A group of sheaves of grain stood on end in a field!

The description makes this challenge sound complicated, with abstract algebra and algebraic geometry but the challenge is actually quite simple

Challenge

The cipher is basically doing where these are polynomials instead of integers, however most normal operations works for polynomials.

We are also given a lot of m,c pairs, though only 2 was needed

Furthermore everything is done in , which simplifies a lot, addition and subtraction are also the same thing which is quite convenient

Solution

Using 2 pairs of m,c, we get(under mod ):

\begin{align*} k_2 &= \frac{c_1m_1+c_2m_2}{m_1+m_2}\\\\ k_1 &= m_1(c_1+k_2) \end{align*}

Now using these keys, we can easily retrive the flag