Verifying a Signature
Alice will have computed

$y_{i} = m_{i}^{d} \,\mbox{mod}\, n$

and Bob will compute

$d_{i} = y_{i}^{e} \,\mbox{mod}\, n$

If Bob finds $d_{i} == m_{i}$ for every $i$, he will probably conclude that they were indeed signed by Alice. His conclusion however, is very unwise, since for this special case where $e=3$, the numbers $y_{i}$ can be easily forged by an attacker even if he does not possess the private key $d$ of Alice.