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proof-explain/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 18 April 2026</td>
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<td class="center">Expires 19 April 2026</td>
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<td class="right">[Page]</td>
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</tr></tfoot>
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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="2025-10-15" class="published">15 October 2025</time>
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<time datetime="2025-10-16" class="published">16 October 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="2026-04-18">18 April 2026</time></dd>
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<dd class="expires"><time datetime="2026-04-19">19 April 2026</time></dd>
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<dt class="label-authors">Authors:</dt>
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<dd class="authors">
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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 18 April 2026.<a href="#section-boilerplate.1-4" class="pilcrow"></a></p>
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This Internet-Draft will expire on 19 April 2026.<a href="#section-boilerplate.1-4" class="pilcrow"></a></p>
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</section>
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</div>
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<div id="copyright">
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<a href="#name-an-example-subtree-consiste" class="selfRef">An example subtree consistency proof for a subtree that is directly contained in the full tree</a>
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</figcaption></figure>
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</div>
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<p id="section-4.4.2-3">The subtree consistency proof for <code>[8, 13)</code> and a tree of size 14 contains <code>MTH({d[12]})</code>, <code>MTH({d[12]})</code>, <code>MTH(D[8:12])</code>, and <code>MTH(D[0:8])</code>, depicted in <a href="#fig-subtree-consistency-example-2" class="auto internal xref">Figure 8</a>. <code>[8, 13)</code> is not directly contained in the tree, so the proof must include sufficient nodes to reconstruct both hashes.<a href="#section-4.4.2-3" class="pilcrow"></a></p>
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<p id="section-4.4.2-3">The subtree consistency proof for <code>[8, 13)</code> and a tree of size 14 contains <code>MTH({d[12]})</code>, <code>MTH({d[13]})</code>, <code>MTH(D[8:12])</code>, and <code>MTH(D[0:8])</code>, depicted in <a href="#fig-subtree-consistency-example-2" class="auto internal xref">Figure 8</a>. <code>[8, 13)</code> is not directly contained in the tree, so the proof must include sufficient nodes to reconstruct both hashes.<a href="#section-4.4.2-3" class="pilcrow"></a></p>
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<span id="name-an-example-subtree-consisten"></span><div id="fig-subtree-consistency-example-2">
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<p id="appendix-B.3-1">A subtree consistency proof for <code>[start, end)</code> and the tree of <code>n</code> elements is similar to an inclusion proof for element <code>end - 1</code>. If one starts from <code>end - 1</code>'s hash, incorporating the whole inclusion proof should reconstruct <code>root_hash</code> and incorporating a subset of the inclusion proof should reconstruct <code>node_hash</code>. Thus <code>end - 1</code>'s hash and this inclusion proof can prove consistency. A subtree consistency proof in this document applies two optimizations over this construction:<a href="#appendix-B.3-1" class="pilcrow"></a></p>
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<ol start="1" type="1" class="normal type-1" id="appendix-B.3-2">
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<li id="appendix-B.3-2.1">
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<p id="appendix-B.3-2.1.1">Instead of starting at level 0 with <code>end - 1</code>, the proof can start at a higher level. Any ancestor of <code>end - 1</code> shared by both the subtree and the overall tree will <code>node_hash</code> and <code>root_hash</code>. Use the highest level with a commmon ancestor. This truncates the inclusion proof portion of the consistency proof.<a href="#appendix-B.3-2.1.1" class="pilcrow"></a></p>
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<p id="appendix-B.3-2.1.1">Instead of starting at level 0 with <code>end - 1</code>, the proof can start at a higher level. Any ancestor of <code>end - 1</code> shared by both the subtree and the overall tree is a valid starting node to reconstruct <code>node_hash</code> and <code>root_hash</code>. Use the highest level with a commmon ancestor. This truncates the inclusion proof portion of the consistency proof.<a href="#appendix-B.3-2.1.1" class="pilcrow"></a></p>
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</li>
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<li id="appendix-B.3-2.2">
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<p id="appendix-B.3-2.2.1">If this starting node is the entire subtree, omit its hash from the consistency proof. The verifier is assumed to already know <code>node_hash</code>.<a href="#appendix-B.3-2.2.1" class="pilcrow"></a></p>

proof-explain/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: 18 April 2026
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Expires: 19 April 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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16 October 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 18 April 2026.
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This Internet-Draft will expire on 19 April 2026.
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Copyright Notice
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is directly contained in the full tree
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The subtree consistency proof for [8, 13) and a tree of size 14
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contains MTH({d[12]}), MTH({d[12]}), MTH(D[8:12]), and MTH(D[0:8]),
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contains MTH({d[12]}), MTH({d[13]}), MTH(D[8:12]), and MTH(D[0:8]),
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depicted in Figure 8. [8, 13) is not directly contained in the tree,
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so the proof must include sufficient nodes to reconstruct both
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hashes.
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1. Instead of starting at level 0 with end - 1, the proof can start
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at a higher level. Any ancestor of end - 1 shared by both the
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subtree and the overall tree will node_hash and root_hash. Use
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the highest level with a commmon ancestor. This truncates the
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inclusion proof portion of the consistency proof.
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subtree and the overall tree is a valid starting node to
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reconstruct node_hash and root_hash. Use the highest level with
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a commmon ancestor. This truncates the inclusion proof portion
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of the consistency proof.
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2. If this starting node is the entire subtree, omit its hash from
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the consistency proof. The verifier is assumed to already know

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