Can one extract a private key from a series of carefully constructed signed messages?
It is not possible if the signature scheme is secure, under the standard notion of &quot;existential unforgeability under chosen message attacks&quot;. According to this definition, the adversary is given the public key and can then choose messages to be signed one after another. If it can forge any signature, then the scheme is not secure. As such, if the scheme is secure, it's not possible to form special messages that result in the key being revealed, or any other vulnerability.