Work

Algorithms for the approximate common divisor problem

Year: 2016

Type: article

Abstract: The security of several homomorphic encryption schemes depends on the hardness of variants of the approximate common divisor (ACD) problem. We survey and compare a number of lattice-based algorithms for the ACD problem, with particular attention to some very recently proposed variants of the ACD problem. One of our main goals is to compare the multivariate polynomial approach with other methods. We find that the multivariate polynomial approach is not better than the orthogonal lattice algorithm for practical cryptanalysis. We also briefly discuss a sample-amplification technique for ACD samples and a pre-processing algorithm similar to the Blum–Kalai–Wasserman algorithm for learning parity with noise. The details of this work are given in the full version of the paper.

Source: LMS Journal of Computation and Mathematics

DOI: 10.1112/s1461157016000218

Authors: Steven D. Galbraith, Shishay W. Gebregiyorgis, Sean Murphy

Institutions: University of Auckland, Royal Holloway University of London

Language: English

Topic: Cryptography and Data Security

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: University of Cambridge, Engineering and Physical Sciences Research Council

Award: Multilinear Maps in Cryptography