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It's interesting to imagine what connected planet with no reliable encryption would be like.

Although I guess we can always fall back on one-time pads.

Quantum computers don't break all encryption. There's no risk of that, fortunately.

Please expand on that. What encryption is vulnerable and what isn't?

I don't know a lot about it, only just enough to know what search term to look for, and Wikipedia had an article that probably fits the bill: https://en.m.wikipedia.org/wiki/Post-quantum_cryptography

Non-mobile link:

Symmetric encryption will need to double key lengths, such as using 256-bit AES keys instead of 128-bit.

All currently popular forms of asymmetric / public key encryption (including RSA and ECC) are vulnerable to quantum attack.