Q$1$: Consider the elliptic curve $E$:$y^2=x^3+ax+1$ modulo $p$ where $p$ is prime of size $512$

bits. Let $n$ be a prime integer of size $512$ bits and $P=(0,1)$ is an element of $E[n].$ Write down

the pseudo code of a method which gives other elements of $E[n].$ What can you say about the

number of elements in $E[n].$

Q$2$:Write down the pseudo code of an algorithm which gives an element $P$ of $E[n]$ where

the inputs are the elliptic curve $E$ modulo $p$ and a random point $Q$ on the curve, a natural

number $n$ and the order of $E$ modulo $p.$