Parameter Selection

Other, random and misc
1

Hi, been deep diving into this paper out of curiosity how parameters are selected and optimized for a given circuit/DAG: https://eprint.iacr.org/2022/704.pdf , really insightful btw.

Looking at Defintion 9 on page 21,

Definition 9 (Noise Feasible Set) Let 𝒢, an FHE DAG such that 𝒢 = (V, L)
with L = {(·, ·, pi)}i∈[[1,|L|]], and let α be a failure probability. Let {σi}i∈|L|
be the standard deviation of the noise in the ciphertexts transiting on every edge of 𝒢. For
every edge i, we must have σi(x) ≤ tα (pi) which defines a subset of the search space

I understand this except what pi specifically relates to? Is it the modulus at every edge i?

2

It looks like it’s the message modulus. I did not read the paper though, just skim read it very quickly. A DAG is a direct acyclic graph and apparently the paper associates a DAG to a set of FHE operators, (whatever that means).