Cohen's cryptosystem

In Cohen's cryptosystem, a private key is a positive integer ${\displaystyle p}$.

The algorithm uses ${\displaystyle k}$ public-keys ${\displaystyle w_{0},\ldots ,w_{k-1}}$ defined as follows:

Generate ${\displaystyle k}$ random integers ${\displaystyle u_{0},\ldots ,u_{k-1}}$ chosen randomly and uniformly between ${\displaystyle -B}$ and ${\displaystyle B}$. Where ${\displaystyle B}$ is some bound.

Let ${\displaystyle A=\lfloor {\frac {p}{2k}}\rfloor }$ and generate ${\displaystyle k}$ random integers ${\displaystyle v_{0},\ldots ,v_{k-1}}$ chosen randomly and uniformly between ${\displaystyle 0}$ and ${\displaystyle A}$.

Define ${\displaystyle w_{i}=(u_{i}p+v_{i})}$.