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arXiv · 2304.08718

Generalized Implicit Factorization Problem

Yansong Feng·Abderrahmane Nitaj·Yanbin Pan
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Abstract

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 bits, or both MSBs and LSBs at the same position. In this paper, we explore a more general case of the Implicit Factorization Problem, where the shared bits are located at different and unknown positions for different primes. We propose a lattice-based algorithm and analyze its efficiency under certain conditions. We also present experimental results to support our analysis.

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Yansong Feng, Abderrahmane Nitaj, Yanbin Pan. 2023-04-18. Generalized Implicit Factorization Problem. https://doi.org/10.1007/978-3-031-53368-6_18

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