The threat of large-scale, general-purpose quantum computers to existing public-key cryptographic solutions has lead to global efforts to standardise post-quantum cryptography as a replacement. In particular, the NIST Post-Quantum Cryptography is now in its third and final round. One of the front-runners for problems to base post-quantum cryptography on are hard problems on lattices. Five out of seven finalists of the NIST processes are based on lattices.
Thus, it is a natural question to ask how long it actually takes to solve these problems on lattices. The better we understand this problem the more confidence we can have in the cryptographic solutions soon to be deployed globally.
The security of lattice-based cryptography is a pressing research question for a second reason. Many innovations in the field of cryptography in recent years rely on lattices as their foundation. For example, all the ways in which we know how to compute arbitrary functions on encrypted data – homomorphic encryption – are based on lattices.
The Information Security Group at Royal Holloway has a strong track record in this area and we are seeking students to join our efforts to address this pressing research question. The directions this PhD can go into are manifold: (asymptotic) algorithm design and analysis, implementations, experimental validation, quantum computing, side-channel analysis, active attacks against protocols using lattice-based primitives, studying special cases relevant in practice.
We seek applicants with a background in mathematics and/or computer science or related disciplines.
Prospective applicants are welcome to discuss with Prof Martin Albrecht.