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Add Shamir's Secret Sharing notes, update templates

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arnaucube
2022-05-13 20:24:59 +02:00
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@@ -72,7 +72,7 @@ Let $(z_0, y_0), (z_1, y_1), …, (z_k, y_k)$ be the points that we want to
The <em>commitment</em> to the polynomial stands the same than for single proofs: $c=[p(\tau)]_1$.</p>
<p>For the evaluation proof, while in the single proofs we compute $q(x) = \frac{p(x)-y}{x-z}$, we will replace $y$ and $x-z$ by the following two polynomials.
The constant $y$ is replaced by a polynomial that has roots at all the points that we want to prove. This is achieved by computing the <a href="https://en.wikipedia.org/wiki/Lagrange_polynomial">Lagrange interpolation</a> for the given set of points:</p>
The constant $y$ is replaced by a polynomial that has roots at all the points that we want to prove. This is achieved by computing the <a href="/blog/shamir-secret-sharing.html#lagrange-polynomial%20interpolation">Lagrange interpolation</a> for the given set of points:</p>
<p>$$
I(x) = \sum_{j=0}^k y_j l_j(x)\newline
@@ -188,6 +188,22 @@ The problem with Merkle Trees is that the proof size grows linearly with the siz
console.log(theme);
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hElem.innerHTML = "<a style='text-decoration:none;color:black;' href='#"+hElem.id+"'>"+hElem.innerHTML+"</a>";
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tagLinks("h2");
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tagLinks("h4");
tagLinks("h5");
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