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draft-davidben-tls-merkle-tree-certs.html

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</tr></thead>
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<tfoot><tr>
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<td class="left">Benjamin, et al.</td>
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<td class="center">Expires 8 May 2026</td>
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<td class="center">Expires 9 May 2026</td>
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<td class="right">[Page]</td>
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</table>
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<dd class="internet-draft">draft-davidben-tls-merkle-tree-certs-latest</dd>
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<dt class="label-published">Published:</dt>
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<dd class="published">
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<time datetime="2025-11-04" class="published">4 November 2025</time>
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<time datetime="2025-11-05" class="published">5 November 2025</time>
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</dd>
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<dt class="label-intended-status">Intended Status:</dt>
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<dd class="intended-status">Experimental</dd>
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<dt class="label-expires">Expires:</dt>
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<dd class="expires"><time datetime="2026-05-08">8 May 2026</time></dd>
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<dd class="expires"><time datetime="2026-05-09">9 May 2026</time></dd>
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<dt class="label-authors">Authors:</dt>
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<div class="author">
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time. It is inappropriate to use Internet-Drafts as reference
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material or to cite them other than as "work in progress."<a href="#section-boilerplate.1-3" class="pilcrow"></a></p>
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<p id="section-boilerplate.1-4">
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This Internet-Draft will expire on 8 May 2026.<a href="#section-boilerplate.1-4" class="pilcrow"></a></p>
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This Internet-Draft will expire on 9 May 2026.<a href="#section-boilerplate.1-4" class="pilcrow"></a></p>
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</section>
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<a href="#section-4.1" class="section-number selfRef">4.1. </a><a href="#name-definition-of-a-subtree" class="section-name selfRef">Definition of a Subtree</a>
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</h3>
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<p id="section-4.1-1">Given an ordered list of <code>n</code> inputs, <code>D_n = {d[0], d[1], ..., d[n-1]}</code>, <span><a href="https://rfc-editor.org/rfc/rfc9162#section-2.1.1" class="relref">Section 2.1.1</a> of [<a href="#RFC9162" class="cite xref">RFC9162</a>]</span> defines the Merkle Tree via the Merkle Tree Hash <code>MTH(D_n)</code>.<a href="#section-4.1-1" class="pilcrow"></a></p>
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<p id="section-4.1-2">A <em>subtree</em> of this Merkle Tree is defined by two integers, <code>start</code> and <code>end</code>, such that:<a href="#section-4.1-2" class="pilcrow"></a></p>
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<p id="section-4.1-2">A <em>subtree</em> of this Merkle Tree is itself a Merkle Tree, defined by <code>MTH(D[start:end])</code>. <code>start</code> and <code>end</code> are integers such that:<a href="#section-4.1-2" class="pilcrow"></a></p>
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<ul class="normal">
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<li class="normal" id="section-4.1-3.1">
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<p id="section-4.1-3.1.1"><code>0 &lt;= start &lt; end &lt;= n</code><a href="#section-4.1-3.1.1" class="pilcrow"></a></p>
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</li>
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<p id="section-4.1-4">Note that, if <code>start</code> is zero, the second condition is always true.<a href="#section-4.1-4" class="pilcrow"></a></p>
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<p id="section-4.1-5">A subtree is itself a Merkle Tree, defined by <code>MTH(D[start:end])</code>. In the context of a single Merkle Tree, the subtree defined by <code>start</code> and <code>end</code> is denoted by half-open interval <code>[start, end)</code>. It contains the entries whose indices are in that half-open interval.<a href="#section-4.1-5" class="pilcrow"></a></p>
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<p id="section-4.1-5">In the context of a single Merkle Tree, the subtree defined by <code>start</code> and <code>end</code> is denoted by half-open interval <code>[start, end)</code>. It contains the entries whose indices are in that half-open interval.<a href="#section-4.1-5" class="pilcrow"></a></p>
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<p id="section-4.1-6">The <em>size</em> of the subtree is <code>end - start</code>. If the subtree's size is a power of two, it is said to be <em>full</em>, otherwise it is said to be <em>partial</em>.<a href="#section-4.1-6" class="pilcrow"></a></p>
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<p id="section-4.1-7">If a subtree is full, then it is directly contained in the tree of hash operations in <code>MTH(D_n)</code> for <code>n &gt;= end</code>.<a href="#section-4.1-7" class="pilcrow"></a></p>
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<p id="section-4.1-8">If a subtree is partial, it is directly contained in <code>MTH(D_n)</code> only if <code>n = end</code>.<a href="#section-4.1-8" class="pilcrow"></a></p>

draft-davidben-tls-merkle-tree-certs.txt

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Network Working Group D. Benjamin
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Internet-Draft Google LLC
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Intended status: Experimental D. O'Brien
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Expires: 8 May 2026
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Expires: 9 May 2026
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B. E. Westerbaan
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L. Valenta
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Cloudflare
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F. Valsorda
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Geomys
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4 November 2025
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Merkle Tree Certificates
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time. It is inappropriate to use Internet-Drafts as reference
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material or to cite them other than as "work in progress."
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This Internet-Draft will expire on 8 May 2026.
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This Internet-Draft will expire on 9 May 2026.
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Copyright Notice
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Section 2.1.1 of [RFC9162] defines the Merkle Tree via the Merkle
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Tree Hash MTH(D_n).
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A _subtree_ of this Merkle Tree is defined by two integers, start and
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end, such that:
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A _subtree_ of this Merkle Tree is itself a Merkle Tree, defined by
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MTH(D[start:end]). start and end are integers such that:
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* 0 <= start < end <= n
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* start is a multiple of BIT_CEIL(end - start)
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Note that, if start is zero, the second condition is always true.
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A subtree is itself a Merkle Tree, defined by MTH(D[start:end]). In
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the context of a single Merkle Tree, the subtree defined by start and
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end is denoted by half-open interval [start, end). It contains the
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entries whose indices are in that half-open interval.
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In the context of a single Merkle Tree, the subtree defined by start
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and end is denoted by half-open interval [start, end). It contains
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the entries whose indices are in that half-open interval.
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The _size_ of the subtree is end - start. If the subtree's size is a
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power of two, it is said to be _full_, otherwise it is said to be

index.html

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<tr>
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<td><a href="subtree-dfn/draft-davidben-tls-merkle-tree-certs.html" class="html draft-davidben-tls-merkle-tree-certs" title="Merkle Tree Certificates (HTML)">Merkle Tree Certificates</a></td>
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<td><a href="subtree-dfn/draft-davidben-tls-merkle-tree-certs.txt" class="txt draft-davidben-tls-merkle-tree-certs" title="Merkle Tree Certificates (Text)">plain text</a></td>
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<td><a href="https://author-tools.ietf.org/api/iddiff?url_1=https://davidben.github.io/merkle-tree-certs/draft-davidben-tls-merkle-tree-certs.txt&amp;url_2=https://davidben.github.io/merkle-tree-certs/subtree-dfn/draft-davidben-tls-merkle-tree-certs.txt" class="diff draft-davidben-tls-merkle-tree-certs">diff with main</a></td>
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<td>same as main</td>
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</tr>
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</table>
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<h2>Preview for branch <a href="lukevalenta-patch-1">lukevalenta-patch-1</a></h2>
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<tr>
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<td><a href="subtree-bit-ceil/draft-davidben-tls-merkle-tree-certs.html" class="html draft-davidben-tls-merkle-tree-certs" title="Merkle Tree Certificates (HTML)">Merkle Tree Certificates</a></td>
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<td><a href="subtree-bit-ceil/draft-davidben-tls-merkle-tree-certs.txt" class="txt draft-davidben-tls-merkle-tree-certs" title="Merkle Tree Certificates (Text)">plain text</a></td>
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<td><a href="https://author-tools.ietf.org/api/iddiff?url_1=https://davidben.github.io/merkle-tree-certs/draft-davidben-tls-merkle-tree-certs.txt&amp;url_2=https://davidben.github.io/merkle-tree-certs/subtree-bit-ceil/draft-davidben-tls-merkle-tree-certs.txt" class="diff draft-davidben-tls-merkle-tree-certs">diff with main</a></td>
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<h2>Preview for branch <a href="proof-explain">proof-explain</a></h2>

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