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2

Here is the optimization in more detail. Start with $[\bar{A} \mid I_n \mid G']$ where $\bar{A} \in \mathbb{Z}_q^{n \times n}$ and $G = [I_n \mid G']$ (where $I_n$ is the $n$-by-$n$ identity matrix). Note that the concrete gadget matrices $G$ constructed in the paper already contain an identity submatrix (up to reordering of columns). But in general, $G$ ...

3

As a quick aside, while Hermite refers to the same person, "Hermitian" means something different for matrices than "Hermite Normal Form". HNF is essentially "Row Echelon Form/Gaussian Elimination where you can't divide". HNF Optimization: First, we can discuss "Reducing the columns of $E$ modulo the HNF", which does ...

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Apologies for the belated reply. I've found that the Simons Institute seminar on "Lattices: Algorithms, Complexity, and Cryptography Boot Camp" was pretty good as a generic intro to lattice crypto. [Thomas mentioned something close to this, but I wanted to be more specific.] This event happened Jan. 21 – Jan. 24, 2020 (just a month or so before ...

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If one expands the discussion to include LWE-type schemes, isn't Module-LWE naturally a "non-commutative" hardness assumption which has practical applications? For example, the Kyber NIST PQC candidate is an MLWE scheme, and is a round 3 finalist. In general though, I mostly see lattices over "exotic" (at least more so than things like ...

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