concept certificate in category cryptography

This is an excerpt from Manning's book Real-World Cryptography MEAP V09.
The draft-barnes-acme-04 mentioned by Andrew Ayer is a document specifying ACME, one of the protocols behind the Let’s Encrypt certificate authority.[52] A certificate authority is the thing that your browser trust and that signs the public keys of websites you visit (I talked about this in the introduction of this chapter). It is called a "certificate" authority due to the fact that it does not sign public keys, but certificates. A certificate is just a blob of data bundling a website’s public key, its domain name, and some other relevant metadata.
Figure 9.11. The authentication part of a handshake starts with the server sending a certificate chain to the client. The certificate chain starts with the leaf certificate (the certificate containing the website’s public key and additional metadata like the domain name) and ends with a root certificate that is trusted by the browser. Each certificate contains a signature from the certificate above it in the chain.
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While certificates are optional in TLS 1.3 (you can always use plain keys), many applications and protocols (not just the web) make heavy use of them in order to certify additional metadata. Specifically, the X.509 certificate standard version 3 is used.
X.509 is a pretty old standard that was meant to be flexible enough to be used in a multitude of scenarios, from email to web pages. The X.509 standards uses a description language called Abstract Syntax Notation One (ASN.1) to specify information contained in a certificate. An ASN.1 looks like this: