AIOL: An Improved Orthogonal Lattice Algorithm for the General Approximate Common Divisor Problem

Yinxia Ran, Yun Pan, Licheng Wang () and Zhenfu Cao ()
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Yinxia Ran: School of Computer and Cyberspace Secrity, Communication University of China (CUC), 1 Dingfuzhuang East Street, Beijing 100024, China
Yun Pan: School of Computer and Cyberspace Secrity, Communication University of China (CUC), 1 Dingfuzhuang East Street, Beijing 100024, China
Licheng Wang: School of Cyberspace Science and Technology, Beijing Insititute of Technology (BIT), 5 Zhongguancun South Street, Beijing 100081, China
Zhenfu Cao: Research Center for Basic Theories of Intelligent Computing, Research Institute of Basic Theories, Zhejiang Lab, Hangzhou 311121, China

Mathematics, 2023, vol. 11, issue 24, 1-12

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 to solve 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 OL algorithm, the well-known LLL reduction method 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. Experimental comparisons between the Ding-Tao algorithm and ours are also provided to validate our improvements.

Keywords: general approximate common divisors; fully homomorphic encryption; lattice attack; orthogonal lattice (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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