Table 5 Concrete security estimation of LWE instances from Regev’s and Lindner-Peikert’s cryptosystems
Parameters | The BKW Algorithms | The Lattice-based Algorithms | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
n | q | \(\sigma\) | Plain BKW | LMS-BKW | FFT-BKW | Coded-BKW | Sieve-Coded-BKW | BKW-FWHT-SR | Primal | Decoding | Dual |
Regev parameters | |||||||||||
128 | 16411 | 11.81 | 119.4 | 114.7 | 107.5 | 84.5 | 84.2 | 59.2 | 57.3 | 61.9 | 69.2 |
256 | 65537 | 25.53 | 269.6 | 220.3 | 200.8 | 145.1 | 130.0 | 107.0 | 103.6 | 121.7 | 121.0 |
512 | 262147 | 57.06 | 429.4 | 403.4 | 384.6 | 287.6 | 247.6 | 243.3 | 201.6 | 252.7 | 231.2 |
Lindner-Peikert parameters | |||||||||||
128 | 2053 | 2.7 | 104.4 | 100.0 | 95.7 | 69.7 | 69.2 | 48.8 | 53.4 | 57.1 | 67.5 |
256 | 4099 | 3.34 | 181.8 | 176.0 | 167.9 | 123.8 | 112.9 | 98.5 | 95.2 | 111.8 | 112.3 |
512 | 4099 | 2.9 | 338.8 | 327.7 | 308.0 | 209.2 | 197.3 | 188.7 | 179.0 | 226.5 | 207.8 |