Let $\mathbb{G}$ be a commutative group under the addition law ($+$) and let $G
\in \mathbb{G}$ be its generator. The group has an order $p$. We define a
scalar multiplication $k \cdot G$ as $\underbrace{G+…+G}_\text{$k$~times}$.
Now assume that given an element $Q \in \mathbb{G}$ it is computationally
unfeasible to find $k$ such that $Q = k \cdot G$. We have seen in a different
challenge that it is easy to go from $G$ to $k \cdot G$ but now we are assuming
that it is hard to go from $k \cdot G$ to $G$. This is called a one-way
function. In this challenge, we will build a signature scheme and an encryption
scheme based on this function.