CAREER: Computing on Encrypted Data

加密的基本性质一直是全有或全无：任何知道密钥的人都可以解码和恢复整个数据;但是，没有密钥，什么都不能透露。换句话说，对加密数据唯一有用的操作就是使用密钥解密。在云计算的现代世界中，我们将大部分个人数据存储在云中，并远程执行计算。云存储和计算的众多安全问题提出了许多具有挑战性的问题：我们能否加密数据并在不解密的情况下运行计算？我们能不能加密程序，让用户在执行程序时，除了最终的结果之外，不会发现任何关于程序内部操作的细节？该项目致力于研究加密数据和程序的计算范式，以及作为这一广泛目标基础的基本密码原语的设计。具体来说，它集中在三个主要的密码原语：（i）全同态加密，它使加密数据的计算;（ii）功能加密，它使表达的访问控制;和（iii）程序混淆，它让我们隐藏程序的结构，同时保留其功能。总体目标是开发这些加密原语的构造，以实现高度的效率，但也保证在经过充分研究的加密假设下的安全性。为此，该项目探索了软件和硬件技术，以及代数，几何和数论中新颖数学工具的使用。

The basic nature of encryption has always been all-or-nothing: anyone who is privy to the secret key can decode and recover the entire data; but, without the key, nothing can be revealed. In other words, the only useful action that could be performed on encrypted data was decryption using the secret key. In the modern world of cloud computing, we store much of our personal data in the cloud, and perform computations on them remotely. The numerous security concerns with cloud storage and computation raise a number of challenging questions: Can we encrypt data and run computations on it without decrypting? Can we encrypt programs and allow users to execute them without discovering any details about their internal operations, other than the eventual result? This project is dedicated to the study of the paradigm of computing on encrypted data and programs, and the design of fundamental cryptographic primitives underlying this broad goal. Specifically, it focuses on three major cryptographic primitives: (i) fully homomorphic encryption, which enables computations on encrypted data; (ii) functional encryption, which enables expressive access control; and (iii) program obfuscation, which lets us hide the structure of programs while preserving their functionality. The overarching goal is to develop constructions of these cryptographic primitives that achieve a high degree of efficiency, but also guarantee security under well-studied cryptographic assumptions. Towards this end, the project explores both software and hardware techniques, and the use of novel mathematical tools from algebra, geometry and number theory.