Algorithm 6 ECDSA_Verify_PK${}_X\left\{msg\right\}$

Input.$(r,s),n,msg,P,Q$ Output. accept/reject $(r,s)$  1: check whether r and s are integers between 1 and $n-1$  2: calculate a 256-bit Hash value $e=H\left(msg\right)$ using hash function SHA-256  3: calculate $w=s^{-1}modn$  4: calculate $u_1=ew$ and $u_2=rw$  5: calculate solution point $X=(x_1,y_1)=u_{1}P+u_{2}Q$  6: if $X=0$, reject $(r,s)$, otherwise compute $v=x_{1}modn$  7: if and only if $v=r$, accept $(r,s)$