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clean up the CRT notes

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brent saner 2025-09-02 00:23:38 -04:00
parent ce2081c811
commit 84838ce0c6
Signed by: bts
GPG Key ID: 8C004C2F93481F6B
3 changed files with 16 additions and 3 deletions
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1
.githooks/pre-commit/01-keymanual
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@ -6,3 +6,4 @@ set -e
cd "${PWD}/_ref"
asciidoctor -o ./KEY_GUIDE.html ./KEY_GUIDE.adoc
git add KEY_GUIDE.html
echo "Generated KEY_GUIDE.html"

11
_ref/KEY_GUIDE.html
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@ -635,7 +635,7 @@ pre.rouge .gs {
<h1>OpenSSH Key Structure Guide</h1>
<div class="details">
<span id="author" class="author">brent saner &lt;bts@square-r00t.net&gt;, https://r00t2.io</span><br>
<span id="revdate">Last updated 2025-09-01 23:58:24 -0400</span>
<span id="revdate">Last updated 2025-09-02 00:23:41 -0400</span>
</div>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
@ -1264,7 +1264,7 @@ ftSfkGNUzTzPFbF5iEukTvKm42a7F/I/ExMVgpN/eQxJ7+m5TOgja0KC1h5fCN4L
4.0.1.5 uint32 allocator for 4.0.1.5.0 (4 bytes)
4.0.1.5.0 private exponent ('d')
4.0.1.6 uint32 allocator for 4.0.1.6.0 (4 bytes)
4.0.1.6.0 CRT (Chinese Remainder Theorem) helper value ('q^(-1) % p')
4.0.1.6.0 CRT
4.0.1.7 uint32 allocator for 4.0.1.7.0 (4 bytes)
4.0.1.7.0 prime #1 ('p')
4.0.1.8 uint32 allocator for 4.0.1.8.0 (4 bytes)
@ -1289,9 +1289,16 @@ ftSfkGNUzTzPFbF5iEukTvKm42a7F/I/ExMVgpN/eQxJ7+m5TOgja0KC1h5fCN4L
<p><strong>Chunk 4.0:</strong> This is technically currently unused; upstream hardcodes to 1 (left zero-padded 0x01).</p>
</div>
<div class="paragraph">
<p><strong>Chunk 4.0.0.1.0, 4.0.1.4.0:</strong> This is almost always <code>65537</code> for a couple reasons. It&#8217;s the <a href="https://en.wikipedia.org/wiki/Fermat_number" target="_blank" rel="noopener">"Fermat Prime"</a> <em>F<sub>4</sub></em>.</p>
</div>
<div class="paragraph">
<p><strong>Chunk 4.0.0.1.0, 4.0.0.2.0, 4.0.1.3.0, 4.0.1.4.0:</strong> Note that the ordering of <code>e</code>/<code>n</code> in <strong>4.0.0</strong> is changed to <code>n</code>/<code>e</code> in <strong>4.0.1</strong>.</p>
</div>
<div class="paragraph">
<p><strong>Chunk 4.0.1.6.0:</strong> The CRT coefficient, or <a href="https://en.wikipedia.org/wiki/Chinese_remainder_theorem" target="_blank" rel="noopener">Chinese Remainder Theorem</a>, is a helper used during decryption and signing. It&#8217;s commonly referred to as <code>qnlv</code> or <em>inverse coefficient</em>.
The value for this chunk is the result of <code>q^(-1) % p</code>.</p>
</div>
<div class="paragraph">
<p><strong>Chunk 4.0.1.10:</strong> The padding used aligns the private key (<strong>4.0.1.0</strong> to <strong>4.0.1.9.0</strong>) to the cipher blocksize. For plaintext keys, a blocksize of 8 is used.</p>
</div>
</td>

7
_ref/rsa/private/v1/plain.adoc
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@ -43,7 +43,7 @@ Since plaintext/unencrypted keys do not have a cipher or KDF (as there's no encr
4.0.1.5 uint32 allocator for 4.0.1.5.0 (4 bytes)
4.0.1.5.0 private exponent ('d')
4.0.1.6 uint32 allocator for 4.0.1.6.0 (4 bytes)
4.0.1.6.0 CRT (Chinese Remainder Theorem) helper value ('q^(-1) % p')
4.0.1.6.0 CRT
4.0.1.7 uint32 allocator for 4.0.1.7.0 (4 bytes)
4.0.1.7.0 prime #1 ('p')
4.0.1.8 uint32 allocator for 4.0.1.8.0 (4 bytes)
@ -59,8 +59,13 @@ Since plaintext/unencrypted keys do not have a cipher or KDF (as there's no encr
*Chunk 4.0:* This is technically currently unused; upstream hardcodes to 1 (left zero-padded 0x01).
*Chunk 4.0.0.1.0, 4.0.1.4.0:* This is almost always `65537` for a couple reasons. It's the https://en.wikipedia.org/wiki/Fermat_number["Fermat Prime"^] __F~4~__.
*Chunk 4.0.0.1.0, 4.0.0.2.0, 4.0.1.3.0, 4.0.1.4.0:* Note that the ordering of `e`/`n` in *4.0.0* is changed to `n`/`e` in *4.0.1*.
*Chunk 4.0.1.6.0:* The CRT coefficient, or https://en.wikipedia.org/wiki/Chinese_remainder_theorem[Chinese Remainder Theorem^], is a helper used during decryption and signing. It's commonly referred to as `qnlv` or _inverse coefficient_.
The value for this chunk is the result of `q^(-1) % p`.
*Chunk 4.0.1.10:* The padding used aligns the private key (*4.0.1.0* to *4.0.1.9.0*) to the cipher blocksize. For plaintext keys, a blocksize of 8 is used.
====