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Add KaTeX support

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This commit is contained in:
Hendrik Eeckhaut
2025-05-13 21:36:02 +02:00
parent e4101bdd79
commit 7dd42235cc
5 changed files with 343 additions and 2 deletions
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4
README.md
View File

@@ -39,3 +39,7 @@ $ GIT_USER=<Your GitHub username> yarn deploy
```
If you are using GitHub pages for hosting, this command is a convenient way to build the website and push to the `gh-pages` branch.
https://docusaurus.io/docs/sidebar/autogenerated

50
docs/mpc/key_exchange.md Normal file
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@@ -0,0 +1,50 @@
# Key Exchange
In TLS, the first step towards obtaining TLS session keys is to compute a shared secret between the client and the server by running the [ECDH protocol](https://en.wikipedia.org/wiki/Elliptic-curve_Diffie–Hellman). The resulting shared secret in TLS terms is **called the pre-master secret `PMS`**.
With TLSNotary, at the end of the key exchange, the `Server` gets the `PMS` as usual. The `Prover` and the `Verifier`, jointly operating as the TLS client, compute additive shares of the `PMS`. This prevents either party from unilaterally sending or receiving messages with the `Server`. Subsequently, the authenticity and integrity of the messages are guaranteed to both the `Prover` and `Verifier`, while also keeping the plaintext hidden from the `Verifier`.
![](../diagrams/key_exchange.svg)
The 3-party ECDH protocol between the `Server` the `Prover` and the `Verifier` works as follows:
1. `Server` sends its public key $Q_b$ to `Prover`, and `Prover` forwards it to `Verifier`
2. `Prover` picks a random private key share $d_c$ and computes a public key share $Q_c = d_c * G$
3. `Verifier` picks a random private key share $d_n$ and computes a public key share $Q_n = d_n * G$
4. `Verifier` sends $Q_n$ to `Prover` who computes $Q_a = Q_c + Q_n $ and sends $Q_a$ to `Server`
5. `Prover` computes an EC point $(x_p, y_p) = d_c * Q_b$
6. `Verifier` computes an EC point $(x_q, y_q) = d_n * Q_b$
7. Addition of points $(x_p, y_p)$ and $(x_q, y_q)$ results in the coordinate $x_r$, which is `PMS`. (The coordinate $y_r$ is not used in TLS)
Using the notation from [here](https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Point_addition), our goal is to compute
$$
x_r = (\frac{y_q-y_p}{x_q-x_p})^2 - x_p - x_q
$$
in such a way that
1. Neither party learns the other party's $x$ value
2. Neither party learns $x_r$, only their respective shares of $x_r$.
We will use two maliciously secure protocols described on p.25 in the paper [Efficient Secure Two-Party Exponentiation](https://www.cs.umd.edu/~fenghao/paper/modexp.pdf):
- `A2M` protocol, which converts additive shares into multiplicative shares, i.e. given shares `a` and `b` such that `a + b = c`, it converts them into shares `d` and `e` such that `d * e = c`
- `M2A` protocol, which converts multiplicative shares into additive shares
We apply `A2M` to $y_q + (-y_p)$ to get $A_q * A_p$ and also we apply `A2M` to $x_q + (-x_p)$ to get $B_q * B_p$. Then the above can be rewritten as:
$$
x_r = (\frac{A_q}{B_q})^2 * (\frac{A_p}{B_p})^2 - x_p - x_q
$$
Then the first party locally computes the first factor and gets $C_q$, the second party locally computes the second factor and gets $C_p$. Then we can again rewrite as:
$$
x_r = C_q * C_p - x_p - x_q
$$
Now we apply `M2A` to $C_q * C_p$ to get $D_q + D_p$, which leads us to two final terms each of which is the share of $x_r$ of the respective party:
$$
x_r = (D_q - x_q) + (D_p - x_p)
$$

17
docusaurus.config.ts
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@@ -1,6 +1,8 @@
import { themes as prismThemes } from 'prism-react-renderer';
import type { Config } from '@docusaurus/types';
import type * as Preset from '@docusaurus/preset-classic';
import remarkMath from 'remark-math';
import rehypeKatex from 'rehype-katex';
// This runs in Node.js - Don't use client-side code here (browser APIs, JSX...)
@@ -41,6 +43,9 @@ const config: Config = {
// Remove this to remove the "edit this page" links.
editUrl:
'https://github.com/tlsnotary/landing-page',
// Enable math support in docs
remarkPlugins: [remarkMath],
rehypePlugins: [rehypeKatex],
},
blog: {
showReadingTime: true,
@@ -48,6 +53,8 @@ const config: Config = {
type: ['rss', 'atom'],
xslt: true,
},
remarkPlugins: [remarkMath],
rehypePlugins: [rehypeKatex],
// Please change this to your repo.
// Remove this to remove the "edit this page" links.
editUrl:
@@ -64,6 +71,16 @@ const config: Config = {
],
],
stylesheets: [
{
href: 'https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css',
type: 'text/css',
integrity:
'sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+',
crossorigin: 'anonymous',
},
],
themeConfig: {
// Replace with your project's social card
image: 'img/docusaurus-social-card.jpg',

270
package-lock.json generated
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@@ -14,7 +14,9 @@
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"prism-react-renderer": "^2.3.0",
"react": "^19.0.0",
"react-dom": "^19.0.0"
"react-dom": "^19.0.0",
"rehype-katex": "^7.0.1",
"remark-math": "^6.0.0"
},
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@@ -4558,6 +4560,12 @@
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"license": "MIT"
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"license": "MIT"
},
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"version": "4.0.4",
"resolved": "https://registry.npmjs.org/@types/mdast/-/mdast-4.0.4.tgz",
@@ -8628,6 +8636,55 @@
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}
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"vfile": "^6.0.0",
"vfile-message": "^4.0.0"
},
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"resolved": "https://registry.npmjs.org/hast-util-from-html-isomorphic/-/hast-util-from-html-isomorphic-2.0.0.tgz",
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"license": "MIT",
"dependencies": {
"@types/hast": "^3.0.0",
"hast-util-from-dom": "^5.0.0",
"hast-util-from-html": "^2.0.0",
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},
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"resolved": "https://registry.npmjs.org/hast-util-from-parse5/-/hast-util-from-parse5-8.0.3.tgz",
@@ -8648,6 +8705,19 @@
"url": "https://opencollective.com/unified"
}
},
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"license": "MIT",
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},
"funding": {
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"version": "4.0.0",
"resolved": "https://registry.npmjs.org/hast-util-parse-selector/-/hast-util-parse-selector-4.0.0.tgz",
@@ -8770,6 +8840,22 @@
"url": "https://github.com/sponsors/wooorm"
}
},
"node_modules/hast-util-to-text": {
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"resolved": "https://registry.npmjs.org/hast-util-to-text/-/hast-util-to-text-4.0.2.tgz",
"integrity": "sha512-KK6y/BN8lbaq654j7JgBydev7wuNMcID54lkRav1P0CaE1e47P72AWWPiGKXTJU271ooYzcvTAn/Zt0REnvc7A==",
"license": "MIT",
"dependencies": {
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"@types/unist": "^3.0.0",
"hast-util-is-element": "^3.0.0",
"unist-util-find-after": "^5.0.0"
},
"funding": {
"type": "opencollective",
"url": "https://opencollective.com/unified"
}
},
"node_modules/hast-util-whitespace": {
"version": "3.0.0",
"resolved": "https://registry.npmjs.org/hast-util-whitespace/-/hast-util-whitespace-3.0.0.tgz",
@@ -9757,6 +9843,31 @@
"graceful-fs": "^4.1.6"
}
},
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"resolved": "https://registry.npmjs.org/katex/-/katex-0.16.22.tgz",
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"funding": [
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"https://github.com/sponsors/katex"
],
"license": "MIT",
"dependencies": {
"commander": "^8.3.0"
},
"bin": {
"katex": "cli.js"
}
},
"node_modules/katex/node_modules/commander": {
"version": "8.3.0",
"resolved": "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz",
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"license": "MIT",
"engines": {
"node": ">= 12"
}
},
"node_modules/keyv": {
"version": "4.5.4",
"resolved": "https://registry.npmjs.org/keyv/-/keyv-4.5.4.tgz",
@@ -10237,6 +10348,25 @@
"url": "https://opencollective.com/unified"
}
},
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"version": "3.0.0",
"resolved": "https://registry.npmjs.org/mdast-util-math/-/mdast-util-math-3.0.0.tgz",
"integrity": "sha512-Tl9GBNeG/AhJnQM221bJR2HPvLOSnLE/T9cJI9tlc6zwQk2nPk/4f0cHkOdEixQPC/j8UtKDdITswvLAy1OZ1w==",
"license": "MIT",
"dependencies": {
"@types/hast": "^3.0.0",
"@types/mdast": "^4.0.0",
"devlop": "^1.0.0",
"longest-streak": "^3.0.0",
"mdast-util-from-markdown": "^2.0.0",
"mdast-util-to-markdown": "^2.1.0",
"unist-util-remove-position": "^5.0.0"
},
"funding": {
"type": "opencollective",
"url": "https://opencollective.com/unified"
}
},
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"version": "3.0.0",
"resolved": "https://registry.npmjs.org/mdast-util-mdx/-/mdast-util-mdx-3.0.0.tgz",
@@ -11036,6 +11166,81 @@
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"license": "MIT"
},
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"type": "GitHub Sponsors",
"url": "https://github.com/sponsors/unifiedjs"
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@@ -15266,6 +15471,25 @@
"node": ">=6"
}
},
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@@ -15371,6 +15595,22 @@
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@@ -16929,6 +17169,20 @@
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@@ -16968,6 +17222,20 @@
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4
package.json
View File

@@ -21,7 +21,9 @@
"clsx": "^2.0.0",
"prism-react-renderer": "^2.3.0",
"react": "^19.0.0",
"react-dom": "^19.0.0"
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"rehype-katex": "^7.0.1",
"remark-math": "^6.0.0"
},
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