It looks like it exploits what Vaudenay warned against in 2004 : "Digital Signature Schemes with Domain Parameters" ( https://lasec.epfl.ch/pub/lasec/doc/Vau04b.pdf … )https://twitter.com/NSAGov/status/1217152211056238593 …
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By choosing the right parameters for C', you can know the private key for C' -- even when you don't know the private key for C -- as Vaudenay noted in 2004.
This caching behaviour seems to be a crucial part of the issue. Good to see it emphasised here.
Ultimately this is about the equality test being based on the public key but not the parameters - one can imagine a similar weakness without caching. "Is this a root cert?"
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