Assume a 256-bit ECDSA private key used with Secp256k1 and SHA-256. This key signs multiple different messages in a fully deterministic manner as described in RFC-6979, so signing the same message always produces the same signature.
A quantum attacker obtains the first 32 bytes of each signature. However, the rest of each signature, the messages, the private key and the public key remain concealed from them.
Can the attacker prove that the signatures were produced with the same private key?
(This is a modification of my previous question: "Given multiple ECDSA signatures with the same key, what can a quantum attacker learn?")