The numbers and should not be "too close", lest the Fermat factorization for be successful. If is less than (, which even for "small" 1024-bit values of is ), solving for and is trivial. Furthermore, if either or has only small prime factors, can be factored quickly by Pollard's p − 1 algorithm, and hence such values of or should be discarded.
The numbers and should not be "too close", lest the Fermat factorization for be successful. If is less than ( which even for "small" 1024-bit values of is ), solving for and is trivial. Furthermore, if either or has only sm,all prime factors, can be factored quickly by Pollard's p − 1 algorithm, and hence such values of or should be discarded.