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> relying on random numbers being both fair and not being tampered with

You can easily validate that a block is valid and has the correct PoW. For this to work an attacker needs to be mining valid blocks (expensive) and partition the bitcoin network in a way that nodes can't talk to each other (mission impossible). Then the attacker needs to make use of this split chain so that a double spend can occur. I wouldn't be that worried.



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