Top personal takeaways are:
- Lattice-based crypto is the perfect sub-direction to contribute in
- Vadim's remark on state of lattice: KEM, signatures, FHE, Functional commitments, ZKPs. Some reduces to more structured Lattices than others for efficiency.
- Confidence in lattice hardness, but IP issue is somewhat tricky.
- The most convincing slide presents the CNSA timeline for mandatory transition to PQC by 2033 -- not a matter of if or when, it's gonna happen!
- Missing:
- threshold crypto (rejection sampling on individual share doesn't guarantee successful secret reconstruction?)
- scripts for parameter selections, the concretely efficient schemes such as LaBRADOR [BS22] uses lots of heuristics.
- Many new assumptions: k-R-ISIS [ACLM+22], BASIS [Wu], especially newer, more compact scheme relies on more strucutres, and these assumptions need more investigations.
- Implementations:
- Gregor at IBM Zurich (and his team) has plans to open source more lattice implementations.
- Russell Lai also seems to have coded up many primitives.
- Chiesa suggested we should spend enough time thinking about the right level of abstraction and API design, and avoid being a hodge-podge of tools.
- Vadim's remark on state of lattice: KEM, signatures, FHE, Functional commitments, ZKPs. Some reduces to more structured Lattices than others for efficiency.
- Interesting perspective: usually we need abstraction to generalize a long list of concrete instantiations, in crypto, we (mostly) only have integer factorization, DLog, and lattice, yet we invented so many higher-level primitives for composing new constructions. It's not a problem, but sometimes in Lattice, leaky abstraction occurs all the time (e.g. use a specific/concrete property of lattice in construction of a FHE scheme).
- Knowledge soundness extractors are highly non-trivial, usually with loose-bounds -- this might affect composability down the road (without generic composer/extractors). E.g. quantum rewinding very different, as measuring the state collapses the quantum states.
- Should try more high-assurance or formally verified toolchains.
Miscellaneous notes: