Last addendum, I promise:

This is factually incoherent.  Rainbow tables attack hash functions:
 they don't attack signature algorithms.  If someone was interested
in using rainbow tables against a signature algorithm they'd make
sure to carefully specify what hash algorithm was used, because
rainbow tables have to be made specifically for a hash algorithm.

A question got raised: "Wouldn't this give you a random message that the
signature would also work for? Could it even be used to forge a useful
message?"

First question: yes.  Second question: probably not.  Maybe, depending
on how the signature was being used.  There are good reasons why nobody
attacks signatures with rainbow tables.

I apologize for not making this clear in my earlier email -- I thought
it went without saying, but maybe the clarification is useful.

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