I have not run the app, but from the Android source code it looks like this "secure" app is uploading your contacts including full names and all their phone numbers into the "cloud": MessagesController.readContacts() [0] is called on creation of the MessagesActivity. When invoked for the first time, it collects first names, last names and phone numbers from the Android Contacts interface, creates a table containing t…
Also, how can you claim to have a secure app when it runs on a closed-source operating system? (Even more, we know about Microsoft handing over security holes to the NSA - why would Apple or Google not do the same?). It's like saying "this heat is really cold". In other words: a contradiction in itself. Only open-source apps on open-source operating systems can start making claims about security and trustworthiness.
...running on Open Source hardware.
Many modern smartphones employ a baseband processor and an application processor with shared memory. While the app processor might be running an open-source compiled Android, the baseband processor is usually on a closed, not externally verified (and very buggy) RTOS provided by the manufacturer (Qualcomm, MediaTek, TI, ...)[0].
Owning the baseband is sufficient to gain access to the raw RAM of the application processor, to read any IM messages and keys, to manipulate data, code and whatever else you like. And all this is completely undetectable by any "antivirus" software running on the app processor.