Quantum computers, which harness the peculiarities of quantum physics to solve hard computational problems, are poised to deliver significant and far-reaching impacts to cryptography and privacy. Significant progress is being made in developing these devices, indicating that quantum computing will likely be viable in the next couple decades. Once viable, quantum computers will open up new attack vectors that will render many current cryptosystems insecure. This project is building new protocols to protect against these new quantum attack vectors. Examples include multiparty computation, public key cryptography, block ciphers, and more. Simultaneously, this research is also devising novel systems that actually take advantage of quantum computing to perform exciting new cryptographic tasks that were not previously possible. As part of these goals, the project is developing new theoretical foundations for studying and analyzing cryptosystems in the presence of quantum computers. Finally, this project is developing and studying a new theory of differential privacy in the quantum setting and devising new quantum differentially-private protocols that provide improved privacy guarantees.