Sure, push notification needs a central server. But guys, we so badly need a mobile IM that meets similar security standards as this project. Do it, and the world will honor you.
Should the central server be the only missing component of a reliable, secure-paranoid, mobile IM system, I would be happy donating some dollars.
Soon I'll be resuming work on a privacy-conscious push server design, originally intended to enhance the poor user experience of the existing ChatSecure iOS client (OTR/XMPP/Tor).
The general idea is that you'd fetch tokens from the server that allow people to send pushes to you, then distribute them to trusted contacts over an secure channel. Contacts would then be able to send you pushes from any endpoint of choice. Somewhat less metadata than existing solutions, and an opportunity for client diversity.
Actually I myself cloned ChatSecure iOS, built it, and played it for a while. It's a nice app with elegant interface yet lacks push notification. If you plan to improve it, I would be happy to be a beta tester :-)
p.s.
So honest is this app to explicitly state that I need to keep it foreground to receive new message from XMPP server.
Does push "need" a central server? I connect to my IMAP server from K-9 Mail on my OnePlus One running Android using a Tor hidden service. And I have IMAP IDLE turned on, so a persistent connection is maintained. So as soon as an email arrives, it is pushed to my phone and I am notified. With no third party push service involved. And my phones battery still lasts about one and a half to two days.
What about Telegram? Seems to work well for me, and a key thing is it has a desktop client. The thing which annoys me about it though is by default it isn't client-to-client encrypted. When you create a "secret chat" which is fully encrypted, it doesn't work on all your devices.
Telegram's crypto is probably broken - they are using weird 90's and unproven crypto modes instead of normal stuff, and their "crypto challenge" is bogus, if you are to believe tptacek.
They also have attitude of "oh we are smart, you just don't get it", which is not the way anyone should think about cryptography.
