This chapter has a detailed discussion of the continued
fraction factoring method and the quadratic sieve. To factor a
composite number n, the continued fraction method uses the
continued fraction expansion of to generate
congruences
. These are combined to
produce a congruence of the form
,and using this, it may possible
factor n. The quadratic
sieve factors numbers of the form
to generate
congruences
, from which a congruence
is obtained.