The cryptosystem encrypts messages encoded as integers by multiplying them by a constant $k$ (the key).
We have these ciphertexts obtained using this method: $$27186406060725269473008806173633$$ $$17353206699927246826577369753699$$ How can we find the key to this cipher?
I thought about finding the $\gcd$ of the 2 numbers we have, but I doubt that'd be of much value.
Finding the $\gcd$ is the way forward. The assumption the question makes is that both ciphertexts were encrypted using the same key, which means multiplication with the same number; the $\gcd$ in this case turns out to be a large prime, $398097621494482543747$. The two messages are the integers $68290802539$ and $43590330017$ respectively.