The Design and Cryptanalysis of Quantum-Resistant Digital Signatures

Quantum computing will break all currently deployed public-key cryptographic algorithms. Therefore, to keep our IT infrastructure secure, we urgently need to design and deploy fundamentally new quantum-resistant cryptographic algorithms. While there are already some candidate quantum-resistant algorithms, they are unfortunately less efficient and less understood than the algorithms that are currently deployed, especially in the case of digital signature algorithms, which are the focus of this research proposal. The ambition of this research proposal is twofold: To improve our understanding of the security of the existing quantum-resistant signatures through cryptanalysis, i.e. by looking for vulnerabilities in the existing schemes, and by developing the algorithmic and mathematical tools to exploit these vulnerabilities. The second aim is to design new digital signature algorithms that are more secure and more efficient than the existing algorithms, by developing some exciting new approaches that have (re)surfaced recently, which have the potential to result in secure and efficient algorithms. Ultimately, this work will improve computer security in the near-term future where quantum computing is possible: the cryptanalytic aspect of the research will help assure that only strong cryptosystems are standardized and deployed, and the design aspect will make quantum-resistant algorithms more efficient, which will facilitate a smooth transition to quantum-resistant cryptography.