Table 1 Security of post-quantum digital signature schemes. Two values of security bits for CRYSTALS-DILITHIUM are given with respect to short integer solution (SIS) and learning with errors (LWE) problems, correspondingly
Algorithm | Basic approach | Variant of the algorithm | Classical security, bit | Quantum security, bit |
|---|---|---|---|---|
Falcon | Lattice | n = 768 | 195 | 172 |
CRYSTALS-DILITHIUM | Lattice | Very high | 176/174 | 160/158 |
Rainbow | Multivariate | Classic | 207 | 169 |
Compressed | 207 | 169 | ||
GeMSS | Multivariate cryptography | GeMSS192 | 192 | 112.2 |
BlueGeMSS192 | 192 | 112.2 | ||
RedGeMSS192 | 192 | 112.2 | ||
Picnic | Zero-knowledge proof systems | picnic-L3-FS | 192 | 96 |
picnic-L3-UR | 192 | 96 | ||
picnic2-L3-FS | 192 | 96 | ||
SPHINCS+ | Hash functions | sphincs-haraka-192f | 194 | 97 |
sphincs-sha256-192s | 196 | 98 | ||
sphincs-shake256-192f | 194 | 97 |