This is a project that runs in the Lattice lab, starting from Hanlin Liu, who first envisioned the possibility of substituting LWE-based cryptography with LPN (spoiler alert we currently do not know how to achieve this goal). A significant goal is to construct a digital signature a la Dilithium at least in terms of performance.
Alas, the Fiat-Shamir with Abort technique does not work directly with LPN, although some folks have come up with variants of the LPN assumption to accommendate with this technqiue (e.g. (“Durandal: A Rank Metric Based Signature Scheme SpringerLink” n.d.)). We consider the status quo unsatisfactory.
Luckily, the MPC-in-the-Head branch is constantly being optimized, with the state-of-the-art proposed under the name “VOLE-in-the-Head” (Baum et al. 2023) in Crypto 2023. We tried this new framework on the RSD problem at the first moment. Anyway, this framework proves to be effective when proving small circuits, and our work is summarized in a PKC 2024 paper.
I have given three talks about this topic:
- One in the group meeting last year (by that time we call the project SPED). Slides
- One on AC 2023 at Guangzhou during Rump Session Slides
- One on PKC 2024 at Syndey Slides .