SaTC 2.0: RES: Classical and quantum algorithms for problems in cryptography

This project focuses on the security and efficiency of certain cryptosystems. Since currently used systems are vulnerable to attacks by quantum computers, it is essential to develop and analyze alternatives that are resistant to quantum computers, so that they remain secure in a post-quantum world. This project investigates both the classical and post-quantum security of cryptosystems based on supersingular isogenies, as well as lattice-based schemes proposed as replacements for currently used systems. The need for such work is increasingly urgent: advances in building quantum computers continue, while designing, implementing, and deploying quantum-resistant infrastructure requires substantial time. Another part of the project examines methods for improving the efficiency of cryptosystems. These are important practical questions. As part of its educational component, the investigator will engage middle and high school students in learning about cryptography and its mathematical foundations, helping to train the next generation of the cybersecurity workforce. One part of the project focuses on the classical and post-quantum security of cryptosystems based on supersingular isogenies. A variety of such schemes have been proposed, employing different techniques and frameworks. The investigator will study systems introduced in the last few years, in particular the ones which exploit the framework of higher-dimensional isogenies. In addition, the project examines the efficiency and security of recently developed protocols that conceal torsion point information, a vulnerability that compromised one of the original schemes. Another part studies the hardness of the endomorphism ring problem for supersingular elliptic curves, which underlies the security of many of these schemes. This is a fundamental problem in arithmetic geometry. The investigator will work to improve her existing algorithm for computing endomorphism rings and extend it to certain classes of abelian surfaces. The final part addresses the security of selected lattice-based systems. The lattice-based cryptosystem called "Soliloquy" was broken by a quantum computer. A key objective is to determine whether other lattice-based constructions, including those based on the Lattice Isomorphism Problem, are similarly susceptible to attacks by quantum computers. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2521084 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Kirsten Eisentraeger | Institution: Pennsylvania State Univ University Park, UNIVERSITY PARK, PA | Award Amount: $600,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2521084 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2521084.html