Modeling and simulating the sample complexity of solving LWE using BKW-style algorithms

Abstract The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance post-quantum cryptography. Among solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for Parity Noise (LPN) problem, performs well, especially certain parameter settings cryptographic importance. BKW algorithm consists of two phases, reduction phase and phase. In this work, we study performance distinguishers used We show that Fast Fourier Transform (FFT) distinguisher from Eurocrypt’15 has same sample complexity as optimal distinguisher, when making number hypotheses. also via simulation it better than previous theory predicts develop a model matches simulations better. introduce an improved, pruned version FFT distinguisher. Finally, indicate, extensive experiments, dependency both LF2 amplification is limited.