Koziel, Brian

It is well known that in the near future, a large-scale quantum computer will be unveiled, one that could be used to break the cryptography that underlies our digital infrastructure. Quantum computers operate on quantum mechanics, enabling exponential speedups to certain computational problems, including hard problems at the cornerstone of our deployed cryptographic algorithms. With a vulnerability in this security foundation, our online identities, banking information, and precious data is now vulnerable. To address this, we must prepare for a transition to post-quantum cryptography, or cryptosystems that are protected from attacks by both classical and quantum computers. This is a dissertation proposal targeting cryptographic engineering that is necessary to deploy isogeny-based cryptosystems, one known family of problems that are thought to be difficult to break, even for quantum computers. Isogeny-based cryptography utilizes mappings between elliptic curves to achieve public-key encryption, digital signatures, and other cryptographic objectives necessary to support our digital infrastructure's security. This proposal focuses on three aspects of isogeny-based cryptography: 1) cryptographic engineering of isogeny-based cryptosystems; 2) developing and optimizing security-enabling isogeny applications; and 3) improving the security from known and emerging implementation attacks. By improving each of these aspects, we are providing confidence in the deployability of isogeny-based cryptography and helping to prepare for a post-quantum transition.