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docs/src/intro.md

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 ## 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.