From learning with errors (LWE) problem to CLWE problem

Abstract

The main purpose of this paper is to introduce the learning with errors problem on cyclic algebras, i.e., the CLWE problem, and to fully discuss and utilize the well-proven LWE-related conclusions and assumptions in cryptography theory. Firstly, this paper provides the basic framework of Learning with Errors (LWE) problems for cyclic algebra samples. Then lattices generated by the two-sided ideal of cyclic algebra with natural order are applied to cryptography. Based on the above contents, the so-called CLWE problem is introduced to point out the dimensions and structures suitable for constructing cryptographic systems for explicit algebra, and the security of corroding problems is discussed in the CLWE samples. Finally, this paper also discusses some possible future research directions, some natural routes to further research the construction and application of CLWE problems, for example, how to choose parameters for a specific security level, so as to offer some references for future study.