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breaking encryption and chatcontrolThe two are not equivalent issues; the first one is ill-formed as stated.
Cryptography is a tool of control. It's "dual-use", in the same sense like a knife or nuclear fission is - its moral valence depends on who is wielding it, and to what end.
In the context we're discussing, encryption is being used against the people. Working encryption is in fact needed to make chat control work - it's fundamental to it, the same way it is to Developer Verification and Safetynet/Remote Attestation. It would be great if EU decided to break that set of encryption applications. Alas, chat control only wants to break E2EE on messages, and uses encryption elsewhere to guarantee E2EE stays broken.
A more general comment about this thread, and related ones in the past: people really need to stop thinking about "encryption" and "security" as inherently good. They're not. Most of the social problems with computing, the attempts at user disempowerment and disenfranchisement, persist because they apply cybersecurity solutions.
The core question of security is always: who exactly is being secured, and from who.