Given a private signature key
sk and a public signature key
SK, does revealing
sk(H(SK)) (in addition to
SK) make it more easy for an attacker to determine
sk or to fake a signature that would appear to have been produced by
sk? Is this scheme a bad idea - in other words, does it compromise the secuity of the signing algorithm? (It seems like this is analogous to key-dependent encryption, but for signatures, and with the interposition of a hash function in between).
If that matters, I'm using ECDSA signatures. Any pointers are appreciated.