Ran, Y.; Pan, Y.; Wang, L.; Cao, Z. AIOL: An Improved Orthogonal Lattice Algorithm for the General Approximate Common Divisor Problem. Mathematics2023, 11, 4989.
Ran, Y.; Pan, Y.; Wang, L.; Cao, Z. AIOL: An Improved Orthogonal Lattice Algorithm for the General Approximate Common Divisor Problem. Mathematics 2023, 11, 4989.
Ran, Y.; Pan, Y.; Wang, L.; Cao, Z. AIOL: An Improved Orthogonal Lattice Algorithm for the General Approximate Common Divisor Problem. Mathematics2023, 11, 4989.
Ran, Y.; Pan, Y.; Wang, L.; Cao, Z. AIOL: An Improved Orthogonal Lattice Algorithm for the General Approximate Common Divisor Problem. Mathematics 2023, 11, 4989.
Abstract
The security of several fully homomorphic encryption (FHE) schemes depends on the intractability assumption of the approximate common divisor (ACD) problem over integers. Subsequent efforts on solving the ACD problem as well as its variants were also developed during the past decade. In this paper, an improved orthogonal lattice (OL) based algorithm, AIOL, is proposed to solve the general approximate common divisor (GACD) problem. The conditions for ensuring the feasibility of AIOL are also presented. Compared to the Ding-Tao’s OL algorithm, the well-know LLL reduction is used only once in AIOL, and when the error vector r is recovered in AIOL, the possible difference between the restored and the true value of p is given. The experimental comparisons towards the Ding-Tao’s algorithm and ours are also provided for validating our improvements.
Keywords
General Approximate Common Divisors; Fully Homomorphic Encryption; Lattice Attack; Orthogonal Lattice
Subject
Computer Science and Mathematics, Computer Science
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.
