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 commented
Every Developer down in Developerville liked SSL a lot
But Microsoft, who lived just North of Developerville did not!
The Microsoft hated SSL! The whole SSL stack!
Now, please don't ask why. No one quite knows the reason.
It could be, perhaps, that the code was too tight.
It could be his head wasn't screwed on just right.
... I'll stop there and continue next Christmas (but by 2017, I'm afraid we'll be forced to move off of Azure) ...