Topological Data Analysis (TDA) provides a suite of tools that extract shape-based features from high-dimensional data, with applications to modern statistical and machine learning (ML) models. Among these tools, persistent homology (PH) summarizes the topological structure of data in compact representations known as persistence diagrams (PDs). Due to their robustness to noise, interpretability, and compatibility with standard ML architectures, PDs are increasingly used in applications involving sensitive data, such as genomics, cancer research, sensor networks, and finance. Thus, there is a growing need to incorporate TDA methods into secure, end-to-end data analysis pipelines. We present the first adaptation of a fundamental TDA algorithm known as boundary matrix reduction to operate on encrypted data using homomorphic encryption (HE). We provide mathematical guarantees for the correctness of the HE-compatible algorithm under appropriate parameter choices and analyze its computational complexity. We support these theoretical results with two distinct empirical studies: (1) a plaintext simulation that explores the extent to which the theoretically sufficient parameters can be relaxed while still preserving correctness, and (2) a working implementation in the OpenFHE framework that validates correctness on encrypted data. This work lays the foundation for fully encrypted topological computations and opens new directions in privacy-preserving data analysis using TDA.

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features of high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. Persistent homology (PH) transforms data (e.g., point clouds, images, time series) into persistence diagrams (PDs)--compact representations of its latent topological structures. Because PDs enjoy inherent noise tolerance, are interpretable, provide a solid basis for data analysis, and can be made compatible with the expansive set of well-established ML model architectures, PH has been widely adopted for model development including on sensitive data. Thus, TDA should be incorporated into secure end-to-end data analysis pipelines. This paper introduces a version of the fundamental algorithm to compute PH on encrypted data using homomorphic encryption (HE).

Encryption provides a method to protect data out-sourced to a DBMS provider, e.g., in the cloud. However, performing database operations over encrypted data requires specialized encryption schemes that carefully balance security and performance. In this paper, we present a new encryption scheme that can efficiently perform equi-joins over encrypted data using only software and a single server with better security than the state-of-the-art. In particular, our encryption scheme reduces the leakage to equality of rows that match a selection criterion and only reveals the transitive closure of the union of the leakages of each query in a series of queries. Our encryption scheme is provable secure. We implemented our encryption scheme and evaluated it over a dataset from the TPC- H benchmark.

As many vulnerabilities of one-time authentication systems have already been uncovered, there is a growing need and trend to adopt continuous authentication systems. Biometrics provides an excellent means for periodic verification of the authenticated users without breaking the continuity of a session. Nevertheless, as attacks to computing systems increase, biometric systems demand more user information in their operations, yielding privacy issues for users in biometric-based continuous authentication systems. However, the current state-of-the-art privacy technologies are not viable or costly for the continuous authentication systems, which require periodic real-time verification. In this article, we introduce a novel, lightweight, privacy-aware, and secure continuous authentication protocol called PACA. PACA is initiated through a password-based key exchange (PAKE) mechanism, and it continuously authenticates users based on their biometrics in a privacy-aware manner. Then, we design an actual continuous user authentication system under the proposed protocol. In this concrete system, we utilize a privacy-aware template matching technique and a wearable-assisted keystroke dynamics-based continuous authentication method. This provides privacy guarantees without relying on any trusted third party while allowing the comparison of noisy user inputs (due to biometric data) and yielding an efficient and lightweight protocol. Finally, we implement our system on an Apple smartwatch and perform experiments with real user data to evaluate the accuracy and resource consumption of our concrete system.

Cancelable biometric schemes generate secure biometric templates by combining user specific tokens and biometric data. The main objective is to create irreversible, unlinkable, and revocable templates, with high accuracy of comparison. In this paper, we cryptanalyze two recent cancelable biometric schemes based on a particular locality sensitive hashing function, index-of-max (IoM): Gaussian Random Projection-IoM (GRP-IoM) and Uniformly Random Permutation-IoM (URP-IoM). As originally proposed, these schemes were claimed to be resistant against reversibility, authentication, and linkability attacks under the stolen token scenario. We propose several attacks against GRP-IoM and URP-IoM, and argue that both schemes are severely vulnerable against authentication and linkability attacks. We also propose better, but not yet practical, reversibility attacks against GRP-IoM. The correctness and practical impact of our attacks are verified over the same dataset provided by the authors of these two schemes.

A large class of biometric template protection algorithms assume that feature vectors are integer valued. However, biometric data is generally represented through real-valued feature vectors. Therefore, secure template constructions are not immediately applicable when feature vectors are composed of real numbers. We propose a generic transformation and extend the domain of biometric template protection algorithms from integer-valued feature vectors to real valued feature vectors. We show that our transformation is accuracy-preserving and verify our theoretical findings by reporting the implementation results using a public keystroke dynamics dataset.

Several papers have studied fault attacks on computing a pairing value e(P,Q), where P is a public point and Q is a secret point. In this paper, we observe that these attacks are in fact effective only on a small number of pairing-based protocols, and that too only when the protocols are implemented with specific symmetric pairings. We demonstrate the effectiveness of the fault attacks on a public-key encryption scheme, an identity-based encryption scheme, and an oblivious transfer protocol when implemented with a symmetric pairing derived from a supersingular elliptic curve with embedding degree 2.

We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Based on operation counts, we expect to gain accelerations of 30% and 18% for computing single point multiplication with and without availability of parallel multipliers, respectively, and these results are verified in our implementations.

We extend the torus-based compression technique for cyclotomic subgroups and show how the elements of certain subgroups in characteristic two and three fields can be compressed by a factor of 4 and 6, respectively. Our compression and decompression functions can be computed at a negligible cost. In particular, our techniques lead to very efficient exponentiation algorithms that work with the compressed representations of elements and can be easily incorporated into pairing-based protocols that require exponentiations or products of pairings.

Galbraith, Lin, and Scott recently constructed efficiently computable endomorphisms for a large family of elliptic curves defined over IFq2 and showed, in the case where q is a prime, that the Gallant-Lambert-Vanstone point multiplication method for these curves is significantly faster than point multiplication for general elliptic curves over prime fields. In this paper, we investigate the potential benefits of using Galbraith-Lin-Scott elliptic curves in the case where q is a power of 2. The analysis differs from the q prime case because of several factors, including the availability of the point halving strategy for elliptic curves over binary fields. Our analysis and implementations show that Galbraith-Lin-Scott point multiplication method offers significant acceleration for curves over binary fields, in both doubling- and halving-based approaches. Experimentally, the acceleration surpasses that reported for prime fields (for the platform in common), a somewhat counterintuitive result given the relative costs of point addition and doubling in each case.