You are asking about SCT auditing. I’ll give a high level explanation of the whole process; but you can directly refer to the last paragraph.
High level
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When a certificate is submitted to a log, the log returns an SCT: a Signed Certificate Timestamp. SCTs are cryptographic proofs of inclusion. The web server includes SCTs in its response to Chrome (or any other user agent) either via OCSP Stapling or by embedding the SCTs in the certificate as a TLS extension.
Chrome requires a TLS certificate to come with a certain number of SCTs, via either method.
Details
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A good starting point is
https://certificate.transparency.dev (see the User Agents section).
For more details of CT, see RFC 6962 (
https://www.rfc-editor.org/rfc/rfc9162.html).
Also, as pointed in the first link, the Chrome policy is here:
https://github.com/GoogleChrome/CertificateTransparency#chromium-certificate-transparency-policy. Specifically, see
https://googlechrome.github.io/CertificateTransparency/ct_policy.html for Chrome’s CT policy.
Finally, the issue that you are talking about is called SCT auditing: Even though a log may issue an SCT for a certificate, it can maliciously(/etc.) not include that certificate. Therefore, user agents (e.g., Chrome) may have to do an extra check to make sure the logs are acting correctly. But, this may raise privacy issues. User agents (e.g., Chrome) may leak the full browsing history of a user when checking the SCTs that the user receives.
See
https://docs.google.com/document/d/16G-Q7iN3kB46GSW5b-sfH5MO3nKSYyEb77YsM7TMZGE/edit and
https://groups.google.com/a/chromium.org/g/ct-policy/c/ItjScsxTjR0 for Chrome’s current approach to this.
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