Update proven security to include IOP terms
Al-Kindi-0 opened this issue · comments
The way we compute the proven security in get_proven_security
takes into account only the FRI soundness error part
I believe the update expression should be like:
where:
-
$H$ is the trace domain of size$k$ -
$D$ is the LDE domain of size$n$ $k^+ := k + 2$ -
$L^+ := \frac{m+0.5}{\sqrt{\rho^+}}$ where$m\geq 3$ is the Johnson proximity parameter which for simiplicity can be taken to be equal to$3$ and$\rho^+ := \frac{k^+}{n}$ -
$\mathbb{F}$ is the extension field. -
$\epsilon_{FRI}$ is the soundness error bound for FRI run with proximity parameter$\theta^+ := 1 - \alpha^+ := 1 - (1 + \frac{1}{2m})\cdot \sqrt{\rho^+}$ -
$d$ is the number of constraint composition column polynomials.
![Screen Shot 2023-07-28 at 12 08 46 PM](https://user-images.githubusercontent.com/15272444/256912773-ff5153d2-39ed-4278-a35b-1cb7aa293b6b.png)
Not sure I'm reading this right; it looks like you're saying constraint composition column polynomials
is the number of segment polynomials?
Ulrich defines
Closed by #215.