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Alice publishes $(n,e)$ where $n$ is exponential modulus and $e$ is the public key. We have $n=80$ digit number and $e=3$. Bob, in correspondence with Alice, asked Alice to prove she is really Alice, by making her signature on the following five numbers: $m1, m2, m3, m4, m5$. Then Alice sent 6 numbers $y1, y2, y3, y4, y5, y6$ where all the 6 numbers are really long, around 80 integers.
How do verify that these five numbers are indeed signed by Alice?
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.
