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Merge pull request #1174 from zama-ai/alex/update_security_curves
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chore(common): add 132 bits security curves
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@BourgerieQuentin
BourgerieQuentin authored Dec 16, 2024
2 parents 21ae59e + 4d6afba commit e00ccea
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278 changes: 278 additions & 0 deletions compilers/concrete-optimizer/v0-parameters/ref/v0_last_132
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security level: 132
target p_error: 6.3e-5
per precision and log norm2:

- 1: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 5, 8, 613, 1, 14, 3, 3, 31, 5.7e-5
- 1 : 5, 8, 645, 1, 14, 3, 3, 32, 6.3e-5
- 2 : 6, 8, 616, 1, 17, 3, 3, 37, 5.6e-5
- 3 : 6, 8, 620, 1, 17, 3, 3, 37, 6.1e-5
- 4 : 6, 8, 656, 1, 17, 3, 3, 39, 6.3e-5
- 5 : 5, 8, 630, 2, 9, 3, 3, 45, 6.1e-5
- 6 : 4, 9, 623, 1, 23, 3, 3, 53, 6.1e-5
- 7 : 4, 9, 624, 1, 23, 3, 3, 53, 5.4e-5
- 8 : 4, 9, 625, 1, 23, 3, 3, 53, 5.8e-5
- 9 : 4, 9, 631, 1, 23, 3, 3, 53, 6.1e-5
- 10: 4, 9, 686, 1, 23, 3, 4, 57, 5.9e-5
- 11: 6, 8, 621, 3, 9, 3, 3, 71, 5.6e-5
- 12: 6, 8, 609, 3, 9, 5, 2, 74, 6.3e-5
- 13: 4, 9, 623, 2, 16, 3, 3, 76, 6.1e-5
- 14: 4, 9, 624, 2, 16, 3, 3, 76, 5.3e-5
- 15: 4, 9, 624, 2, 16, 3, 3, 76, 6.3e-5
- 16: 4, 9, 629, 2, 16, 3, 3, 76, 5.7e-5
- 17: 4, 9, 610, 2, 16, 5, 2, 79, 6.0e-5
- 18: 4, 9, 591, 3, 12, 5, 2, 98, 5.7e-5
- 19: 4, 9, 592, 3, 12, 5, 2, 99, 5.7e-5
- 20: 4, 9, 596, 3, 12, 5, 2, 99, 6.1e-5
- 21: 4, 9, 630, 3, 12, 5, 2, 104, 6.0e-5
- 22: 4, 9, 596, 4, 9, 5, 2, 121, 5.7e-5
- 23: 4, 9, 625, 4, 9, 5, 2, 127, 6.1e-5
- 24: 4, 9, 601, 5, 8, 5, 2, 144, 5.4e-5
- 25: 4, 9, 603, 6, 7, 5, 2, 167, 5.7e-5
- 26: 4, 9, 606, 7, 6, 5, 2, 190, 5.7e-5
- 27: 4, 9, 661, 8, 5, 6, 2, 233, 6.3e-5
- 28: 4, 9, 621, 11, 4, 5, 2, 285, 6.2e-5
- 29: 4, 9, 651, 15, 3, 6, 2, 396, 6.2e-5
- 30: 4, 9, 633, 44, 1, 11, 1, 1070, 6.1e-5
# no solution starting from log norm2 = 31

- 2: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 4, 8, 699, 2, 7, 4, 3, 41, 6.2e-5
- 1 : 6, 8, 702, 1, 17, 3, 4, 42, 6.0e-5
- 2 : 6, 8, 709, 1, 17, 3, 4, 42, 6.0e-5
- 3 : 3, 9, 716, 1, 17, 3, 4, 45, 6.0e-5
- 4 : 5, 8, 711, 2, 9, 4, 3, 52, 6.3e-5
- 5 : 4, 9, 694, 1, 23, 3, 4, 58, 6.0e-5
- 6 : 4, 9, 695, 1, 23, 3, 4, 58, 5.0e-5
- 7 : 4, 9, 696, 1, 23, 3, 4, 58, 5.2e-5
- 8 : 4, 9, 701, 1, 23, 3, 4, 59, 5.4e-5
- 9 : 4, 9, 712, 1, 23, 4, 3, 62, 6.2e-5
- 10: 6, 8, 676, 3, 9, 4, 3, 79, 6.3e-5
- 11: 4, 9, 663, 2, 16, 4, 3, 83, 5.4e-5
- 12: 4, 9, 663, 2, 16, 4, 3, 83, 5.4e-5
- 13: 4, 9, 663, 2, 16, 4, 3, 83, 5.7e-5
- 14: 4, 9, 664, 2, 16, 4, 3, 83, 5.4e-5
- 15: 4, 9, 667, 2, 16, 4, 3, 83, 5.8e-5
- 16: 4, 9, 687, 2, 16, 4, 3, 85, 6.0e-5
- 17: 4, 9, 645, 3, 12, 5, 2, 107, 5.8e-5
- 18: 4, 9, 647, 3, 12, 5, 2, 107, 5.6e-5
- 19: 4, 9, 669, 3, 12, 4, 3, 108, 6.2e-5
- 20: 4, 9, 688, 3, 12, 6, 2, 116, 6.3e-5
- 21: 4, 9, 654, 4, 9, 5, 2, 132, 6.2e-5
- 22: 4, 9, 680, 4, 9, 6, 2, 140, 6.2e-5
- 23: 4, 9, 648, 5, 8, 6, 2, 157, 5.8e-5
- 24: 4, 9, 651, 6, 7, 6, 2, 182, 5.5e-5
- 25: 4, 9, 654, 7, 6, 6, 2, 206, 6.0e-5
- 26: 4, 9, 662, 9, 5, 6, 2, 257, 5.8e-5
- 27: 4, 9, 674, 11, 4, 6, 2, 311, 6.3e-5
- 28: 5, 9, 682, 15, 3, 6, 2, 529, 6.3e-5
- 29: 4, 9, 708, 45, 1, 13, 1, 1228, 6.3e-5
# no solution starting from log norm2 = 30

- 3: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 3, 9, 747, 1, 17, 3, 4, 47, 6.3e-5
- 1 : 3, 9, 757, 1, 17, 3, 4, 48, 6.2e-5
- 2 : 4, 9, 755, 1, 23, 3, 4, 62, 6.0e-5
- 3 : 4, 9, 755, 1, 23, 3, 4, 62, 6.0e-5
- 4 : 4, 9, 755, 1, 23, 3, 4, 62, 6.2e-5
- 5 : 4, 9, 756, 1, 23, 3, 4, 63, 5.9e-5
- 6 : 4, 9, 759, 1, 23, 3, 4, 63, 5.8e-5
- 7 : 4, 9, 774, 1, 23, 3, 4, 64, 6.1e-5
- 8 : 3, 9, 715, 3, 9, 4, 3, 87, 6.0e-5
- 9 : 3, 9, 726, 3, 9, 4, 3, 88, 5.9e-5
- 10: 4, 9, 722, 2, 16, 4, 3, 89, 6.3e-5
- 11: 4, 9, 723, 2, 16, 4, 3, 89, 5.7e-5
- 12: 4, 9, 723, 2, 16, 4, 3, 89, 6.0e-5
- 13: 4, 9, 725, 2, 16, 4, 3, 90, 5.8e-5
- 14: 4, 9, 733, 2, 16, 4, 3, 91, 6.1e-5
- 15: 2, 10, 765, 2, 15, 5, 3, 110, 6.2e-5
- 16: 4, 9, 723, 3, 12, 4, 3, 116, 6.2e-5
- 17: 4, 9, 726, 3, 12, 4, 3, 116, 5.9e-5
- 18: 4, 9, 740, 3, 12, 4, 3, 118, 6.3e-5
- 19: 4, 9, 726, 4, 9, 4, 3, 143, 5.8e-5
- 20: 4, 9, 739, 4, 9, 4, 3, 145, 6.1e-5
- 21: 4, 9, 701, 5, 8, 6, 2, 169, 5.9e-5
- 22: 4, 9, 734, 5, 8, 6, 2, 177, 6.2e-5
- 23: 4, 9, 733, 6, 7, 7, 2, 207, 6.3e-5
- 24: 4, 9, 718, 8, 5, 6, 2, 252, 6.2e-5
- 25: 4, 9, 709, 11, 4, 6, 2, 327, 6.2e-5
- 26: 4, 9, 726, 14, 3, 7, 2, 417, 6.2e-5
- 27: 4, 9, 737, 22, 2, 7, 2, 639, 6.3e-5
# no solution starting from log norm2 = 28

- 4: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 2, 10, 794, 1, 23, 4, 3, 78, 6.3e-5
- 1 : 2, 10, 831, 1, 23, 3, 4, 78, 6.2e-5
- 2 : 2, 10, 831, 1, 23, 3, 4, 78, 6.2e-5
- 3 : 2, 10, 795, 1, 23, 4, 3, 78, 6.3e-5
- 4 : 2, 10, 798, 1, 23, 4, 3, 78, 6.3e-5
- 5 : 2, 10, 838, 1, 23, 3, 5, 79, 6.3e-5
- 6 : 2, 10, 789, 1, 23, 5, 3, 81, 6.2e-5
- 7 : 2, 10, 766, 2, 15, 5, 3, 110, 5.9e-5
- 8 : 2, 10, 766, 2, 15, 5, 3, 110, 5.9e-5
- 9 : 2, 10, 766, 2, 15, 5, 3, 110, 6.0e-5
- 10: 2, 10, 766, 2, 15, 5, 3, 110, 6.1e-5
- 11: 2, 10, 767, 2, 15, 5, 3, 110, 5.7e-5
- 12: 2, 10, 769, 2, 15, 5, 3, 110, 6.0e-5
- 13: 2, 10, 781, 2, 15, 5, 3, 112, 6.1e-5
- 14: 2, 10, 766, 3, 12, 5, 3, 141, 6.2e-5
- 15: 2, 10, 768, 3, 12, 5, 3, 142, 5.6e-5
- 16: 2, 10, 773, 3, 12, 5, 3, 143, 5.7e-5
- 17: 2, 10, 797, 3, 12, 7, 2, 153, 6.3e-5
- 18: 2, 10, 742, 4, 9, 7, 2, 173, 5.9e-5
- 19: 2, 10, 759, 4, 9, 7, 2, 177, 6.3e-5
- 20: 2, 10, 749, 5, 8, 7, 2, 206, 6.2e-5
- 21: 2, 10, 752, 6, 7, 7, 2, 237, 6.1e-5
- 22: 2, 10, 756, 7, 6, 7, 2, 270, 6.0e-5
- 23: 2, 10, 792, 8, 5, 7, 2, 315, 6.3e-5
- 24: 2, 10, 779, 11, 4, 7, 2, 405, 6.2e-5
- 25: 2, 10, 766, 21, 2, 7, 2, 713, 6.3e-5
- 26: 2, 10, 782, 45, 1, 15, 1, 1522, 6.3e-5
# no solution starting from log norm2 = 27

- 5: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 11, 809, 1, 23, 5, 3, 105, 5.9e-5
- 1 : 1, 11, 809, 1, 23, 5, 3, 105, 5.9e-5
- 2 : 1, 11, 809, 1, 23, 5, 3, 105, 6.2e-5
- 3 : 1, 11, 811, 1, 23, 5, 3, 106, 5.8e-5
- 4 : 1, 11, 818, 1, 23, 5, 3, 107, 5.8e-5
- 5 : 1, 11, 809, 2, 15, 5, 3, 150, 5.9e-5
- 6 : 1, 11, 809, 2, 15, 5, 3, 150, 5.9e-5
- 7 : 1, 11, 809, 2, 15, 5, 3, 150, 5.9e-5
- 8 : 1, 11, 809, 2, 15, 5, 3, 150, 5.9e-5
- 9 : 1, 11, 809, 2, 15, 5, 3, 150, 6.1e-5
- 10: 1, 11, 810, 2, 15, 5, 3, 150, 6.0e-5
- 11: 1, 11, 814, 2, 15, 5, 3, 151, 6.1e-5
- 12: 1, 11, 845, 2, 15, 5, 3, 156, 6.2e-5
- 13: 1, 11, 810, 3, 11, 5, 3, 194, 5.7e-5
- 14: 1, 11, 812, 3, 11, 5, 3, 195, 6.2e-5
- 15: 1, 11, 826, 3, 11, 5, 3, 198, 6.3e-5
- 16: 1, 11, 786, 4, 9, 7, 2, 238, 6.1e-5
- 17: 1, 11, 794, 4, 9, 7, 2, 240, 5.9e-5
- 18: 1, 11, 792, 5, 8, 7, 2, 283, 6.2e-5
- 19: 1, 11, 794, 6, 7, 7, 2, 327, 6.2e-5
- 20: 1, 11, 796, 7, 6, 7, 2, 371, 6.3e-5
- 21: 1, 11, 804, 8, 5, 7, 2, 419, 6.0e-5
- 22: 1, 11, 821, 10, 4, 8, 2, 521, 6.2e-5
- 23: 1, 11, 815, 14, 3, 8, 2, 695, 6.3e-5
- 24: 1, 11, 793, 43, 1, 15, 1, 1956, 6.1e-5
# no solution starting from log norm2 = 25

- 6: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 12, 909, 1, 22, 4, 4, 243, 5.9e-5
- 1 : 1, 12, 910, 1, 22, 4, 4, 243, 6.2e-5
- 2 : 1, 12, 917, 1, 22, 4, 4, 245, 6.3e-5
- 3 : 1, 12, 886, 2, 15, 5, 3, 348, 6.0e-5
- 4 : 1, 12, 886, 2, 15, 5, 3, 348, 6.0e-5
- 5 : 1, 12, 886, 2, 15, 5, 3, 348, 6.0e-5
- 6 : 1, 12, 886, 2, 15, 5, 3, 348, 6.0e-5
- 7 : 1, 12, 886, 2, 15, 5, 3, 348, 6.1e-5
- 8 : 1, 12, 887, 2, 15, 5, 3, 348, 6.3e-5
- 9 : 1, 12, 893, 2, 15, 5, 3, 350, 6.3e-5
- 10: 1, 12, 899, 2, 15, 6, 3, 360, 6.3e-5
- 11: 1, 12, 887, 3, 11, 5, 3, 452, 6.0e-5
- 12: 1, 12, 890, 3, 11, 5, 3, 454, 6.1e-5
- 13: 1, 12, 859, 3, 11, 8, 2, 459, 6.3e-5
- 14: 1, 12, 850, 4, 9, 8, 2, 553, 6.0e-5
- 15: 1, 12, 856, 4, 9, 8, 2, 557, 5.9e-5
- 16: 1, 12, 856, 5, 8, 8, 2, 658, 6.0e-5
- 17: 1, 12, 858, 6, 7, 8, 2, 760, 5.9e-5
- 18: 1, 12, 860, 7, 6, 8, 2, 862, 5.9e-5
- 19: 1, 12, 864, 8, 5, 8, 2, 967, 6.1e-5
- 20: 1, 12, 881, 10, 4, 8, 2, 1193, 6.2e-5
- 21: 1, 12, 880, 14, 3, 9, 2, 1611, 6.1e-5
- 22: 1, 12, 863, 42, 1, 17, 1, 4466, 6.3e-5
# no solution starting from log norm2 = 23

- 7: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 13, 946, 1, 22, 6, 3, 564, 6.1e-5
- 1 : 1, 13, 978, 1, 22, 6, 3, 582, 6.2e-5
- 2 : 1, 13, 941, 2, 15, 6, 3, 796, 5.9e-5
- 3 : 1, 13, 941, 2, 15, 6, 3, 796, 5.9e-5
- 4 : 1, 13, 941, 2, 15, 6, 3, 796, 5.9e-5
- 5 : 1, 13, 941, 2, 15, 6, 3, 796, 6.1e-5
- 6 : 1, 13, 942, 2, 15, 6, 3, 797, 5.9e-5
- 7 : 1, 13, 945, 2, 15, 6, 3, 799, 6.1e-5
- 8 : 1, 13, 966, 2, 15, 6, 3, 817, 6.3e-5
- 9 : 1, 13, 941, 3, 11, 6, 3, 1031, 6.2e-5
- 10: 1, 13, 943, 3, 11, 6, 3, 1034, 6.0e-5
- 11: 1, 13, 950, 3, 11, 6, 3, 1041, 6.3e-5
- 12: 1, 13, 943, 4, 9, 6, 3, 1269, 5.9e-5
- 13: 1, 13, 949, 4, 9, 6, 3, 1277, 6.2e-5
- 14: 1, 13, 922, 5, 8, 9, 2, 1516, 6.2e-5
- 15: 1, 13, 924, 6, 7, 9, 2, 1750, 6.3e-5
- 16: 1, 13, 927, 7, 6, 9, 2, 1987, 6.1e-5
- 17: 1, 13, 931, 8, 5, 9, 2, 2228, 6.1e-5
- 18: 1, 13, 944, 10, 4, 9, 2, 2731, 6.3e-5
- 19: 1, 13, 959, 14, 3, 10, 2, 3748, 6.3e-5
- 20: 1, 13, 930, 42, 1, 19, 1, 10276, 6.3e-5
# no solution starting from log norm2 = 21

- 8: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 14, 1040, 2, 15, 5, 4, 1819, 6.0e-5
- 1 : 1, 14, 1040, 2, 15, 5, 4, 1819, 6.0e-5
- 2 : 1, 14, 1040, 2, 15, 5, 4, 1819, 6.1e-5
- 3 : 1, 14, 1040, 2, 15, 5, 4, 1819, 6.2e-5
- 4 : 1, 14, 1041, 2, 15, 5, 4, 1820, 6.1e-5
- 5 : 1, 14, 1045, 2, 15, 5, 4, 1827, 6.2e-5
- 6 : 1, 14, 1035, 2, 15, 7, 3, 1875, 6.2e-5
- 7 : 1, 14, 1008, 3, 11, 7, 3, 2363, 6.1e-5
- 8 : 1, 14, 1010, 3, 11, 7, 3, 2368, 5.8e-5
- 9 : 1, 14, 1016, 3, 11, 7, 3, 2382, 6.3e-5
- 10: 1, 14, 1010, 4, 9, 7, 3, 2904, 5.9e-5
- 11: 1, 14, 1017, 4, 9, 7, 3, 2924, 6.1e-5
- 12: 1, 14, 990, 5, 8, 10, 2, 3467, 6.2e-5
- 13: 1, 14, 991, 6, 6, 10, 2, 3997, 6.3e-5
- 14: 1, 14, 996, 7, 6, 10, 2, 4546, 6.2e-5
- 15: 1, 14, 1001, 8, 5, 10, 2, 5100, 6.1e-5
- 16: 1, 14, 1016, 10, 4, 10, 2, 6255, 6.3e-5
- 17: 1, 14, 1004, 20, 2, 10, 2, 11516, 6.2e-5
- 18: 1, 14, 1004, 42, 1, 20, 1, 23564, 6.3e-5
# no solution starting from log norm2 = 19

- 9: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 15, 1074, 2, 15, 7, 3, 4089, 6.0e-5
- 1 : 1, 15, 1074, 2, 15, 7, 3, 4089, 6.1e-5
- 2 : 1, 15, 1075, 2, 15, 7, 3, 4092, 6.1e-5
- 3 : 1, 15, 1079, 2, 15, 7, 3, 4107, 6.3e-5
- 4 : 1, 15, 1122, 2, 15, 7, 3, 4266, 6.3e-5
- 5 : 1, 15, 1074, 3, 11, 7, 3, 5297, 6.2e-5
- 6 : 1, 15, 1076, 3, 11, 7, 3, 5306, 6.0e-5
- 7 : 1, 15, 1084, 3, 11, 7, 3, 5345, 6.2e-5
- 8 : 1, 15, 1076, 4, 9, 7, 3, 6517, 6.2e-5
- 9 : 1, 15, 1086, 4, 9, 7, 3, 6576, 6.3e-5
- 10: 1, 15, 1083, 5, 7, 7, 3, 7777, 6.2e-5
- 11: 1, 15, 1084, 6, 6, 7, 3, 9003, 6.2e-5
- 12: 1, 15, 1068, 7, 6, 11, 2, 10341, 6.2e-5
- 13: 1, 15, 1075, 8, 5, 11, 2, 11618, 6.2e-5
- 14: 1, 15, 1109, 10, 4, 12, 2, 14546, 6.3e-5
- 15: 1, 15, 1068, 20, 2, 11, 2, 25961, 6.2e-5
- 16: 1, 15, 1098, 42, 1, 23, 1, 54687, 6.3e-5
# no solution starting from log norm2 = 17

- 10: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 16, 1176, 2, 14, 6, 4, 9224, 6.0e-5
- 1 : 1, 16, 1180, 2, 14, 6, 4, 9254, 6.1e-5
- 2 : 1, 16, 1170, 2, 14, 8, 3, 9471, 6.3e-5
- 3 : 1, 16, 1141, 3, 11, 8, 3, 11952, 6.2e-5
- 4 : 1, 16, 1143, 3, 11, 8, 3, 11973, 6.1e-5
- 5 : 1, 16, 1152, 3, 11, 8, 3, 12065, 6.2e-5
- 6 : 1, 16, 1144, 4, 9, 8, 3, 14700, 6.0e-5
- 7 : 1, 16, 1156, 4, 9, 8, 3, 14851, 6.3e-5
- 8 : 1, 16, 1148, 5, 7, 8, 3, 17477, 6.2e-5
- 9 : 1, 16, 1124, 6, 6, 11, 2, 20209, 6.2e-5
- 10: 1, 16, 1146, 7, 6, 12, 2, 23464, 6.3e-5
- 11: 1, 16, 1163, 8, 5, 12, 2, 26571, 6.3e-5
- 12: 1, 16, 1127, 13, 3, 12, 2, 39139, 6.2e-5
- 13: 1, 16, 1137, 20, 2, 12, 2, 58387, 6.3e-5
# no solution starting from log norm2 = 14
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