A fuzzy extractor is a foundational cryptographic component that enables the extraction of reproducible and uniformly random strings from sources with inherent noise, such as biometric traits. Reusable fuzzy extractor guarantees the security of multiple extractions from the same noisy source. In addition, although isogeny-based cryptography has become an important branch in post-quantum cryptography, the study of fuzzy extractors based on isogeny assumptions is still in its early stages and holds much room for improvement. In this paper, we give two reusable fuzzy extractor schemes derived from isogeny-based assumptions: one is based on the linear hidden shift assumption over group actions, while the other is built upon the group-action decisional Diffie–Hellman assumption within the isogeny framework. Both proposed constructions achieve post-quantum security and are capable of correcting a linear proportion of errors. They rely solely on fundamental cryptographic primitives, which ensure simplicity and efficiency. Additionally, the second construction is based on restricted effective group action, which is weaker than the effective group action used in the first construction, thereby offering greater practical applicability.
A fuzzy extractor is a foundational cryptographic component that enables the extraction of reproducible and uniformly random strings from sources with inherent noise, such as biometric traits. Reusable fuzzy extractor guarantees the security of multiple extractions from the same noisy source. In addition, although isogeny-based cryptography has become an important branch in post-quantum cryptography, the study of fuzzy extractors based on isogeny assumptions is still in its early stages and holds much room for improvement. In this paper, we give two reusable fuzzy extractor schemes derived from isogeny-based assumptions: one is based on the linear hidden shift assumption over group actions, while the other is built upon the group-action decisional Diffie–Hellman assumption within the isogeny framework. Both proposed constructions achieve post-quantum security and are capable of correcting a linear proportion of errors. They rely solely on fundamental cryptographic primitives, which ensure simplicity and efficiency. Additionally, the second construction is based on restricted effective group action, which is weaker than the effective group action used in the first construction, thereby offering greater practical applicability.
Abstract A fuzzy extractor derives uniformly random strings from noisy sources that are neither reliably reproducible nor uniformly random. The basic definition of fuzzy extractor was first formally introduced by Dodis et al. and has achieved various applications in cryptographic systems. However, it has been proved that a fuzzy extractor could become totally insecure when the same noisy random source is extracted multiple times. To solve this problem, the reusable fuzzy extractor is proposed. In this paper, we propose the first reusable fuzzy extractor based on the LPN assumption, which is efficient and resilient to linear fraction of errors. Furthermore, our construction serves as an alternative post-quantum reusable fuzzy extractor.
Abstract Fuzzy extractors allow for the extraction and reproduction of a nearly uniform string from a noisy and non-uniform source. Reusable and robust fuzzy extractors further require that the output string should remain pseudorandom under multiple extractions and any modification of public value should be detectable. Existing constructions of reusable and robust fuzzy extractors are all designed in the Common Reference String (CRS) model and work only for CRS-independent sources. In this work, we introduce a construction of reusable and robust fuzzy extractor for CRS-dependent sources. Our construction is built upon some well-studied cryptography, including a collision resistant hash function, a symmetric key encryption that keeps secure with respect to auxiliary input, a public key encryption and simulation-sound non-interactive zero-knowledge argument. We also present some instantiations of these primitives from Learning with Parity Noise (LPN) assumption and Short Integer Solution (SIS) assumption. These instantiations result in the first reusable and robust fuzzy extractor for CRS-dependent sources that can tolerate linear errors.
Our modern world is dependent on online communications and transactions. To ensure privacy in these digital actions, it is extremely common to use protocols such as the Diffie-Hellman key exchange scheme. Unfortunately, these systems have been shown to be vulnerable to attacks from a quantum adversary. This means that an overhaul of the field of cryptography is needed in order to anticipate and mitigate this threat.Over the past years, the community has begun to answer this call by proposing and analyzing new techniques that are conjectured to be quantum safe. One such example is the study of cryptographic group actions. These mappings mimic some of the structure from the Diffie-Hellman protocol,but abstract it enough so that new mathematical operations can be employed that avoid quantum attacks. Currently, the main examples of group actions come from isogenies, codes, and lattices.In order for a protocol to be used in the real-world we would hope for it to be secure, fast, and requiring little storage. This means that in these early stages of research and development of cryptographic group actions, it is essential to begin to answer some of the questions surrounding security and efficiency. This thesis contributes to this effort by focusing on these aspects across different group actions that have been proposed for use in the literature.It is certainly true that each individual group action needs its own study of security. When designers are trying to achieve some advanced functionalities in a protocol, they may sometimes alter the underlying security assumptions.Each time this is done, the new assumptions need their own careful study as well. In this thesis we consider four different variants of group action security assumptions spanning the isogeny, tensor, linear code, and matrix code group actions. We analyze their security by either offering concrete attacks or giving a polynomial time reduction to a more well-studied assumption. This helps to indicate whether a problem is appropriate for use in cryptography, and what parameters to use if so.In addition to security, this thesis is also inscribed in the effort to study the efficiency of group actions by including three works studying the isogeny group action and related subroutines. They span the core isogeny problem for oriented elliptic curves, evaluating isogenies from a kernel generator, and supersingularity testing. With an effort from the community to improve overall runtimes, we can hope to get closer to reasonable speeds for real-life use.By studying the security and efficiency of cryptographic group actions, this thesis shines light on group actions as a promising framework for post-quantum cryptographic solutions.
A fuzzy extractor is a security primitive that allows for reproducible extraction of an almost uniform key from a non-uniform noisy source. We analyze a fuzzy extractor scheme that uses universal hash functions for both information reconciliation and privacy amplification. This is a useful scheme when the number of error patterns likely to occur is limited, regardless of the error probabilities. We derive a sharp bound on the uniformity of the extracted key, making use of the concatenation property of universal hash functions and a recent tight formulation of the leftover hash lemma.
Many practical security applications rely on inherently noisy data sources, such as biometric measurements, sensor-derived features, and physical unclonable functions (PUFs). This variability makes it difficult to develop reliable cryptographic primitives. Conventional solutions-like fuzzy commitment schemes, fuzzy vaults, secure sketches, and fuzzy extractors-enable key binding or generation from noisy data by combining cryptography with error-correcting codes to handle variations. However, using ECCs can cause information leakage. In this paper, we construct ISNR-PQC, an isometry noise resilient post-quantum cryptographic primitive designed for natural noisy sources, using secure biometric data as an application. ISNR-PQC specifically uses lattice-based cryptography based on the National Institute of Standards and Technology (NIST) standard FIPS 203. Our approach provides security guarantees against quantum adversaries under the Learning with Errors (LWE) assumption. We formalise correctness, robustness, and [Formula: see text]-restricted IND-CPA indistinguishability in a unified security model. Our ISNR-PQC is noise resilient because it accepts ancillary data that is close to the original encrypting data, as measured by an isometry-based threshold mapping. Our results demonstrate that ISNR-PQC addresses a major challenge in biometric authentication theory and is a promising base for future biometric and noisy-data security systems.
We address the problem of designing optimal schemes for the generation of secure crypto-\ngraphic keys from continuous noisy data. We argue that, contrary to the discrete case, a\nuniversal fuzzy extractor does not exist. This implies that in the continuous case, key ex-\ntraction schemes have to be designed for particular probability distributions. We extend the\nknown definitions of the correctness and security properties of fuzzy extractors. Our defini-\ntions apply to continuous as well as discrete variables.\nWe propose a generic construction for fuzzy extractors from noisy continuous sources, using independent partitions. The extra freedom in the choice of discretisation, which does not exist in the discrete case, is advantageously used to give the extracted key a uniform distribution. We analyze the privacy properties of the scheme and the error probabilities in a one-dimensional toy model with simplified noise.\nFinally, we study the security implications of incomplete knowledge of the source's probability distribution P. We derive a bound on the min-entropy of the extracted key under the worst case assumption, where the attacker knows P exactly.