PQ provers for P2PKH outputs

The process of simplifying cryptographic verification within a circuit is highlighted, emphasizing the elimination of full ECDSA (Elliptic Curve Digital Signature Algorithm) verification when considering environments that can parse Zero-Knowledge (ZK) proofs. The suggestion pivots towards a more streamlined approach involving simple key-generation mechanisms within the circuit itself. This method significantly reduces the computational requirements by limiting the operations to a single elliptic curve point multiplication and one SHA256 function call.

The proposed methodology involves two primary components: the witness and the public signal. The witness comprises a secret key and the actual message, denoted as $(sk, m')$, while the public signal consists of the public key hash and the expected message, represented as $(h, m)$. The circuit's function is to compute the public key from the secret key through elliptic curve multiplication ($pk = sk \cdot G$), followed by generating a hash of the public key using SHA256 ($h' = \text{SHA256}(pk)$). The core of this simplified verification process lies in the circuit’s ability to ensure that the actual message matches the expected message ($m = m'$) and that the computed public key hash aligns with the given public key hash ($h = h'$). This approach not only asserts the same statement as the traditional full ECDSA verification but does so with fewer computational steps, thereby offering a more efficient solution for transaction verification within systems capable of interpreting ZK proofs.