0
$\begingroup$

It is mentioned here that the public value $N=p*q$ of the RSA cryptosystem can be factorized if one of the factors is reused. Thus, if $N_1=p*q_1$ and $N_2=p*q_2$ and only $N_1$ and $N_2$ are known, then one can factor $N_1$ and $N_2$.

I wasn't able to come up how this can be achieved. Is that statement really true?

$\endgroup$
3
$\begingroup$

Since $p$ is a factor in both $N_1$ and $N_2$ you can simply calculate $p$ by using Euclid's algorithm.

Once you have $p$ you can then calculate $q_1$ and $q_2$ (simply divide $N_1$ by $p$ to get $q_1$ and divide $N_2$ by $p$ to get $q_2$).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.