Taking EdDSA as an example, given the length of a signature is 512-bits for a given data payload, what is the probability of a collision where there is another 512-bit value that is also a valid signature?
With symmetric crypto we know there is only one single key in the entire space that will validly decrypt data encrypted with the same key.
Can we provably state that for a given payload and given private key, there is only one valid signature in the 512-bit signature space?
Ie. That no other signature exists that could be validated with the public key counterpart to the private key that created the signature.