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

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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.