Quantum resistant algo for TLS

It’s a little bit more complicated. The node’s identity is a certificate, so it uses a TLS some kind to establish a connection, but the data itself is encrypted in a different way, client-side. See How Encryption is Implemented - Storj DCS Docs
In other words, to break the TLS and intercept the encrypted data is not enough to get the data. You also need to collect at least 29 pieces (which are not exposed, where they are), and then - assemble them to the one segment and only then try to break an encryption. But it’s also not the end of the story. You need to find all segments of the file and combine them in a right sequence. For this you need also break the metadata information from the satellite, which is also encrypted. And also gather the API key, or guess it before our civilization would disappear…
So,… good luck to break all of this even with a quantum computing.

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