I had never heard of Threema before, but it popped up in a list of secure messenger applications that doesn’t require a phone number or email address.
HIGHEST ENCRYPTION STRENGTH
Threema end-to-end encrypts all your communication, including messages, voice calls, group chats, files and even status messages. Only the intended recipient, and nobody else, can read your messages. Threema uses the trusted open source NaCl cryptography library for encryption. The encryption keys are generated and safely stored on user’s’ devices to prevent backdoor access or copies.
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Each Threema user receives a random Threema ID for identification. A phone number or email address is not required to use Threema. This unique feature allows you to use Threema completely anonymously – no need to give up private information or to open an account.
It looks like the biggest concern with Threema’s security model is the fact that its source code is closed source.