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<ahref="#section-4.1" class="section-number selfRef">4.1. </a><ahref="#name-definition-of-a-subtree" class="section-name selfRef">Definition of a Subtree</a>
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<pid="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><ahref="https://rfc-editor.org/rfc/rfc9162#section-2.1.1" class="relref">Section 2.1.1</a> of [<ahref="#RFC9162" class="cite xref">RFC9162</a>]</span> defines the Merkle Tree via the Merkle Tree Hash <code>MTH(D_n)</code>.<ahref="#section-4.1-1" class="pilcrow">¶</a></p>
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<pid="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:<ahref="#section-4.1-2" class="pilcrow">¶</a></p>
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<pid="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:<ahref="#section-4.1-2" class="pilcrow">¶</a></p>
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<ulclass="normal">
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<liclass="normal" id="section-4.1-3.1">
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<pid="section-4.1-3.1.1"><code>0 <= start < end <= n</code><ahref="#section-4.1-3.1.1" class="pilcrow">¶</a></p>
<pid="section-4.1-4">Note that, if <code>start</code> is zero, the second condition is always true.<ahref="#section-4.1-4" class="pilcrow">¶</a></p>
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<pid="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.<ahref="#section-4.1-5" class="pilcrow">¶</a></p>
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<pid="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.<ahref="#section-4.1-5" class="pilcrow">¶</a></p>
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<pid="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>.<ahref="#section-4.1-6" class="pilcrow">¶</a></p>
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<pid="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 >= end</code>.<ahref="#section-4.1-7" class="pilcrow">¶</a></p>
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<pid="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>.<ahref="#section-4.1-8" class="pilcrow">¶</a></p>
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<td><ahref="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><ahref="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><ahref="https://author-tools.ietf.org/api/iddiff?url_1=https://davidben.github.io/merkle-tree-certs/draft-davidben-tls-merkle-tree-certs.txt&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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</table>
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<h2>Preview for branch <ahref="lukevalenta-patch-1">lukevalenta-patch-1</a></h2>
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<td><ahref="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><ahref="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>same as main</td>
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<td><ahref="https://author-tools.ietf.org/api/iddiff?url_1=https://davidben.github.io/merkle-tree-certs/draft-davidben-tls-merkle-tree-certs.txt&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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</table>
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<h2>Preview for branch <ahref="proof-explain">proof-explain</a></h2>
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