Cryptography is the basic infrastructural element enabling privacy and security for electronic transactions. However, when a large-scale quantum computer is finally built, it will force us to abandon established methods of cryptography, such as RSA and Diffie-Hellman, which are in common use today. The proposed research will further this line of disruptive quantum algorithmic research; but it also aims to erect a new framework of secure post-quantum cryptography, in order to maintain this societally critical infrastructure.
The most attractive approach for salvaging modern cryptography would be to develop classical cryptosystems for which we have compelling evidence of security even in the face of quantum adversaries. Recent work by the PIs and their collaborators has shown that certain algebraic problems possess hardness properties relevant even for quantum algorithms. We propose to strengthen and leverage these results in order to develop cryptographic schemes which can be carried out by today's computers, but which will remain secure even against quantum attack in the future.
In tandem with this effort, we propose to develop new quantum algorithms for breaking cryptosystems based on conjugacy in the braid group. This is one of the few remaining classical cryptosystems which has not already been shown to be vulnerable to quantum attack.
Our research program is also directly integrated with graduate student training at all four institutions, undergraduate educational innovation, educational outreach, and broad scientific dissemination.
