Documentation - Centralized Telescope: Parameters #103
Conversation
curiecrypt
force-pushed
the
curiecrypt/doc-centralized-param
branch
from
747148f to
57b2b07
Compare
curiecrypt
force-pushed
the
curiecrypt/doc-centralized-param
branch
from
0c5f1b6 to
e7a719e
Compare
| $$ | ||
|
|
||
| Then, we check the prover's set size. | ||
| If $n_p \geq \frac{d^2 \cdot \log{e}}{9 \cdot (\lambda_{rel}^{(2)} + 2)}$, we abort the process. |
There was a problem hiding this comment.
These are assumptions in the paper from theorem 13/14 for the soundness and completeness bounds to be valid. We added them in code as we noticed that Case 1/2/3 and Small/Intermediary/High did not necessarily respect these. @curiecrypt must have added them here for exhaustivity
| - If $s_1 < 1 \implies \lambda_{rel}^{(1)} \coloneqq \bot$, else $\implies \lambda_{rel}^{(1)} \coloneqq \mathsf{min}(\lambda_{rel}, s_1)$ | ||
| - If $s_2 < 1 \implies \lambda_{rel}^{(2)} \coloneqq \bot$, else $\implies \lambda_{rel}^{(2)} \coloneqq \mathsf{min}(\lambda_{rel}, s_2)$ | ||
|
|
||
| ### Cases |
There was a problem hiding this comment.
The cases here don't really correspond to small, intermediate and high cases that you outlined in strategy.md. The intermediate case there implies the number of repetitions r > 1, but cases 2 and 3 in this file can in principle set r = 1. So, cases 2 and 3 here really cover both intermediate and high cases but in different ways, depending on how u and lam_rel^(2) compare. Suggest changing wording.
There was a problem hiding this comment.
@curiecrypt Just precise here that we use a different comparison for the intermediary and high cases instead of lambda^2 <= u < lambda^3 and u >= lambda^3
There was a problem hiding this comment.
I think the documentation should provide a bridging content between the code and the theory. I tried to create an intermediate-level text for someone who looks at the code first. Matching structure with code is more convenient to understand the content of the paper, I guess.
Co-authored-by: Tolik Zinovyev <[email protected]>
| - If $s_1 < 1 \implies \lambda_{rel}^{(1)} \coloneqq \bot$, else $\implies \lambda_{rel}^{(1)} \coloneqq \mathsf{min}(\lambda_{rel}, s_1)$ | ||
| - If $s_2 < 1 \implies \lambda_{rel}^{(2)} \coloneqq \bot$, else $\implies \lambda_{rel}^{(2)} \coloneqq \mathsf{min}(\lambda_{rel}, s_2)$ | ||
|
|
||
| ### Cases |
There was a problem hiding this comment.
@curiecrypt Just precise here that we use a different comparison for the intermediary and high cases instead of lambda^2 <= u < lambda^3 and u >= lambda^3
| $$ | ||
|
|
||
| Then, we check the prover's set size. | ||
| If $n_p \geq \frac{d^2 \cdot \log{e}}{9 \cdot (\lambda_{rel}^{(2)} + 2)}$, we abort the process. |
There was a problem hiding this comment.
These are assumptions in the paper from theorem 13/14 for the soundness and completeness bounds to be valid. We added them in code as we noticed that Case 1/2/3 and Small/Intermediary/High did not necessarily respect these. @curiecrypt must have added them here for exhaustivity
Co-authored-by: Raphael <[email protected]>
Content
Documentation of parameter setup for the centralized telescope.
This PR includes:
src/centralized_telescope/params.rsis updated to include doc links to related sections.Pre-submit checklist
Issue(s)
Blocked by #142
Closes #102