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Signal is really secure, and a damn good replacement/add-on for SMS.
It does ask for a chunk of permissions, but most of these allow it to replace the existing SMS app fully, i.e. when you start a message that you can choose contacts, that you could share your location with a contact, that you could start a phonecall (dropping back to a regular call if the recipient isn't on Signal).
The guy behind it, Moxie, is one of the greatest coders of our time, and the entire codebase has been peer reviewed by people obsessed with security and privacy.
It's about as good as you're ever going to get to offering all of the features that they do for the least possible intrusion... but because of how Android assigns permissions it definitely looks intrusive.
I've just gone to install Signal, and ironically baulked because it seems to want all of the permissions. I'm sure it is fine, but just seemed a bit ironic.
(Looking forward to getting 6.0 to have the app by app control over permissions)