Congruences and Public-key Cryptography

Two numbers $a$ and $b$ are congruent modulo another number $n$ if $a=b+nk$ for some integer $k$. That $a$ and $b$ are congruent just means you can ``get from $a$ to $b$ on the number line'' by adding or subtracting lots of copies of $n$. For example, $14\equiv 2\pmod{12}$ since $14=2+12\cdot 1$.

$$\mathbf{Z}/n\mathbf{Z}= \{$$ equivalence classes of numbers modulo $n$ $$\}.$$

Your web browser's ``secret code language'' uses arithmetic in $\mathbf{Z}/pq\mathbf{Z}$ to send messages in broad weblight to amazon.com. How can this possibly be safe!? You will find out exactly what is going on.