In the mid 1990's, Peter Shor found his famous algorithm to factorize large numbers. It soon turned out that this algorithm can be used to break essentially all public-key cryptosystems in practical use today. On the positive side, the type of quantum computer required to run Shor's algorithm isn't available yet -- but there is an urgent need for new "post-quantum" asymmetric cryptosystems, which will survive the advent of reliable large-scale quantum computers.
There is an ongoing effort to study and eventually standardise such cryptosystems, specifically for new "key encapsulation mechanisms" and new "digital signature schemes":
https://nvlpubs.nist.gov/nistpubs/ir/2020/NIST.IR.8309.pdf
"Post-Quantum Security" refers to cryptographic security against an attacker that can utilize a powerful quantum computer. Currently, such a device does not exist. However, as technology advances, many currently used algorithms labeled as secure will be useless against an attacker that has access to a sufficiently large quantum computer.
Topics for Bachelor Students
- The McElice KEM
- The CRYSTALS-KYBER KEM and CRYSTALS-DILITIUM signatures
- The NTRU and NTRU-Prime KEMs
- SPHINCS+: A stateless hash-based signature scheme
Topics for Master Students
- Lattice-Based Cryptosystems
- Code-Based Cryptosystems
- Hash-based Digital Signatures
The specific scope for the topics below can be adjusted for either Bachelor or Master Students.
Knowledge of (basic) quantum-computing concepts is recommended or required (e.g. through the lecture: Quantum Algorithms and Cryptanalysis).
Not only for asymmetric cryptographic algorithms, "Post-Quantum Security" is an important topic to look at. While only some years ago, most researchers agreed that symmetric cryptography algorithms and schemes are quite safe against quantum computers, recent research has shown that many of the currently used constructions are unsafe against a quantum attacker.
- Post-Quantum Security of Symmetric Encryption Algorithms
- Post-Quantum Unforgeability in Symmetric Authentication or Authenticated Encryption Schemes
- Exploration of newly designed or modified Encryption, Authentication and Authenticated Encryption Constructions that claim Post-Quantum Security