International Association
for Cryptologic Research

The Implicit Factorization Problem (IFP) was first introduced by May and Ritzenhofen at PKC'09, which concerns the factorization of two RSA moduli $N_1=p_1q_1$ and $N_2=p_2q_2$, where $p_1$ and $p_2$ share a certain consecutive number of least significant bits. Since its introduction, many different variants of IFP have been considered, such as the cases where $p_1$ and $p_2$ share most significant bits or middle bits at the same positions. In this paper, we consider a more generalized case of IFP, in which the shared consecutive bits can be located at $any$ positions in each prime, not necessarily required to be located at the same positions as before. We propose a lattice-based algorithm to solve this problem under specific conditions, and also provide some experimental results to verify our analysis.