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.

中文翻译：

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多密钥下同态加密数据的蒙眼计算：一项调查

同态加密 (HE) 能够在不需要密钥的情况下对加密数据执行计算，是一种很有前途的加密技术，可以使外包计算安全并保护隐私。在 Gentry 突破性地发现我们如何支持对加密数据进行任意计算的十年后，许多研究跟进并改进了 HE 的各个方面，例如更快的引导和密文打包。然而，如何支持对在多个密钥下加密的密文进行安全计算的话题并没有得到足够的关注。在数据所有者希望参与联合计算并希望在自己的密钥下保护其敏感数据的许多应用场景中，此功能至关重要。启用此功能是一项艰巨的任务。在本文中，我们对针对不同系统和威胁模型的最先进的多密钥技术和方案进行了全面调查。特别是，我们回顾了基于阈值同态加密（ThHE）和多密钥同态加密（MKHE）的最新结构。我们基于一种新的安全外包计算模型分析了这些密码技术和方案，并检查了它们的复杂性。我们分享经验教训并得出观察结果，以设计更好的方案并减少开销。我们基于一种新的安全外包计算模型分析了这些密码技术和方案，并检查了它们的复杂性。我们分享经验教训并得出观察结果，以设计更好的方案并减少开销。我们基于一种新的安全外包计算模型分析了这些密码技术和方案，并检查了它们的复杂性。我们分享经验教训并得出观察结果，以设计更好的方案并减少开销。