New method for factoring two RSA moduli with implicit hint

This paper presents a new method for factoring two RSA moduli N
₁
= p
₁
q
₁
and N
₂
= p
₂
q
₂
with an implicit hint, p
₁
≡ p
₂
(mod 2
^t
). We show that the new method can factor N
₁
and N
₂
with much smaller hint compared with the conventional methods.