Generalized Implicit Factorization Problem. (arXiv:2304.08718v1 [cs.CR])

The Implicit Factorization Problem was first introduced by May and
Ritzenhofen at PKC'09. This problem aims to factorize two RSA moduli
$N_1=p_1q_1$ and $N_2=p_2q_2$ when their prime factors share a certain number
of least significant bits (LSBs). They proposed a lattice-based algorithm to
tackle this problem and extended it to cover $k>2$ RSA moduli. Since then,
several variations of the Implicit Factorization Problem have been studied,
including the cases where $p_1$ and $p_2$ share some most significant bits
(MSBs), middle …

algorithm bits cases least significant bits may pkc prime problem rsa share