How do we know what we know? -- as a mathematical question. Designing knowledge assumptions and asymmetric encryption schemes in lattice-based cryptography., Yuxi Zheng, UG '23 (2279885)
Assumptions of various hard problems are essential in modern cryptography. There is a group of assumptions known as the “knowledge assumptions.” They assume that in order for the adversary to break a scheme, it must possess some form of secret knowledge. And there would be an extractor that acts like the subconsciousness of the adversary, which could extract that secret knowledge. Knowledge assumptions are very useful in constructing encryption scheme that have better provable security guarantees. Previous work has been done exploiting knowledge assumptions to construct encryption scheme in group-based cryptography. In the spirit of post-quantum cryptography, i.e. constructing schemes that are post-quantum secure, we try to propose lattice-based knowledge assumptions and lattice-based encryption scheme based on those assumptions.