From 7291be1689532b466f2a4928dea7b40482483363 Mon Sep 17 00:00:00 2001 From: Arnaud Bailly Date: Tue, 1 Oct 2024 14:38:53 +0200 Subject: [PATCH] Update text --- docs/src/intro.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/src/intro.md b/docs/src/intro.md index 3aa88593..09f8ac39 100644 --- a/docs/src/intro.md +++ b/docs/src/intro.md @@ -2,13 +2,13 @@ ## Definition -_Approximate Lower Bound Arguments_ are a form of cryptographic certificates that allow a _prover_ to convince a _verifier_ they know some set of elements by providing only a small subset of those elements. More formally, given some set of _unique_ elements, and some bounds \(n_p\) and \(n_f\), where \(n_p > n_f\), about the size of this set, ALBA provides an algorithm that allows to build a _proof_ they know _at least_ \(n_f\) elements, where the proof size is a constant value derived from the \(\frac{n_p}{n_f}\) ratio. +_Approximate Lower Bound Arguments_ are a form of cryptographic certificates that allow a _prover_ to convince a _verifier_ they know some set of elements by providing only a small subset of those elements. More formally, given some set of _unique_ elements, and some bounds \\(n_p\\) and \\(n_f\\), where \\(n_p > n_f\\), about the size of this set, ALBA provides an algorithm that allows to build a _proof_ they know _at least_ \\(n_f\\) elements, where the proof size is a constant value derived from the \\(\frac{n_p}{n_f}\\) ratio. -The algorithm provides the following guarantees, given the prover has \(S_p\) elements and a security parameter \(\lambda\): +The algorithm provides the following guarantees, given the prover has \\(S_p\\) elements and a security parameter \\(\lambda\\): -* if \(|S_p| \geq n_p\) then the prover has a probability lower than \(2^{-128}\) of _failure_ to build a proof, or in other words they are sure to find one, -* if \(|S_p| \leq n_f\) then the prover has a probability lower than \(2^{-128}\) of _success_ to build a proof, -* in between those 2 bounds, the probability of being able to build a proof drops exponentially (see our [simulation](#simulation) page for a graphical exploration of this probability). +* if \\(|S_p| \geq n_p\\) then the prover has a probability lower than \\(2^{-\lambda}\\) of _failure_ to build a proof, or in other words they are sure to find one, +* if \\(|S_p| \leq n_f\\) then the prover has a probability lower than \\(2^{-\lambda}\\) of _success_ to build a proof, +* in between those 2 bounds, the probability of being able to build a proof drops exponentially (see our [simulation](./simulation.md) page for a graphical exploration of this probability). Details of the theory behind this construction are beyond the scope of this introduction and can be found in the paper.