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Tedious and pedantic note: You can’t mindlessly compare the bytes of the host name: you have to know that it’s the presentation format of the name, not the DNS wire format; you have to deal with ASCII case insensitivity; you have to guess what to do about trailing dots (because that isn’t specified); you have to deal with wildcards (being careful to note that PKIX wildcard matching is different from DNS wildcard matc…
In practice it's much easier than you seem to have understood The names PKIX writes into dnsName are exactly the same as the hostnames in DNS. They are defined to always be Fully Qualified, and yet not to have a trailing dot, you don't have to like that but it's specified and it's exactly how the web browsers worked already 25+ years ago. You're correct that they're not the on-wire label-by-label DNS structure, but t…
The DNS is case-insensitive, though only for ASCII. So you have to compare names case-insensitively (again, for ASCII). It _is_ possible to have DNS servers return non-lowercase names! E.g., way back when sun.com's DNS servers would return Sun.COM if I remember correctly. So you do have to be careful about this, though if you do a case-sensitive, memcmp()-like comparison, 999 times out of 1,000 everything will work, and you won't fail open when it doesn't.