Security estimation of LWE via BKW algorithms

Abstract

Abstract The Learning With Errors (LWE) problem is widely used in lattice-based cryptography, which is the most promising post-quantum cryptography direction. There are a variety of LWE-solving methods, which can be classified into four groups: lattice methods, algebraic methods, combinatorial methods, and exhaustive searching. The Blum–Kalai–Wasserman (BKW) algorithm is an important variety of combinatorial algorithms, which was first presented for solving the Learning Parity With Noise (LPN) problem and then extended to solve LWE. In this paper, we give an overview of BKW algorithms for solving LWE. We introduce the framework and key techniques of BKW algorithms and make comparisons between different BKW algorithms and also with lattice methods by estimating concrete security of specific LWE instances. We also briefly discuss the current problems and potential future directions of BKW algorithms.

Keywords

• Post-quantum cryptography
• Learning with errors problem
• Lattice-based cryptography
• Security estimation