We introduce a new construction method for one-time multi-client functional encryption schemes that support noisy quadratic functions, are resistant against corruption and allow for labels. Such schemes can be used as building blocks in many practical applications, e.g. privacy-preserving machine learning on arbitrarily split data. In contrast to earlier constructions, ours uses a different structural design that allows to make use of less complex, hence more efficient building blocks. The security of our construction relies solely on its underlying building blocks and no additional hardness assumptions, making it more generic than related work. More specifically, the construction itself does not rely on structures given by bilinear groups.

Functional encryption (FE) has recently attracted interest in privacy-preserving machine learning (PPML) for its unique ability to decrypt to the evaluation of functions on encrypted data instead of the data itself. A related line of work focuses on noisy FE, which ensures differential privacy in the output while keeping the data encrypted. We extend the notion of noisy multi-input functional encryption (NMIFE) to tagged (dynamic) NMIFE (tg(Dy)NMIFE), enabling greater flexibility in the number of data holders and supported analyses. Our construction enhances privacy by incorporating fine-grained access control via tags and provides stronger security guarantees by supporting corruption resilience. Following our new definition of tgDyNMIFE, we present DyNo, a concrete inner-product tgDyNMIFE scheme. Our scheme captures all the functionalities previously introduced in noisy FE schemes, while being significantly more efficient in terms of space and runtime. To further prove the applicability of tgDyNMIFE, we present a protocol for PPML based on DyNo. According to this protocol, we train a privacy-preserving logistic regression.

We address the question of realizing privacy preserving analysis of user data. The abstract scenario considered is that an analyst aims to evaluate a function f on some user data X. To achieve comprehensive privacy, it is necessary to protect the input X directly. However, it is known that f(X) may leak too much information about X as well. A common approach to mitigate such risks is to make the computation differential private. In practice, this is often accomplished by replacing f by a noisy variant f^*. We investigate the use of multi-input functional encryption (MIFE) for achieving input- and output-privacy in one cryptographic mechanism. In a MIFE scheme, a setup authority can generate restricted decryption keys which enable to learn specific functions of encrypted messages, without revealing any additional information. To achieve differential privacy in this process, we introduce as a new cryptographic primitive: noisy multi-input functional encryption (NMIFE). It extends the concept of MIFE such that the decryption key may also encode a noisy function where the noise value is secret. While the change from MIFE to NMIFE is rather straightforward, the challenge is to come up with precise and workable definitions of correctness and security definition that we propose and explain in this work. Here, the security definition is tailored to the use case of differential privacy. As it is a special case of the established notion of full-hiding security, we present a generic transformation that allows to turn any full-hiding MIFE scheme into a secure NMIFE scheme that has practically the same performance as the initial MIFE scheme. Moreover, we make use of the fact that the proposed security definition is less restrictive and present a new concrete NMIFE scheme for evaluating the inner product. It is dubbed DiffPIPE (short for DIFFerentially Private Inner Product Evaluation). DiffPIPE is not the result from the transformation and outperforms all from existing full-hiding MIFE schemes constructed NMIFE schemes. In experiments, we demonstrate its applicability for realizing privacy preserving counting queries on data sets.