<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>Certificates · XB Field Notes</title><link>https://hk.xbcatm.com/tags/certificates/</link><description>Illustrated field notes on HTTP, DNS, TLS, Caddy, SSH, releases, and recovery.</description><generator>Hugo</generator><language>en-us</language><atom:link href="https://hk.xbcatm.com/tags/certificates/index.xml" rel="self" type="application/rss+xml"/><item><title>Certificate transparency makes issuance observable</title><link>https://hk.xbcatm.com/posts/tls-certificate-transparency-not-a-secret/</link><pubDate>Wed, 03 Nov 2027 00:00:00 +0000</pubDate><guid>https://hk.xbcatm.com/posts/tls-certificate-transparency-not-a-secret/</guid><description>Distinguish SCT promises, Merkle inclusion, and append-only consistency; test a three-leaf proof without claiming that CT establishes issuance authorization.</description><content:encoded>&lt;p&gt;Certificate Transparency makes public TLS certificate issuance observable. It does not determine whether a domain owner authorized an issuance, replace certificate-chain validation, or guarantee that every certificate everywhere is logged. A misissued certificate can have valid transparency evidence. The benefit is a public trail that monitors and affected owners can investigate.&lt;/p&gt;
&lt;h2 id="a-promise-is-not-an-inclusion-proof"&gt;A promise is not an inclusion proof&lt;/h2&gt;
&lt;p&gt;An SCT, or Signed Certificate Timestamp, is a log&amp;rsquo;s signed promise to incorporate a submitted certificate or precertificate within its Maximum Merge Delay. It is not another certificate and is not itself proof that the entry already exists in the tree. Its timestamp records the log&amp;rsquo;s statement, not necessarily the exact issuance instant.&lt;/p&gt;
&lt;p&gt;A Merkle inclusion proof connects a particular serialized leaf to a particular tree root and size. The verifier must authenticate that root through the relevant signed log statement and trusted log key. Accepting whatever root accompanies an untrusted proof establishes no useful external fact: an attacker can construct an entirely different tree.&lt;/p&gt;
&lt;p&gt;Consistency proofs answer another question: whether a later tree extends an earlier tree without changing its existing prefix. One inclusion proof cannot establish that history. Signed checkpoints, consistency verification, and comparisons between independently observed views help expose a log that equivocates. Hashes make alterations detectable under these checks; they do not physically prevent a malicious operator from changing data.&lt;/p&gt;
&lt;p&gt;Chrome applies its own CT policy to publicly trusted TLS certificates, considering SCT delivery, accepted log states, counts, and operator diversity. That is not equivalent to searching a public log during every page load, nor to deciding whether the owner requested the certificate. RFC 9162 specifies version 2 and obsoletes RFC 6962; publication alone does not establish which protocol a particular deployed log supports.&lt;/p&gt;
&lt;h2 id="when-it-breaks"&gt;When it breaks&lt;/h2&gt;
&lt;p&gt;A valid SCT from an unacceptable log, an insufficient set of SCTs, or an incorrect delivery mechanism may fail the target client&amp;rsquo;s policy. Conversely, satisfying CT does not fix an expired, untrusted, or wrongly named certificate. Keep normal TLS validation, CT compliance, and issuance authorization as separate decisions.&lt;/p&gt;
&lt;p&gt;Domain monitoring also needs interpretation. A newly observed name may belong to an authorized CDN, wildcard, or renewal. Compare issuer, names, fingerprints, and your issuance inventory before escalating; unexplained issuance needs investigation and corrective action, not an assumption that logging already blocked it.&lt;/p&gt;
&lt;p&gt;Public logging can reveal certificate names. Do not submit private certificates or sensitive internal naming solely to try an experiment. A monitor&amp;rsquo;s incomplete coverage or stale data also cannot prove absence. Operational monitoring needs a declared scope and freshness, rather than treating an empty search result as a universal guarantee.&lt;/p&gt;
&lt;h2 id="check-it-quickly"&gt;Check it quickly&lt;/h2&gt;
&lt;p&gt;Save this as &lt;code&gt;ct_probe.go&lt;/code&gt; and run &lt;code&gt;go run ct_probe.go&lt;/code&gt; with Go 1.23 or newer. This offline exercise uses RFC 6962&amp;rsquo;s SHA-256 Merkle construction with three synthetic strings, not real certificates or serialized CT leaves. It verifies only the middle leaf at index one in this fixed tree.&lt;/p&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-go" data-lang="go"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kn"&gt;package&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;main&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kn"&gt;import&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;crypto/sha256&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fmt&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;runtime&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;func&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;ok&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;ok&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;panic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;func&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;sha256&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Sum256&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;append&lt;/span&gt;&lt;span class="p"&gt;([]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt;&lt;span class="nb"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;...&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;func&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;var&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;65&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;copy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="mi"&gt;33&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;[:])&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;copy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;33&lt;/span&gt;&lt;span class="p"&gt;:],&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;[:])&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;sha256&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Sum256&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[:])&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// Only verifies index 1 of a three-leaf fixture; not a general CT verifier.&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;func&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[][&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;func&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-C&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fmt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Sprintf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;%x&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;111b905d16e9388f6e9079aaec820ab176d649b9daecabcdb3aca45fe4b6b646&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;root differs from independent fixture vector&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fmt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Sprintf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;%x&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;empty leaf vector differs&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;!=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;sha256&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Sum256&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;nil&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;an empty tree and an empty leaf are different&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[][&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;correct inclusion proof must pass&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-X&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;altered entry must fail&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;badProof&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;append&lt;/span&gt;&lt;span class="p"&gt;([][&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="nb"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;nil&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="o"&gt;...&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;badProof&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;^=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;badProof&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;altered sibling must fail&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[][&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="kt"&gt;byte&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;sibling order matters&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;[:&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;short proof must fail&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;extra proof element must fail&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;badRoot&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;badRoot&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;^=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;badRoot&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;wrong trusted root must fail&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;nextRoot&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;branch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;leaf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-D&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;nextRoot&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;!=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;appending an entry changes this fixture root&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(!&lt;/span&gt;&lt;span class="nf"&gt;middleOfThree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;fixture-B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;proof&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;nextRoot&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;old proof must not verify against the new root&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;fmt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Println&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;correct proof accepted; altered entry, sibling, order, length, and root rejected&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;fmt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Println&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;empty tree differs from empty leaf; fourth entry changes root; old proof fails&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;fmt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;three-leaf fixture root: %x\n&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nx"&gt;fmt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Println&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;runtime&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;Version&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;A leaf hashes a 0x00 byte followed by its data; an internal node hashes a 0x01 byte followed by its two child hashes. These prefixes provide domain separation. For three leaves, the left subtree contains A and B, while C stands alone on the right. An empty tree and a single empty leaf also have different hashes.&lt;/p&gt;
&lt;p&gt;The correct proof contains A&amp;rsquo;s hash and C&amp;rsquo;s hash. Recombining them with B reproduces the expected root, which was independently cross-checked with Python&amp;rsquo;s hashlib. Changing B, a sibling, their order, proof length, or the expected root fails. Appending D changes this fixture&amp;rsquo;s root, and the old three-leaf proof no longer verifies against it.&lt;/p&gt;
&lt;figure class="technical-diagram"&gt;
&lt;img loading="lazy" src="https://hk.xbcatm.com/visuals/posts-tls-certificate-transparency-not-a-secret.detail.en.svg" alt="The fixed three-leaf Merkle tree combines A and B on the left with C on the right. The proof for fixture-B contains A and C hashes in that order. The toy trusted root proves neither SCT validity, append-only history, nor issuance authorization." width="560" height="2050"&gt;
&lt;figcaption&gt;The article uses three synthetic strings and RFC 6962 hash prefixes. The fixed proof for B consists of A and C hashes, rebuilding branch(branch(A, B), C). Its hardcoded root is trusted only within the exercise. No SCT signature, live log key, consistency proof, browser policy, or issuance authorization is established.&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;The retained article reports that all assertions passed with Go 1.27.0 on macOS; this review did not rerun the Go fixture. The hardcoded test root represents an already trusted three-leaf checkpoint only within this exercise. No SCT signature, real log key, certificate encoding, network endpoint, generic inclusion verifier, or consistency proof is implemented. In particular, observing a changed root does not prove append-only growth. Browser policy enforcement and live misissuance monitoring remain separate, untested operations.&lt;/p&gt;
&lt;h2 id="further-reading"&gt;Further reading&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="https://hk.xbcatm.com/posts/tls-certificate-expiry-is-a-date-not-a-guess/"&gt;A TLS certificate expiry is a date you can read&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://hk.xbcatm.com/posts/tls-1-3-handshake-basics/"&gt;TLS 1.3 handshake basics&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id="sources"&gt;Sources&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.rfc-editor.org/rfc/rfc6962.html"&gt;RFC 6962: Certificate Transparency&lt;/a&gt;, version-1 Merkle hashing, SCT promises, and proof distinctions, checked 2026-09-09.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.rfc-editor.org/rfc/rfc9162.html"&gt;RFC 9162: Certificate Transparency version 2&lt;/a&gt;, protocol scope, misissuance limits, and version history, checked 2026-09-09.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://googlechrome.github.io/CertificateTransparency/ct_policy.html"&gt;Chrome Certificate Transparency policy&lt;/a&gt;, client-specific SCT and log acceptance requirements, checked 2026-09-09.&lt;/li&gt;
&lt;/ul&gt;</content:encoded></item><item><title>A certificate chain is a path you should be able to print</title><link>https://hk.xbcatm.com/notes/a-certificate-chain-is-a-path-you-should-be-able-to-print/</link><pubDate>Mon, 08 Jun 2026 00:00:00 +0000</pubDate><guid>https://hk.xbcatm.com/notes/a-certificate-chain-is-a-path-you-should-be-able-to-print/</guid><description>Check the server’s certificate list, the client’s trust anchor, and the requested hostname as separate parts of TLS validation.</description><content:encoded>&lt;p&gt;A TLS client must build a valid certificate path to an anchor it already trusts, and verify the requested hostname. Printing certificates is a useful diagnostic, but does not establish either result by itself.&lt;/p&gt;
&lt;figure class="technical-diagram"&gt;&lt;img loading="lazy" src="https://hk.xbcatm.com/visuals/cert-chain.detail.en.svg" alt="A server-sent leaf and needed intermediates feed client path building. A separately configured trust anchor supplies trust. Requested hostname and certificate validity are additional checks; printing or counting certificates proves none of these alone." width="720" height="1740"&gt;&lt;figcaption&gt;The server supplies certificates; trust comes from the client’s anchor. Validate the path, requested hostname and validity period. Printed certificate counts cannot establish those results.&lt;/figcaption&gt;&lt;/figure&gt;
&lt;h2 id="the-leaf-is-not-the-whole-story"&gt;The leaf is not the whole story&lt;/h2&gt;
&lt;p&gt;The endpoint presents the &lt;em&gt;leaf&lt;/em&gt; first. It contains the public key, validity period, and subject alternative names used for hostname checks. A public-CA deployment normally also sends the intermediates needed to build a path. Missing intermediates can break clients that do not already have them cached or cannot retrieve them.&lt;/p&gt;
&lt;p&gt;The self-signed root normally need not be sent: trust comes from the client’s configured anchors, not from a server including a certificate. A cross-signed certificate whose subject says “Root” can instead be an intermediate in the selected path. Certificate count alone is therefore not a completeness or trust test.&lt;/p&gt;
&lt;h2 id="read-the-chain-the-edge-actually-sends"&gt;Read the chain the edge actually sends&lt;/h2&gt;
&lt;p&gt;OpenSSL documents &lt;code&gt;s_client -showcerts&lt;/code&gt; as the server’s certificate list, not a verified chain. The earlier version of this note recorded this site snapshot:&lt;/p&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;certificate 0: CN=www.xbcatm.com
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; issuer : C=US, O=Let&amp;#39;s Encrypt, CN=YE1
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; notAfter : Nov 19 08:37:12 2026 GMT
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;certificate 1: CN=YE1 (intermediate)
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; issuer : C=US, O=ISRG, CN=Root YE
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;certificate 2/3: Root YE / ISRG Root … (CA certificates)
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;The original report counted four blocks. Its raw handshake log is not retained here, and this review did not reproduce the live handshake; treat the values as a historical report, not current edge evidence. Let’s Encrypt’s chain documentation does describe YE1 and a cross-signed Root YE path, so those names alone are not evidence of an invalid chain. Which certificate terminates trust depends on the client’s trust store and path building.&lt;/p&gt;
&lt;h2 id="keep-issuance-authorization-separate"&gt;Keep issuance authorization separate&lt;/h2&gt;
&lt;p&gt;Intermediates let a CA keep its root key offline and separate issuance operations. Revoking an intermediate can invalidate dependent leaf paths and may require replacement certificates; it does not preserve every leaf automatically.&lt;/p&gt;
&lt;p&gt;CAA authorizes a CA’s documented issuer-domain identifier at issuance time. It does not pin an intermediate, change browser trust, or prove that an existing certificate complied with historical CAA. The &lt;code&gt;dns-caa-records&lt;/code&gt; note covers that separate policy check.&lt;/p&gt;
&lt;h2 id="count-for-inventory-validate-for-trust"&gt;Count for inventory, validate for trust&lt;/h2&gt;
&lt;p&gt;The earlier inventory command was:&lt;/p&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;$ echo | openssl s_client -connect www.xbcatm.com:443 -servername www.xbcatm.com -showcerts 2&amp;gt;/dev/null | grep &amp;#39;BEGIN CERT&amp;#39; | wc -l
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;4
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;This is read-only network traffic, but it suppresses diagnostics and the final count can succeed even when an earlier command failed. Do not use &lt;code&gt;4&lt;/code&gt;, or any other fixed count, as a health threshold. A leaf-only result warrants checking the expected issuer path rather than declaring every one-certificate chain invalid.&lt;/p&gt;
&lt;p&gt;For actual validation, configure hostname checking and failure on verification errors with OpenSSL’s &lt;code&gt;-verify_hostname&lt;/code&gt; and &lt;code&gt;-verify_return_error&lt;/code&gt; options, retain diagnostics, and record the trust store and client version. Also test the clients you support; one OpenSSL trust store cannot establish compatibility with all browsers.&lt;/p&gt;
&lt;h2 id="sources"&gt;Sources&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.rfc-editor.org/rfc/rfc8446.html"&gt;RFC 8446 — TLS 1.3&lt;/a&gt;, section 4.4.2 certificate-list order and optional trust-anchor omission, checked 2026-10-15.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.rfc-editor.org/rfc/rfc5280.html"&gt;RFC 5280 — X.509 PKI&lt;/a&gt;, section 6 trust-anchor input and path validation, checked 2026-10-15.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://letsencrypt.org/docs/faq/"&gt;Let&amp;rsquo;s Encrypt FAQ&lt;/a&gt;, certificate compatibility overview, checked 2026-10-15.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://letsencrypt.org/certificates/"&gt;Let&amp;rsquo;s Encrypt: Chains of Trust&lt;/a&gt;, YE1 and cross-signed Root YE paths, checked 2026-10-15.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://docs.openssl.org/3.0/man1/openssl-s_client/"&gt;OpenSSL &lt;code&gt;s_client&lt;/code&gt;&lt;/a&gt;, presented-list and verification options, checked 2026-10-15.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.rfc-editor.org/rfc/rfc8659.html"&gt;RFC 8659 — CAA&lt;/a&gt;, issuance authorization rather than client trust, checked 2026-10-15.&lt;/li&gt;
&lt;/ul&gt;</content:encoded></item></channel></rss>