this post was submitted on 13 Oct 2023
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RSA1024 is presumed to be breakable (was the default for decades), while RSA1280 (used by iMessage) is presumed to be near the limit of what an agency like NSA could break, and 2048 or 4096 is the medium term standard while long term it's either ECC or post quantum algorithms.
Today most of the cat and mouse game is about protocol design security and implementions. Just look at sidechannel attacks.