本文为瑞典哥德堡大学（作者：EMELIE WIDEGREN）的硕士论文，共60页。

完全同态加密（FHE）被称为密码学的圣杯。它打开了许多新功能的大门，目标是解决IT世界的安全和信任问题。2009年之后，当克雷格·金特里（Craig Gentry）证明可以实现这一目标时，这一领域的研究迅速展开，在寻找更实际、更有效的方案方面取得了实质性进展。FHE是一种密码原语，允许在加密数据上计算任意函数。这样的方案有许多应用，因为它允许用户在本地加密他们的私有数据，但仍然外包加密数据的计算，而不冒暴露实际数据的风险。2012年，LTV12发布了第一个多密钥FHE方案，并证明了任何同态加密（SHE）方案都可以成为多密钥。与单钥匙设置一样，虽然在这方面取得了很大进展，但在实施多钥匙方案方面却没有做任何工作。本文是对FHE和MKFHE的综述，特别关注现有的最新实现以及三种本文的实现，包括我们所知的多钥匙设置中的第一种实现。

Fully Homomorphic Encryption (FHE) has been dubbed as cryptography’s holy grail. It opens the door to many new capabilities with the goal to solve the IT world’s problems of security and trust. After 2009, when Craig Gentry showed that FHE can be realised, research in the area exploded and substantial progress has been made in finding more practical and more efficient schemes. FHE is a cryptographic primitive that allows one to compute arbitrary functions over encrypted data. Such schemes have numerous applications since it allows users to encrypt their private data locally but still outsource the computation of the encrypted data without risking exposing the actual data. In 2012, LTV12 published the first multi-key FHE scheme and proved that any Somewhat Homomorphic Encryption (SHE) scheme could be made multi-key. As in the single key setting, a lot of progress been made in the area but no work has been done in implementing the multi-key schemes. This thesis is survey on FHE and MKFHE, with special attention to the state of the art implementations available as well as three implementations including the first implementation in the multi-key settings to the best of our knowledge.

1.       引言

2. 项目背景

3. 全同态加密

4. 研究方法

5. 结果与比较

6. 讨论

7. 结论

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