Cryptanalysis of post-quantum hardness assumptions and design of advanced protocols

• Applicant: Simon-Philipp Merz, Ph.D.
• Subject Area: Security and Dependability, Operating-, Communication- and Distributed Systems
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 547417243

Public-key cryptography is a tool enabling modern digital communications over secure connections and crucial services of modern society could not exist without it. The security of public-key cryptography relies on the computational hardness of mathematical problems - none of which have a proof that they are actually hard to solve and without major breakthroughs in complexity theory such proofs seem unlikely. In fact, assuming access to a large-scale quantum computer, the problems at the foundation of currently deployed cryptography can be solved efficiently. Advances in quantum computing and the need for long-term security in cryptography have therefore led to a surge of interest in developing secure replacements based on new mathematical problems. Post-quantum cryptography (PQC) is the research area that aims to develop cryptographic protocols that will remain secure in the presence of quantum computers. This project’s objectives are twofold. Firstly, I will scrutinise several new hardness assumptions that form the foundation for the proposals in the ongoing standardisation processes for post-quantum cryptography. For many of these problems, attack vectors exist that have not been sufficiently studied and improving the complexity of algorithms solving the underlying mathematical problems seems feasible. My research will focus on improving cryptanalysis in isogeny-based and multivariate cryptography. These two branches of PQC are being considered in order to obtain a more diverse family of post-quantum hardness assumptions beyond the ones that are currently being standardised already. Further, I want to collaborate to improve quantum algorithms solving these problems. By developing new cryptanalytic techniques, this project will help determine which cryptographic constructions should be further considered as secure building blocks, and it will determine their appropriate parameter sets, which will directly impact the primitives’ performance in practice. Secondly, this project will be concerned with the optimisation and design of more advanced cryptographic protocols. As part of this, I want to develop more efficient solutions for advanced building blocks such as OPRFs, which can be found in multiple practical privacy preserving applications. Moreover, I want to contribute to the design and the standardisation process of efficient post-quantum solutions for vital network security protocols such as TLS or WireGuard. Integrating basic primitives from ongoing standardisation processes into real world applications raises many practical challenges. Security proofs that work for the single building blocks by themselves might suffer from subtle problems in composition with other cryptographic protocols and the computational as well as the bandwidth requirements of post-quantum primitives can be vastly different from their classical counterparts. I want to build upon previous research in the domain, and increase efficiency of the protocols.

• DFG Programme: WBP Fellowship
• International Connection: Switzerland
• Host: Professor Kenneth Graham Paterson, Ph.D.