$(20$pt$)$ Write a GQ signature scheme. Using the random oracle model, you can compute $(\frac{Z}{Z^{\text{'}}}{)}^e=H(ID{)}^{H(Y||m)-H^{\text{'}}(Y||m)}$ where $Y=R^e$ in the GQ$.$ Assume that $H(*)$ returns a $256-$bit number and $Z,Z^{\text{'}},Yin{Z}_N^{**}$ where $N$ is a $2048-$bit. Using the previous problem, you can break the factoring problem of $N$ if adversary can forge a signature in the GQ when $N$ is a blum integer. Explain how to factor $N.$