广义隐式分解问题
Generalized Implicit Factorization Problem
AI总结：
针对不同素数的共享位处于不同且未知位置的情形，论文提出广义隐式分解问题及一种基于格的求解算法，并通过条件分析与实验验证其效率。
摘要：
隐式分解问题（Implicit Factorization Problem）最早由 May 和 Ritzenhofen 在 PKC'09 上提出。该问题旨在当两个 RSA 模数 $N_1=p_1q_1$ 与 $N_2=p_2q_2$ 的素因子共享一定数量的最低有效位（LSBs）时对其进行分解。他们提出了一种基于格的算法来解决该问题，并将其扩展到覆盖 $k>2$ 个 RSA 模数的情形。此后，研究者研究了隐式分解问题的若干变体，包括 $p_1$ 与 $p_2$ 共享部分最高有效位（MSBs）、中间位，或在相同位置同时共享 MSBs 和 LSBs 的情况。本文探索隐式分解问题的一种更一般情形：对于不同素数，共享位位于不同且未知的位置。我们提出一种基于格的算法，并在特定条件下分析其效率；同时给出实验结果以支持分析。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
