Computing Blindfolded on Data Homomorphically Encrypted under Multiple Keys: A Survey

With capability of performing computations on encrypted data without needing the secret key, homomorphic encryption (HE) is a promising cryptographic technique that makes outsourced computations secure and privacy-preserving. A decade after Gentry’s breakthrough discovery of how we might support arbitrary computations on encrypted data, many studies followed and improved various aspects of HE, such as faster bootstrapping and ciphertext packing. However, the topic of how to support secure computations on ciphertexts encrypted under multiple keys does not receive enough attention. This capability is crucial in many application scenarios where data owners want to engage in joint computations and are preferred to protect their sensitive data under their own secret keys. Enabling this capability is a non-trivial task. In this article, we present a comprehensive survey of the state-of-the-art multi-key techniques and schemes that target different systems and threat models. In particular, we review recent constructions based on Threshold Homomorphic Encryption (ThHE) and Multi-Key Homomorphic Encryption (MKHE). We analyze these cryptographic techniques and schemes based on a new secure outsourced computation model and examine their complexities. We share lessons learned and draw observations for designing better schemes with reduced overheads.

An Efficient Privacy-preserving Approach for Secure Verifiable Outsourced Computing on Untrusted Platforms

In outsourcing computation models, weak devices (clients) increasingly rely on remote servers (workers) for data storage and computations. However, most of these servers are hackable or untrustworthy, which makes their computation questionable. Therefore, there is need for clients to validate the correctness of the results of their outsourced computations and ensure that servers learn nothing about their clients other than the outputs of their computation. In this work, an efficient privacy preservation validation approach is developed which allows clients to store and outsource their computations to servers in a semi-honest model such that servers' computational results could be validated by clients without re-computing the computation. This article employs a morphism approach for the client to efficiently perform the proof of correctness of its outsourced computation without re-computing the whole computation. A traceable pseudonym is employed by clients to enforce anonymity.