Computing the distance between two non-normalized vectors x and y, represented by Δ (x, y) and comparing it to a predefined public threshold τ is an essential functionality used in privacy-sensitive applications such as biometric authentication, identification, machine learning algorithms (e.g., linear regression, k-nearest neighbors, etc.), and typo-tolerant password-based authentication. Tackling a widely used distance metric, Nomadic studies the privacy-preserving evaluation of cosine similarity in a two-party (2PC) distributed setting. We illustrate this setting in a scenario where a client uses biometrics to authenticate to a service provider, outsourcing the distance calculation to two computing servers. In this setting, we propose two novel 2PC protocols to evaluate the normalising cosine similarity between non-normalised two vectors followed by comparison to a public threshold, one in the semi-honest and one in the malicious setting. Our protocols combine additive secret sharing with function secret sharing, saving one communication round by employing a new building block to compute the composition of a function f yielding a binary result with a subsequent binary gate. Overall, our protocols outperform all prior works, requiring only two communication rounds under a strong threat model that also deals with malicious inputs via normalisation. We evaluate our protocols in the setting of biometric authentication using voice, and the obtained results reveal a notable efficiency improvement compared to existing state-of-the-art works.

This paper introduces a novel protocol for privacy-preserving biometric identification, named Monchi, that combines the use of homomorphic encryption for the computation of the identification score with function secret sharing to obliviously compare this score with a given threshold and finally output the binary result. Given the cost of homomorphic encryption, BFV in this solution, we study and evaluate the integration of two packing solutions that enable the regrouping of multiple templates in one ciphertext to improve efficiency meaningfully. We propose an end-to-end protocol, prove it secure and implement it. Our experimental results attest to Monchi's applicability to the real-life use case of an airplane boarding scenario with 1000 passengers,taking less than one second to authorize/deny access to the plane to each passenger via biometric identification while maintaining the privacy of all passengers.

This paper proposes a novel method to perform privacy-preserving face identification based on the notion of group testing, and applies it to a solution using the Cheon-Kim-Kim-Song (CKKS) homomorphic encryption scheme. Securely computing the closest reference template to a given live template requires K comparisons, as many as there are identities in a biometric database. Our solution, named Grote, replaces element-wise testing by group testing to drastically reduce the number of such costly, non-linear operations in the encrypted domain from K to up to 2\sqrtK . More specifically, we approximate the max of the coordinates of a large vector by raising to the α-th power and cumulative sum in a 2D layout, incurring a small impact in the accuracy of the system while greatly speeding up its execution. We implement Grote and evaluate its performance.

We propose a novel privacy-preserving, two-party computation of various distance metrics (e.g., Hamming distance, Scalar Product) followed by a comparison with a fixed threshold, which is known as one of the most useful and popular building blocks for many different applications including machine learning, biometric matching, etc. Our solution builds upon recent advances in function secret sharing and makes use of an optimized version of arithmetic secret sharing. Thanks to this combination, our new solution named Funshade is the first to require only one round of communication and two ring elements of communication in the online phase, outperforming all prior state-of-the-art schemes while relying on lightweight cryptographic primitives. Lastly, we implement our solution from scratch in portable C and expose it in Python, testifying its high performance by running secure biometric identification against a database of 1 million records in ~10 seconds with full correctness and 32-bit precision, without parallelization.

This paper proposes a novel collaborative decryption protocol for the Brakerski-Fan-Vercauteren (BFV) homomorphic encryption scheme in a multiparty distributed setting, and puts it to use in designing a leakage-resilient biometric identification solution. Allowing the computation of standard homomorphic operations over encrypted data, our protocol reveals only one least significant bit (LSB) of a scalar/vectorized result resorting to a pool of N parties. By employing additively shared masking, our solution preserves the privacy of all the remaining bits in the result as long as one party remains honest. We formalize the protocol, prove it secure in several adversarial models, implement it on top of the open-source library Lattigo and showcase its applicability as part of a biometric access control scenario.

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