I used to think Threema was worth my time before reading this blog post. I personally stick with Signal since it's the convenient gold standard.
Privacy Guides
The moment the author used the birthday paradox in a wrong way to try and prove some point with the ID's, I stopped reading.
The points before that:
Being forced to use a unique mobile phone number is a major issue for many (me included). As is being based in the US.
Threema didn't yet have Perfect Forward Secrecy back in 2021, when this article was published, but it has now.
Yes, Threema isn't perfect. But neither is Signal.
Choosing which one you should prefer is up to your specific scenario.
Use a recent and trustworthy comparison chart, like e.g. the one by Kuketz.
How is the birthday paradox being used incorrectly?
With 365 unique possible IDs, only 23 are needed to break the 50% chance threshold of new IDs colliding with an existing one. With 2.8 trillion unique possible IDs, only 1.7 million are needed to break the 50% chance threshold of new IDs colliding with an existing one.
It seems like an apples to apples comparison to me. Is it not?
Yes, for any single one out of these 1.7 million to collide with one other the probability might be 0.5 (didn't check it).
But he uses it in the sense that it is true for each of them, which it isn't.
To stay with the birthday example:
If I enter a room with 22 of the unique people already in there, the chance that one of them has the same birthday as me is 22/365=0.06 and not 0.5.
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This depends on your scenario.
You can use a comparison chart to find suitable fits.
Threema and Signal are both ok, Teleguard in general doesn't look like a trustworthy option.
Yes, Signal and Threema have great encryption, and Teleguard is not as popular but it is anonymous and from Switzerland.
It's mainly about Teleguard apparently being completely closed source and using an unknown proprietary encryption protocol.
Personally I would omit it based on this and use it only for non-sensitive stuff if completely omitting were not possible.
Yes, Teleguard is not particularly reliable, even though it is owned by Swisscows, a company that has its own search engine and secure alternatives to Google. Furthermore, Teleguard is not that old; it was launched in 2021.