Algorithm 5 ECDSA_Sign_SK${}_X\left\{msg\right\}$

Input.$n,P,msg,d$, Output.$(r,s)$  1: select a random integer or a pseudo-random integer $k\in [1,n-1]$  2: calculate the solution point of the curve $P=(x,y)=kP$, and $r=xmodn$. If $r=0$, then skip to step 1  3: calculate $t=k^{-1}modn$  4: calculate $e=H\left(msg\right)$, where H is the hash function SHA-256, which produces a 256-bit hash value  5: calculate $s=k^{-1}(e+dr)modn$. If $s=0$, then skip to step 1  6: return the signature of $msg$ is $(r,s)$