Verifiable Encodings for Secure Homomorphic Analytics

Abstract

Homomorphic encryption, which enables the execution of arithmetic operations directly on ciphertexts, is a promising solution for protecting privacy of cloud-delegated computations on sensitive data. However, the correctness of the computation result is not ensured. We propose two error detection encodings and build authenticators that enable practical client-verification of cloud-based homomorphic computations under different trade-offs and without compromising on the features of the encryption algorithm. Our authenticators operate on top of trending ring learning with errors based fully homomorphic encryption schemes over the integers. We implement our solution in VERITAS, a ready-to-use system for verification of outsourced computations executed over encrypted data. We show that contrary to prior work VERITAS supports verification of any homomorphic operation and we demonstrate its practicality for various applications, such as ride-hailing, genomic-data analysis, encrypted search, and machine-learning training and inference.

Verifiable encodings in multigroup fully homomorphic encryption

“…As the main contributions in this paper we have adopted the recent construction MGHE from [17] to generate a verifiable variation built upon the ideas from [6]. We also adapted the work from [15] to improve the efficiency of the most expensive operations, namely the product and the relinearization algorithms.…”

“…Our approach is inspired by the proposal Veritas [6] and the use of homomorphic authenticators started by Gennaro and Wichs in [13]. Here we will use a homomorphic authenticator called replication encoding which can be described, informally, as follows: for each input message, one generates an extended vector a random half of which is filled with challenge values whereas the other half is filled with copies of the original message.…”

“…Theorem 3.1 (Theorem IV.1, [6]) Let λ be a power-of-2 security parameter. If the PRF F , the CRHF H, and the associated homomorphic scheme are at least λ-bit secure, then the replication encoding authenticator is a secure authenticator.…”

“…The previous studies were limited to specific HE schemes and lacked essential functionalities such as relinearization, rotations, and bootstrapping, rendering them theoretical and impractical for many applications. To address these limitations, we propose a solution for verifying outsourced computations based on the works of [6,13]. Unlike the SNARK-based approaches that prioritize efficient verification and succinctness, our primary goal is to provide versatility for homomorphic computations with reasonable costs for both clients and the cloud.…”