“ There was a bug in an OpenPGP library which finally gave us an excuse to tear encrypted email via PGP to shreds. Our special guest William Woodruff joined us to help explain the vuln and indulge our gnashing of teeth on why email was never meant to be encrypted and how other modern tools do the job much, much better.”
I dug into this once and the "theoretical ideal" of 3 originated in a 1950s paper about vacuum tube computers, which itself immediately backed off and said the choice of base 2 is frequently justified.
In this case, the context are {-1, 0, 1} weights in a LLM model, which I don't think is being used for any hardware efficiency argument. I think it's just quantizing weights into 3 states.
NIST P-256 curve seed came from the X9.62 specification drafted in 1997. It was provided by an NSA employee, Jerry Solinas, as an example seed among many other seeds, including those provided by Certicom. Read this for more details: https://eprint.iacr.org/2015/1018
I'm stuck on trying to work out what it would mean to de-lattice something. Would that transform a lattice basis into a standard vector space basis in R or something, or, like MOV, would it send the whole lattice to an element of some prime extension field?
In my mind's eye, it's cooler: it's like, you render the ciphertext as a raster image, and then "de-lattice" it to reveal the underlying plaintext, scanline by scanline.
i'm still working on understanding lattices better
but i can imagine, based on my own ignorance, creativity, and lack of correct understanding, would be some kind of factorization.
as I think while trying to better know what's a lattice, I imagine a lattice like a coordinate pair, but instead of each coordinate existing on a line, they exist on a binary tree (or some other directed graph explored from a root outwards without cycles)
which means you have two such binary-trees (not necessarily binary, but it's just easier to work with them seemingly)
and then you combine these into ONE lattice. so then, to de-lattice means to recover the binary trees.
but when I say binary tree I'm thinking about rational numbers (because stern broccott trees)
A lattice is like a vector space, but with exclusively integer coefficients. It's not a coordinate pair. If you think of vectors as coordinate pairs, a vector space is a (possibly unbounded) set of coordinate pairs. If you haven't done any linear algebra, a decent intuition would be mathematical objects like "the even numbers" or "the odd numbers", but substituting vectors (fixed-sized tuples of numbers) for scalars.
The record quantum computers can factor is 21 -- and that is by cheating by already knowing the factors are 3 and 7. There are other results that use special form composites which don't count.
So a QC can factor a 5 bit number with Shor's algorithm in 2023 (with some cheating). That record has not changed for 10+ years.
I publicly bet 8 years ago that nobody would factor the number 35 by 2030. I hope I'm proved wrong.
