The Modulus Supply Company sells RSA moduli. To save money,

it has one $300-$digit prime $p$ and, for each customer, it randomly

chooses another $300-$digit prime $q($different from $p$ and different

from $q$ supplied to other customers$).$ Then it sells $n=pq,$ along

with encryption and decryption exponents, to unsuspecting

customers.

Suppose Eve suspects that the company is using this

method of providing moduli to customers. How can she

read their messages? $($As usual, the modulus $n$ and the

encryption exponent $e$ for each customer are public

information.$)$