Describe the RSA system with public key $(N, e)$ and private key $(N, d)$. Briefly discuss the possible advantages or disadvantages of taking (i) $e=2^{16}+1$ or (ii) $d=2^{16}+1$.

Explain how to factor $N$ when both the private key and public key are known.

Describe the bit commitment problem, and briefly indicate how RSA can be used to solve it.