Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 12K / b / i / Solution

For the RSA cryptosystem, choose $N=pq$ and a public exponent $e$ coprime to $\varphi (N)$. The public key is $(N,e)$, while the private exponent satisfiesEncryption sends $m$ to $c\equiv m^e(\mathrm{mod}N)$, and decryption computes $c^d\equiv m(\mathrm{mod}N)$.