Version 1
: Received: 8 June 2023 / Approved: 9 June 2023 / Online: 9 June 2023 (11:40:26 CEST)
Version 2
: Received: 9 June 2023 / Approved: 12 June 2023 / Online: 12 June 2023 (13:47:43 CEST)
How to cite:
Ran, Y.; Pan, Y.; Wang, L. Alogrithms for the ACD Problem and Cryptanalysis of ACD-based FHE schemes, Revisited. Preprints2023, 2023060712. https://doi.org/10.20944/preprints202306.0712.v1
Ran, Y.; Pan, Y.; Wang, L. Alogrithms for the ACD Problem and Cryptanalysis of ACD-based FHE schemes, Revisited. Preprints 2023, 2023060712. https://doi.org/10.20944/preprints202306.0712.v1
Ran, Y.; Pan, Y.; Wang, L. Alogrithms for the ACD Problem and Cryptanalysis of ACD-based FHE schemes, Revisited. Preprints2023, 2023060712. https://doi.org/10.20944/preprints202306.0712.v1
APA Style
Ran, Y., Pan, Y., & Wang, L. (2023). Alogrithms for the ACD Problem and Cryptanalysis of ACD-based FHE schemes, Revisited. Preprints. https://doi.org/10.20944/preprints202306.0712.v1
Chicago/Turabian Style
Ran, Y., Yun Pan and Licheng Wang. 2023 "Alogrithms for the ACD Problem and Cryptanalysis of ACD-based FHE schemes, Revisited" Preprints. https://doi.org/10.20944/preprints202306.0712.v1
Abstract
The security of several full homomorphic encryption (FHE) schemes depends on the hardness of the approximate common divisor (ACD) problem. The analysis of attack and defense against the system is one of the frontiers of cryptography research. In this paper, the performance of existing algorithms, including orthogonal lattice, simultaneous diophantine approximation, multivariate polynomial and sample pre-processing are reviewed and analyzed for solving the ACD problem. Orthogonal lattice (OL) algorithms are divided into two categories (OL-$\land$ and OL-$\vee$) for the first time. And an improved algorithm of OL-$\vee$ is presented to solve the GACD problem. This new algorithm works well in polynomial time if the parameter satisfies certain conditions. Compared with Ding and Tao's OL algorithm, the lattice reduction algorithm is used only once, and when the error vector $\mathbf{r}$ is recovered in Ding et al.'s OL algorithm, the possible difference between the restored and the true value of $p$ is given. It is helpful to expand the scope of OL attacks.
Keywords
Approximate common divisors; Fully homomorphic encryption; lattice attack; orthogonal lattice
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
