# Signing the hash of a key with the same key

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.

-
I'm not sure I understand the confusion. A fundamental requirement of a digital signature scheme is that it doesn't leak information about the secret. Otherwise an attacker can recover the secret and forge messages which would defeat the entire purpose. –  Stephen Touset Feb 4 '14 at 0:40
Right. I'm wondering if this would be a special case that needs to be avoided. Not that I see an attack, it's just that I've never seen this been done and I'm wondering if it's cryptographically sound. –  louism Feb 4 '14 at 1:00
@louism: It should be noted that your question is a good one in terms of encryption, where encrypting the key does lead to a different notion of security - key dependent messaging –  figlesquidge Feb 4 '14 at 9:12
Would people really use a signature scheme were signing a piece of public information could compromise your signing key? Wouldn't that be an obvious catastrophic deficiency? –  David Schwartz Feb 4 '14 at 20:02
@figlesquidge So there isn't an analogue to the "key-dependent encryption" attack for signatures ("key-dependent signatures")? –  louism Feb 5 '14 at 2:45