivated by the most pertinent applications – key derivation from biometrics and physical unclonable functions – which typically demonstrate low entropy with additional statistical correlations and benefit from extractors that can leverage confidence information for efficiency. Code offset in the exponent is a group encoding of the code offset construction (Juels and Wattenberg, CCS 1999). A random codeword of a linear error-correcting code is used as a one-time pad for a sampled value from the noisy source. Rather than encoding this directly, code offset in the exponent encodes by exponentiation of a generator in a cryptographically strong group. We introduce and characterize a condition on noisy sources that directly translates to security of our construction in the generic group model. Our condition requires the inner product between the source distribution and all vectors in the null space of the code to be unpredictable. 

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4. Hardness Against Linear Branching Programs and More

   https://doi.org/10.4230/LIPIcs.CCC.2023.9  

   Chattopadhyay, Eshan; Liao, Jyun-Jie (January 2023, Leibniz International Proceedings in Informatics (LIPIcs):38th Computational Complexity Conference (CCC 2023))

   Ta-Shma, Amnon (Ed.)

   In a recent work, Gryaznov, Pudlák and Talebanfard (CCC '22) introduced a linear variant of read-once branching programs, with motivations from circuit and proof complexity. Such a read-once linear branching program is a branching program where each node is allowed to make 𝔽₂-linear queries, and is read-once in the sense that the queries on each path is linearly independent. As their main result, they constructed an explicit function with average-case complexity 2^{n/3-o(n)} against a slightly restricted model, which they call strongly read-once linear branching programs. The main tool in their lower bound result is a new type of extractor, called directional affine extractors, that they introduced. Our main result is an explicit function with 2^{n-o(n)} average-case complexity against the strongly read-once linear branching program model, which is almost optimal. This result is based on a new connection from this problem to sumset extractors, which is a randomness extractor model introduced by Chattopadhyay and Li (STOC '16) as a generalization of many other well-studied models including two-source extractors, affine extractors and small-space extractors. With this new connection, our lower bound naturally follows from a recent construction of sumset extractors by Chattopadhyay and Liao (STOC '22). In addition, we show that directional affine extractors imply sumset extractors in a restricted setting. We observe that such restricted sumset sources are enough to derive lower bounds, and obtain an arguably more modular proof of the lower bound by Gryaznov, Pudlák and Talebanfard. We also initiate a study of pseudorandomness against linear branching programs. Our main result here is a hitting set generator construction against regular linear branching programs with constant width. We derive this result based on a connection to Kakeya sets over finite fields. 

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5. A Study of Privacy Preservation in Average Consensus Algorithm via Deterministic Obfuscation Signals

   https://doi.org/10.1109/TCNS.2023.3290114  

   Rezazadeh, Navid; Kia, Solmaz S. (March 2024, IEEE Transactions on Control of Network Systems)

   This article is a study on the use of additive obfuscation signals to keep the reference values of the agents in the continuous-time Laplacian average consensus algorithm private from eavesdroppers. Obfuscation signals are perturbations that agents add to their local dynamics and their transmitted-out messages to conceal their private reference values. An eavesdropper is an agent inside or outside the network that has access to some subset of the interagent communication messages, and its knowledge set also includes the network topology. Rather than focusing on using a zero-sum and vanishing additive signal, our work determines the necessary and sufficient conditions that define the set of admissible obfuscation signals that do not perturb the convergence point of the algorithm from the average of the reference values of the agents. Of theoretical interest, our results show that this class includes nonvanishing signals as well. Given this broader class of admissible obfuscation signals, we define a deterministic notion of privacy preservation. In this definition, privacy preservation for an agent means that neither the private reference value nor a finite set of values to which the private reference value of the agent belongs to can be obtained. Then, we evaluate the agents’ privacy against eavesdroppers with different knowledge sets. 

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