Sorry if this question is misguided, I'm a software developer and not a cryptographer.
Let's say I have a public key, and 2 signed messages.
Signed message 1:
message_hash_1
signature_1.r
signature_1.s
Signed message 2:
message_hash_2
signature_2.r
signature_2.s
Assumptions:
message_hash_1 == message_hash_2
signature_1.r != signature_2.r
signature_1.s != signature_2.s
I've read in https://www.bertcmiller.com/2021/12/28/glimpse_nonce_reuse.html that it is possible to recover the private key if r is the same across the signed messages, but s is different.
Is it possible to recover the private key if the message_hash is the same, but signature_1.r/signature_2.r and signature_1.s/signature_2.r are both different? So the nonce with which the message was signed was different, but the message and private key were the same across both signatures.
I'm using NIST P-256 elliptic curve.
