Investigate "Accurate BGV Parameters Selection: Accounting for Secret and Public Key Dependencies in Average-Case Analysis"

**Accurate BGV Parameters Selection: Accounting for Secret and Public Key Dependencies in Average-Case Analysis**
_Beatrice Biasioli, Chiara Marcolla, Nadir Murru, Matilda Urani_
> The Brakerski-Gentry-Vaikuntanathan (BGV) scheme is one of the most significant fully homomorphic encryption (FHE) schemes. It belongs to a class of FHE schemes whose security is based on the presumed intractability of the Learning with Errors (LWE) problem and its ring variant (RLWE). Such schemes deal with a quantity, called noise, which increases each time a homomorphic operation is performed. Specifically, in order for the scheme to work properly, it is essential that the noise remains below a certain threshold throughout the process. For BGV, this threshold strictly depends on the ciphertext modulus, which is one of the initial parameters whose selection heavily affects both the efficiency and security of the scheme. In this paper, we provide a new method to estimate noise growth, closely aligning with experimental results and forming the basis for parameter selection that ensures correctness and improves efficiency.

https://arxiv.org/abs/2504.18597

Upon skimming it, I wonder to what the claim of being implementation-independent really means here?
"In this paper, we propose the first average-case noise analysis for BGV that does not provide underestimates, taking in account the dependencies introduced by the common secret and public key. [...] A related average-case analysis for the BGV scheme is presented in [Optimisations and Tradeoffs for HElib], where the authors develop a noise estimation method tailored to the specific implemen-tation of BGV in HElib [..]. In contrast, our work proposes a general analysis that does not depend on the specific library and instead focuses on capturing the structural dependencies among the errors."