Algorithm 1 KeyGen.

Input:

$1^N$: security parameter;

Output:

$pk,sk$: a public/private key pair;

1: $\left(n,p,q\right)\leftarrow GenModulus\left(1^N\right)$;

2: $\varphi \left(n\right)=\left(p-1\right)\left(q-1\right)$;

3: Find e, such that $gcd\left(e,\varphi \left(n\right)\right)=1$, where $1<e<\varphi \left(n\right)$;

4: Compute $d=e^{-1}\mathrm{mod}\varphi \left(n\right)$

return $pk=\left(n,e\right)$, $sk=\left(p,q,d\right)$.