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Server-assisted fully homomorphic computation protocols

机译：服务器辅助的完全同态计算协议

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摘要

Fully homomorphic encryption is a cryptographic primitive with significant application potential, such as the capability of computing over encrypted data. However, even after a breakthrough result and several other valuable research efforts, fully homomorphic encryption solutions still come today with highly impractical complexity even for moderately large circuits. We consider the problem of designing protocols for arbitrary homomorphic computations from much simpler ones with the help of a (cloud-based) server. In a participant model where users are assisted by a single (cloud-based) server, we show how users can homomorphically compute any arbitrary arithmetic circuit, with inputs in any ring with efficient operations, over ciphertexts generated according to partially malleable encryption schemes (in fact, only malleable with respect to addition and multiplication). We also show that in the case of a binary ring, these latter schemes can be constructed based on any public-key encryption scheme, a clearly minimal assumption. We also show several other relationships of independent interest between homomorphic public-key encryption schemes, malleable public-key encryption schemes and server-assisted homomorphic computation protocols.
机译：完全同态加密是一种具有重要应用潜力的加密原语，例如具有对加密数据进行计算的能力。但是，即使取得了突破性的成果和其他一些有价值的研究成果，即使对于中等规模的电路，全同态加密解决方案如今仍具有高度不切实际的复杂性。我们考虑在（基于云的）服务器的帮助下，从简单得多的协议中为任意同态计算设计协议的问题。在参与者模型中，用户由单个（基于云的）服务器协助，我们展示了用户如何根据根据部分可延展的加密方案生成的密文，同态计算任何算术电路，并以有效操作在任何环中进行输入。实际上，仅在加法和乘法方面具有延展性）。我们还表明，在二进制环的情况下，可以基于任何公钥加密方案（显然是最小的假设）来构造这些后一种方案。我们还展示了同态公钥加密方案，可延展公钥加密方案和服务器辅助同态计算协议之间的其他一些具有独立利益的关系。

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