Cryptanalysis of post-quantum hardness assumptions

The ongoing transition to post-quantum cryptography (PQC) has so far seen success in replacing fundamental public-key cryptographic primitives such as public-key encryption and digital signatures with new ones offering strong security guarantees against quantum computing adversaries. These guarantees are obtained by grounding the security of the new primitives on well-understood hardness assumptions such as the “learning with errors” (LWE) and “short integer solutions” (SIS) problems, computational problems conjectured to be hard to solve even with a quantum computer.

Yet, as our understanding of LWE and SIS has matured, their limitations have become apparent. While efficient encryption and signatures can be obtained, practical secure solutions for advanced functionality such as oblivious pseudorandom functions, updatable encryption, or polylogarithmic-verifier arguments of knowledge have not been achieved. To realise this richer functionality, new exotic assumptions have instead been proposed, such as “vanishing” SIS (Cini et al, Crypto 2023), “sparse” LWE (Jain et al, Crypto 2024), “hollow” LWE (Albrecht et al, Eurocrypt 2025), “equivocal” LWE (Cini et al, Crypto 2025).

These new “spins” on LWE and SIS are usually proposed together with heuristic or asymptotic evidence of their security. So far, little research on their practical security against concrete attacks exists. Yet, practical security must be understood at the time of commercialising or standardising new cryptographic schemes.

The objective of this project is to study the concrete security of new cryptographic assumptions proposed to build practical advanced functionality in PQC. The candidate will work with the primary and secondary supervisors to design new attacks targeting the gaps between the new and prior assumptions. The student will also work on new constructions using these assumptions, applying the results of their cryptanalysis to the problem of designing secure systems.

We seek applicants with a strong background in mathematics and/or computer science. Familiarity with cryptography, number theory, computational algebra or quantum computing will be appreciated, but are not mandatory.

Open to any UK or international candidates. Up to 30% of our UKRI funded studentships can be awarded to candidates paying international rate fees. Find out more about eligibility.