Setup of the RSA system

To set up the RSA system we need to do the following:

1.

Choose two very large prime (no nontrivial factors) numbers p and q (in this case they have 64 and 65 digits). RSA did not tell us what these are, because they form the ``hidden key.''

2.

Form the product n=pq. This is the first part of the ``public key'', and this is the 129-digit number now known as RSA-129:
$$\begin{align*}n=\ & 114381625757888867669235779976146 \\ & 6120102182967212423... ...52457338978305971235639587 \\ & 05058989075147599290026879543541 \end{align*}$$

3.

Randomly choose a moderately large positive integer e which is relatively prime to (p-1)(q-1). RSA gave us this number as e=9007; the pair (n,e) are the complete public key.