Create Sig and PubKey with unknown PrivKey

unknownPrivkeySig.ts

import { bsv } from 'scrypt-ts'

async function main() {
    const msg = 'I am Satoshi'
    const hBuff = bsv.crypto.Hash.sha256(Buffer.from(msg))
    const h = bsv.crypto.BN.fromBuffer(hBuff)

    const G = bsv.crypto.Point.getG()
    const n = bsv.crypto.Point.getN()

    const s = bsv.PrivateKey.fromRandom().bn

    let r: bsv.crypto.BN = new bsv.crypto.BN(0)
    let R: bsv.crypto.Point = G
    let isValidR = false
    // find a `r` on the curve
    while (!isValidR) {
        r = bsv.PrivateKey.fromRandom().bn
        try {
            R = bsv.crypto.Point.fromX(false, r)
            isValidR = true
        } catch (e) {
            isValidR = false
        }
    }

    const sR = R.mul(s)
    const hG = G.mul(h)
    
    const sR_hG = sR.add(hG.neg())
    const inv_r = r.invm(n)
    
    const Y = sR_hG.mul(inv_r)
    
    const pubKey = new bsv.PublicKey(Y)
    const sig = new bsv.crypto.Signature(r, s)
    
    const valid = bsv.crypto.ECDSA.verify(
        hBuff,
        sig,
        pubKey
    )
    
    console.log(`Message: ${msg}`)
    console.log(`Public key: ${pubKey.toString()}`)
    console.log(`Signature: ${sig.toString()}`)
    console.log(`Verified: \x1b[32m${valid}\x1b[0m`)
}

main()

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