You can now use the Azure CDN to access blobs with custom domains over HTTPS. See the following article for instructions on how to do so: https://docs.microsoft.com/en-us/azure/storage/storage-https-custom-domain-cdn. Having talked to a number of customers, we concluded that this solution addresses many scenarios where the need for HTTPS access to blobs with custom domains exists.
Native Azure Storage support for using SSL to access blobs at custom domains is still on our backlog. We would love to hear about your scenarios where using the Azure CDN is not an acceptable solution, either by posting on this thread or sending us an email at firstname.lastname@example.org.Nathan commented
Daresay you could meet this use-case now using Web App Firewalls, but an integrated solution would be better.
We have custom dictionary / synonyms functionality available in private preview. If you’d like to try it out, please contact Nate Ko (nateko at the usual Microsoft domain).
Thanks for using Azure Search!
Your Azure Search team