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schemes.py
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schemes.py
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# -*- coding: utf-8 -*-
"""
Parameter selection for lattice based schemes submitted to NIST.
NOTATION:
LWE
n lwe secret dimension (d*n for module lwe)
q lwe modulo
sd lwe error standard deviation
(if secret is normal form, also the secret standard devation)
m number of lwe samples
NTRU-like
n dimension of f,g,h
q modulus
norm_f expected norm of f -- we can swap norm_f and norm_g such that norm_g <= norm_f for a potentially better attack
norm_g expected norm of g -- we can swap norm_f and norm_g such that norm_g <= norm_f for a potentially better attack
m number of lwe samples
AUTHOR:
Ben Curtis - 2017, 2018
Alex Davidson - 2017, 2018
Amit Deo - 2018
Rachel Player - 2017, 2018
Eamonn Postlethwaite - 2018
Fernando Virdia - 2017, 2018
Thomas Wunderer - 2018
"""
from sage.all import sqrt, ln, floor, RR, ZZ
try:
from config import DEBUG
except ImportError:
DEBUG = False
if not DEBUG:
# List of proposed schemes
LWE_SCHEMES = [
{
"name": "KCL‑RLWE",
"params": [
{
"n": 1024,
"sd": sqrt(8),
"q": 12289,
"secret_distribution": "normal",
"m": 2*1024,
"claimed": 255,
"category": [
5,
],
"ring": "x^n+1",
},
],
"assumption": [
"RLWE",
],
"primitive": [
"KEM",
],
},
{
"name": "KCL‑MLWE",
"params": [
{
"n": 256*3,
"sd": 1,
"q": 7681,
"k": 3,
"secret_distribution": "normal",
"m": 6*768,
"claimed": 147,
"category": [
4,
],
"ring": "x^{n/k}+1",
},
{
"n": 256*3,
"sd": sqrt(5),
"q": 7681,
"k": 3,
"secret_distribution": "normal",
"m": 6*768,
"claimed": 183,
"category": [
4,
],
"ring": "x^{n/k}+1",
},
],
"assumption": [
"MLWE",
],
"primitive": [
"KEM",
],
},
{
"name": "BabyBear",
"params": [
{
"n": 2*312,
"sd": 1.,
"q": 2**10,
"k": 2,
"secret_distribution": "normal",
"claimed": 152,
"category": [
2,
],
"ring": "q^{n/k} - q^{n/(2k)} - 1",
},
{
"n": 2*312,
"sd": sqrt(5/ZZ(8)),
"q": 2**10,
"k": 2,
"secret_distribution": "normal",
"claimed": 141,
"category": [
2,
],
"ring": "q^{n/k} - q^{n/(2k)} - 1",
},
],
"assumption": [
"ILWE",
],
"primitive": [
"KEM",
],
},
{
"name": "MamaBear",
"params": [
{
"n": 3*312,
"sd": sqrt(7/ZZ(8)),
"q": 2**10,
"k": 3,
"secret_distribution": "normal",
"claimed": 237,
"category": [
5,
],
"ring": "q^{n/k} - q^{n/(2k)} - 1",
},
{
"n": 3*312,
"sd": sqrt(1/ZZ(2)),
"q": 2**10,
"k": 3,
"secret_distribution": "normal",
"claimed": 219,
"category": [
4,
],
"ring": "q^{n/k} - q^{n/(2k)} - 1",
},
],
"assumption": [
"ILWE",
],
"primitive": [
"KEM",
],
},
{
"name": "PapaBear",
"params": [
{
"n": 4*312,
"sd": sqrt(3/ZZ(4)),
"q": 2**10,
"k": 4,
"secret_distribution": "normal",
"claimed": 320,
"category": [
5,
],
"ring": "q^{n/k} - q^{n/(2k)} - 1",
},
{
"n": 4*312,
"sd": sqrt(3/ZZ(8)),
"q": 2**10,
"k": 4,
"secret_distribution": "normal",
"claimed": 292,
"category": [
5,
],
"ring": "q^{n/k} - q^{n/(2k)} - 1",
},
],
"assumption": [
"ILWE",
],
"primitive": [
"KEM",
],
},
{
"name": "CRYSTALS‑Dilithium",
"params": [
{
"n": 256*3,
"sd": sqrt((13**2-1)/ZZ(12)).n(),
"q": 8380417,
"k": 3,
"secret_distribution": (-6, 6),
"m": 256*4,
"claimed": 91,
"category": [
1,
],
"ring": "x^{n/k}+1",
},
{
"n": 256*4,
"sd": sqrt((11**2-1)/ZZ(12)).n(),
"q": 8380417,
"k": 4,
"secret_distribution": (-5, 5),
"m": 256*5,
"claimed": 125,
"category": [
2,
],
"ring": "x^{n/k}+1",
},
{
"n": 256*5,
"sd": sqrt((7**2-1)/ZZ(12)).n(),
"q": 8380417,
"k": 5,
"secret_distribution": (-3, 3),
"m": 256*6,
"claimed": 158,
"category": [
3,
],
"ring": "x^{n/k}+1",
},
],
"assumption": [
"MLWE",
],
"primitive": [
"SIG",
],
},
{
"name": "CRYSTALS‑Kyber",
"params": [
{
"n": 256*2,
"sd": sqrt(5/ZZ(2)),
"q": 7681,
"k": 2,
"secret_distribution": "normal",
"m": 256*3,
"claimed": 102,
"category": [
1,
],
"ring": "x^{n/k}+1",
},
{
"n": 256*3,
"sd": sqrt(4/ZZ(2)),
"q": 7681,
"k": 3,
"secret_distribution": "normal",
"m": 256*4,
"claimed": 161,
"category": [
3,
],
"ring": "x^{n/k}+1",
},
{
"n": 256*4,
"sd": sqrt(3/ZZ(2)),
"q": 7681,
"k": 4,
"secret_distribution": "normal",
"m": 256*5,
"claimed": 218,
"category": [
5,
],
"ring": "x^{n/k}+1",
},
],
"assumption": [
"MLWE",
],
"primitive": [
"KEM",
"PKE",
],
},
{
"name": "Ding Key Exchange",
"params": [
{
"n": 512,
"sd": 4.19,
"q": 120883,
"secret_distribution": "normal",
"claimed": None,
"category": [
1,
],
"ring": "x^n+1",
},
{
"n": 1024,
"sd": 2.6,
"q": 120883,
"secret_distribution": "normal",
"claimed": None,
"category": [
3,
5,
],
"ring": "x^n+1",
},
],
"assumption": [
"RLWE",
],
"primitive": [
"KEM",
],
},
{
"name": "EMBLEM",
"params": [
{
"n": 770,
"sd": 25,
"q": 2**24,
"secret_distribution": (-1, 1),
"m": 1003,
"claimed": 128.3,
"category": [
1,
],
},
{
"n": 611,
"sd": 25,
"q": 2**24,
"secret_distribution": (-2,2),
"m": 832,
"claimed": 128.3,
"category": [
1,
],
},
],
"assumption": [
"LWE",
],
"primitive": [
"PKE",
"KEM",
],
},
{
"name": "R EMBLEM",
"params": [
{
"n": 512,
"sd": 25,
"q": 2**16,
"secret_distribution": (-1,1),
"claimed": 128.1,
"category": [
1,
],
"ring": "x^n+1 \\text{ \\textdagger}",
},
{
"n": 512,
"sd": 3,
"q": 2**14,
"secret_distribution": (-1,1),
"claimed": 128.3,
"category": [
1,
],
"ring": "x^n+1 \\text{ \\textdagger}",
},
],
"assumption": [
"RLWE"
],
"primitive": [
"PKE",
"KEM",
],
},
{
"name": "Frodo",
"params": [
{
"n": 640,
"sd": 2.75,
"q": 2**15,
"secret_distribution": "normal",
"claimed": 103,
"category": [
1,
],
},
{
"n": 976,
"sd": 2.3,
"q":2**16,
"secret_distribution": "normal",
"claimed": 150,
"category": [
3,
],
},
],
"assumption": [
"LWE",
],
"primitive": [
"KEM",
"PKE",
],
},
{
"name": "NewHope",
"params": [
{
"n": 512,
"sd": 2,
"q": 12289,
"secret_distribution": "normal",
"claimed": 101,
"category": [
1,
],
"ring": "x^n+1",
},
{
"n": 1024,
"sd": 2,
"q": 12289,
"secret_distribution": "normal",
"claimed": 233,
"category": [
5,
],
"ring": "x^n+1",
},
],
"assumption": [
"RLWE",
],
"primitive": [
"KEM",
"PKE",
],
},
{
"name": "HILA5",
"params": [
{
"n": 1024,
"sd": sqrt(8),
"q": 12289,
"secret_distribution": "normal",
"claimed": 255,
"category": [
5,
],
"ring": "x^n+1",
},
],
"assumption": [
"RLWE",
],
"primitive": [
"KE",
],
},
{
"name": "KINDI",
"params": [
{
"n": 256*3,
"sd": sqrt((8**2-1)/ZZ(12)),
"q": 2**14,
"k": 3,
"secret_distribution": (-4, 4), # (-4,3),
"claimed": 164,
"category": [
2,
],
"ring": "x^{n/k}+1",
},
{
"n": 512*2,
"sd": sqrt((4**2-1)/ZZ(12)),
"q": 2**13,
"k": 2,
"secret_distribution": (-2, 2), # (-2,1),
"claimed": 207,
"category": [
4,
],
"ring": "x^{n/k}+1",
},
{
"n": 512*2,
"sd": sqrt((8**2-1)/ZZ(12)),
"q": 2**14,
"k": 2,
"secret_distribution": (-4, 4), # (-4,3),
"claimed": 232,
"category": [
4,
],
"ring": "x^{n/k}+1",
},
{
"n": 256*5,
"sd": sqrt((4**2-1)/ZZ(12)),
"q": 2**14,
"k": 5,
"secret_distribution": (-2, 2), # (-2,1),
"claimed": 251,
"category": [
5,
],
"ring": "x^{n/k}+1",
},
{
"n": 512*3,
"sd": sqrt((4**2-1)/ZZ(12)),
"q": 2**13,
"k": 3,
"secret_distribution": (-2, 2), # (-2,1),
"claimed": 330,
"category": [
5,
],
"ring": "x^{n/k}+1",
},
],
"assumption": [
"MLWE",
],
"primitive": [
"PKE",
"KEM",
],
},
{
"name": "LAC",
"params": [
{
"n": 512,
"sd": 1/sqrt(2),
"q": 251,
"secret_distribution": "normal",
"m": 2*512,
"claimed": 128,
"category": [
1,
2,
],
"ring": "x^n+1",
},
{
"n": 1024,
"sd": 0.5,
"q": 251,
"secret_distribution": "normal",
"m": 2*1024,
"claimed": 192,
"category": [
3,
4,
],
"ring": "x^n+1",
},
{
"n": 1024,
"sd": 1/sqrt(2),
"q": 251,
"secret_distribution": "normal",
"m": 2*1024,
"claimed": 256,
"category": [
5,
],
"ring": "x^n+1",
}
],
"assumption": [
"PLWE",
],
"primitive": [
"PKE",
"KEM",
"KE",
],
},
{
"name": "LIMA-2p",
"params": [
{
"n": 1024,
"sd": sqrt(10),
"q": 133121,
"secret_distribution": "normal",
"claimed": 208.8,
"category": [
3,
],
"ring": "x^n+1",
},
{
"n": 2048,
"sd": sqrt(10),
"q": 184321,
"secret_distribution": "normal",
"claimed": 444.5,
"category": [
4,
],
"ring": "x^n+1",
}
],
"assumption": [
"RLWE",
],
"primitive": [
"KEM",
"PKE",
],
},
{
"name": "LIMA‑sp",
"params": [
{
"n": 1018,
"sd": sqrt(10),
"q": 12521473,
"secret_distribution": "normal",
"claimed": 139.2,
"category": [
1,
],
"ring": "\sum_{i=0}^n x^i",
},
{
"n": 1306,
"sd": sqrt(10),
"q": 48181249,
"secret_distribution": "normal",
"claimed": 167.8,
"category": [
2,
],
"ring": "\sum_{i=0}^n x^i",
},
{
"n": 1822,
"sd": sqrt(10),
"q": 44802049,
"secret_distribution": "normal",
"claimed": 247.9,
"category": [
3,
],
"ring": "\sum_{i=0}^n x^i",
},
{
"n": 2062,
"sd": sqrt(10),
"q": 16900097,
"secret_distribution": "normal",
"claimed": 303.5,
"category": [
4,
],
"ring": "\sum_{i=0}^n x^i",
}
],
"assumption": [
"RLWE",
],
"primitive": [
"KEM",
"PKE",
],
},
{
"name": "Lizard",
"params": [
[
#CCA_CATEGORY1_N536
{ # ephemeral
"n": 1024,
"sd": sqrt(4**2/ZZ(12)),
"q": 2048,
"secret_distribution": ((-1,1), 140),
"claimed": 130,
"category": [
1,
],
},
{ # keygen
"n": 536,
"sd": 2.58555,
"q": 2048,
"secret_distribution": ((-1,1), 268), #rho=1/2
"m": 1024,
"claimed": 133,
"category": [
1,
],
},
],
[
#CCA_CATEGORY1_N663
{ # ephemeral
"n": 1024,
"sd": sqrt(4**2/ZZ(12)),
"q": 1024,
"secret_distribution": ((-1,1), 128),
"claimed": 147,
"category": [
1,
],
},
{ # keygen
"n": 663,
"sd": 0.891,
"q": 1024,
"secret_distribution": ((-1,1), 497), #rho=1/4
"m": 1024,
"claimed": 131,
"category": [
1,
],
},
],
[
#CCA_CATEGORY3_N816
{ # ephemeral
"n": 1024,
"sd": sqrt(4**2/ZZ(12)),
"q": 2048,
"secret_distribution": ((-1,1), 200),
"claimed": 195,
"category": [
3,
],
},
{ # keygen
"n": 816,
"sd": 1.3394,
"q": 2048,
"secret_distribution": ((-1,1), 408), #rho=1/2
"m": 1024,
"claimed": 193,
"category": [
3,
],
},
],
[
# CCA_CATEGORY3_N952
{ # ephemeral
"n": 1024,
"sd": sqrt(4**2/ZZ(12)),
"q": 2048,
"secret_distribution": ((-1,1), 200),
"claimed": 195,
"category": [
3,
],
},
{ # keygen
"n": 952,
"sd": 1.675967,
"q": 2048,
"secret_distribution": ((-1,1), 714), #rho=1/4
"m": 1024,
"claimed": 203,
"category": [
3,
],
},
],
[
# CCA_CATEGORY5_N1088
{ # ephemeral
"n": 2048,
"sd": sqrt(4**2/ZZ(12)),
"q": 4096,
"secret_distribution": ((-1,1), 200),
"claimed": 257,
"category": [
5,
],
},
{ # keygen
"n": 1088,
"sd": 3.11251,
"q": 4096,
"secret_distribution": ((-1,1), 544), #rho=1/2
"m": 2048,
"claimed": 266,
"category": [
5,
],
},
],
[
# CCA_CATEGORY5_N1300
{ # ephemeral
"n": 2048,
"sd": sqrt(4**2/ZZ(12)),
"q": 2048,
"secret_distribution": ((-1,1), 200),
"claimed": 291,
"category": [
5,
],
},
{ # keygen
"n": 1300,
"sd": 1.072223,
"q": 2048,
"secret_distribution": ((-1,1), 975), #rho=1/4
"m": 2048,
"claimed": 264,
"category": [
5,
],
},
],
],
"assumption": [
"LWR",
"LWE",
],
"primitive": [
"PKE",
"KEM",
],
},
{
"name": "RLizard",
"params": [
[
#RING_CATEGORY1
{ # ephemeral
"n": 1024,
"sd": sqrt(4**2/ZZ(12)),
"q": 1024,
"secret_distribution": ((-1,1), 128),
"claimed": 147,
"category": [
1,
],
"ring": "x^n+1",
},
{ # keygen
"n": 1024,
"sd": 1.069416,
"q": 1024,
"secret_distribution": ((-1,1), 128),
"claimed": 153,
"category": [
1,
],
"ring": "x^n+1",
},
],
[
#RING_CATEGORY3_N1024
{ # ephemeral
"n": 1024,
"sd": sqrt(4**2/ZZ(12)),
"q": 2048,
"secret_distribution": ((-1,1), 264),
"claimed": 195,
"category": [
3,
],
"ring": "x^n+1",
},
{ # keygen
"n": 1024,
"sd": 1.458989,
"q": 2048,
"secret_distribution": ((-1,1), 256),
"claimed": 195,
"category": [
3,
],
"ring": "x^n+1",
},
],
[
#RING_CATEGORY3_N2048
{ # ephemeral
"n": 2048,
"sd": sqrt(4**2/ZZ(12)),
"q": 2048,
"secret_distribution": ((-1,1), 164),
"claimed": 291,
"category": [
3,
],
"ring": "x^n+1",
},
{ # keygen
"n": 2048,
"sd": 2.002534,
"q": 2048,
"secret_distribution": ((-1,1), 184),
"claimed": 304,
"category": [
3,
],
"ring": "x^n+1",
},
],
[
# RING_CATEGORY5
{ # ephemeral
"n": 2048,
"sd": sqrt(4**2/ZZ(12)),
"q": 4096,
"secret_distribution": ((-1,1), 256),
"claimed": 348,
"category": [
5,
],
"ring": "x^n+1",
},
{ # keygen
"n": 2048,
"sd": 2.635593,
"q": 4096,
"secret_distribution": ((-1,1), 256),
"claimed": 318,
"category": [
5,
],
"ring": "x^n+1",
},
],
],
"assumption": [
"RLWR",
"RLWE",
],
"primitive": [
"PKE",
"KEM",
],
},
{
"name": "LOTUS",
"params": [
{
"n": 576,
"sd": 3,
"q": 8192,
"secret_distribution": "normal",
"claimed": None,
"category": [
1,
2,
],
},
{
"n": 704,
"sd": 3,
"q": 8192,
"secret_distribution": "normal",