NSFSaTC-BSF: TWC: Small: Horizons of Symmetric-Key Cryptography

对称密钥原语是实用密码学的生命线，也是几乎所有计算机安全系统的关键组件。 密码学社区已经在理论上健全的对称对象上开发了大量的工作，但是它们对于实际使用来说太慢了许多数量级。 因此，从业者使用快速原语，这些原语被设计为能够抵御已知的攻击，但缺乏基于自然数学问题的严格安全保证。最近的研究结果表明，基于理论上合理设计的对称基元也可以享受现实的效率水平。这个项目利用这一洞察力来展示一系列新的对称对象的可行性，效率和广泛的适用性，以实现新的安全应用。这个项目的重点是设计理论上合理和计算效率高的公钥密码方案。 这些将从基本的原语，如伪随机函数和分组密码;到应用程序，如证明系统，数字签名，函数加密和广播加密，还将包括实际的实现，如完全同态评估的密钥原语。本研究的一个核心主题是利用代数结构，并证明公钥对象的设置中，公钥的出现显着更困难（或不可能）获得的可行性。该项目还将开发开源软件库，在实践中展示这些结构，并促进进一步的实施。

Symmetric-key primitives are the lifeblood of practical cryptography, and are critical components of nearly any computer security system. The cryptographic community has developed a rich body of work on theoretically sound symmetric objects, but they are many orders of magnitude too slow for realistic usage. Thus, practitioners use fast primitives that have been designed to withstand known attacks, but which lack rigorous security guarantees based on natural mathematical problems. Recent results demonstrate that symmetric primitives based on theoretically sound designs can also enjoy realistic levels of efficiency. This project leverages this insight to demonstrate the feasibility, efficiency, and broad applicability of a wide array of new symmetric objects to enable new security applications.The focus of this project is the design of theoretically sound and computationally efficient symmetric-key cryptographic schemes. These will range from basic primitives like pseudorandom functions and block ciphers; to applications like proof systems, digital signatures, functional encryption, and broadcast encryption, and will also include practical implementations such as fully homomorphic evaluation of symmetric-key primitives. A core theme of this research is to exploit the algebraic structure, and to demonstrate feasibility of symmetric-key objects in settings where public-key ones appear significantly more difficult (or impossible) to obtain. The project will also develop open-source software library that exhibits these constructions in practice, and facilitates further implementations.