Improvements on Making BKW Practical for Solving LWE

The learning with errors (LWE) problem is one of the main mathematical foundations post-quantum cryptography. One groups algorithms for solving LWE Blum–Kalai–Wasserman (BKW) algorithm. This paper presents new improvements BKW-style instances. We target minimum concrete complexity, and we introduce a reduction step where partially reduce last position in an iteration finish next iteration, allowing non-integer sizes. also procedure secret recovery by mapping to binary problems applying fast Walsh Hadamard transform. complexity resulting algorithm compares favorably all other previous approaches, including lattice sieving. additionally show steps implementing approach large provide two implementations algorithm, RAM-based that optimized speed, file-based which overcomes RAM limitations using storage.