Threshold Fully Homomorphic Encryption (FHE) enables arbitrary computation on encrypted data, while distributing the decryption capability across multiple parties. A primary application of interest is low-communication multi-party computation (MPC), which benefits from a fast and secure threshold FHE decryption protocol.

In the era of cloud computing and machine learning, data has become a highly valuable resource. Recent history has shown that the benefits brought forth by this data driven culture come at a cost of potential data leakage. Such breaches have a devastating impact on individuals and industry, and lead the community to seek privacy preserving solutions. A promising approach is to utilize Fully Homomorphic Encryption ( \( \mathsf {FHE } \) ) to enable machine learning over encrypted data, thus providing resiliency against information leakage. However, computing over encrypted data incurs a high computational overhead, thus requiring the redesign of algorithms, in an “ \( \mathsf {FHE } \) -friendly” manner, to maintain their practicality. In this work we focus on the ever-popular tree based methods, and propose a new privacy-preserving solution to training and prediction for trees over data encrypted with homomorphic encryption. Our solution employs a low-degree approximation for the step-function together with a lightweight interactive protocol, to replace components of the vanilla algorithm that are costly over encrypted data. Our protocols for decision trees achieve practical usability demonstrated on standard UCI datasets encrypted with fully homomorphic encryption. In addition, the communication complexity of our protocols is independent of the tree size and dataset size in prediction and training, respectively, which significantly improves on prior works. 1

Abstract We present a novel secure search protocol on data and queries encrypted with Fully Homomorphic Encryption (FHE). Our protocol enables organizations (client) to (1) securely upload an unsorted data array x = (x[1], . . . , x[n]) to an untrusted honest-but-curious sever, where data may be uploaded over time and from multiple data-sources; and (2) securely issue repeated search queries q for retrieving the first element (i*, x[i*]) satisfying an agreed matching criterion i* = min { i ∈ [n] | IsMatch(x[i], q) = 1 }, as well as fetching the next matching elements with further interaction. For security, the client encrypts the data and queries with FHE prior to uploading, and the server processes the ciphertexts to produce the result ciphertext for the client to decrypt. Our secure search protocol improves over the prior state-of-the-art for secure search on FHE encrypted data (Akavia, Feldman, Shaul (AFS), CCS’2018) in achieving: – Post-processing free protocol where the server produces a ciphertext for the correct search outcome with overwhelming success probability. This is in contrast to returning a list of candidates for the client to postprocess, or suffering from a noticeable error probability, in AFS. Our post-processing freeness enables the server to use secure search as a sub-component in a larger computation without interaction with the client. – Faster protocol: (a) Client time and communication bandwidth are improved by a log2 n/ log log n factor. (b) Server evaluates a polynomial of degree linear in log n (compare to cubic in AFS), and overall number of multiplications improved by up to log n factor. (c) Employing only GF(2) computations (compare to GF(p) for p ≫ in AFS) to gain both further speedup and compatibility to all current FHE candidates. – Order of magnitude speedup exhibited by extensive benchmarks we executed on identical hardware for implementations of ours versus AFS’s protocols. Additionally, like other FHE based solutions, our solution is setup-free: to outsource elements from the client to the server, no additional actions are performed on x except for encrypting it element by element (each element bit by bit) and uploading the resulted ciphertexts to the server.