Curve detail
Definition
| Name | secp192k1 |
|---|---|
| Category | secg |
| Description | A Koblitz curve. |
| Field | Prime (0xfffffffffffffffffffffffffffffffffffffffeffffee37) |
| Field bits | 192 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x000000000000000000000000000000000000000000000000 |
| Param $b$ | 0x000000000000000000000000000000000000000000000003 |
| Generator $x$ | 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d |
| Generator $y$ | 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d |
Characteristics
| Order | 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d |
| Cofactor | 0x1 |
| $j$-invariant | 0x0 |
| Trace $t$ | 0x1d90d03e8f096b9948b20f0ab |
| Embedding degree $k$ | 0x7fffffffffffffffffffffff13797e0b87b4a3353a6f7ec6 |
| CM discriminant | -0x3 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x3 |
| factorization | ['0x3', '0x1f', '0x1f', '0x1f', '0x1f', '0x1343', '0x1343', '0xd32b', '0xd32b', '0x1e563f01ef28cf1', '0x1e563f01ef28cf1'] |
| max_conductor | 0x71169be7330b3038edb025f1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x1000000000000000000000001d90d03e8f096b9938b20dee3 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffffffffffffffdffffdc6f6a21191c2ec4b2ae3edaa7e3ce2f0d126dee58e2c03d859d |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x2', '0x49', '0xb29', '0x1273a13ceb3', '0x22e08c624dcd7d99a364586e95e9260cad'] |
| (+)largest_factor_bitlen | 0x86 |
| (-)factorization | ['0x2', '0x2', '0x3', '0xd', '0xd', '0x11', '0x1f', '0x29', '0x62041f6e94d523eef565dfbdbc1c7a4b195f66b2df'] |
| (-)largest_factor_bitlen | 0xa7 |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x3', '0x3', '0x3', '0x5', '0x7', '0x6d', '0x13422815483', '0x10ea3a7835788c83c4ddf06dc365b61c31d'] |
| (+)largest_factor_bitlen | 0x89 |
| (-)factorization | ['0x3b3', '0x5cf', '0x42d75af', '0x1707af4b4f5', '0x123e0a2d03286d', '0x379c0cc0ae7b93'] |
| (-)largest_factor_bitlen | 0x36 |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x2', '0x2', '0x2', '0x5fffffffffffffffffffffff4e9b1e88a5c77a67ebd39f15'] |
| (+)largest_factor_bitlen | 0xbf |
| (-)factorization | ['0x2', '0x5', '0x110b', '0x40e77', '0x25ef1f74f4195', '0x77f2ccf1cc43878fc95c97fc2957'] |
| (-)largest_factor_bitlen | 0x6f |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | ['0x4cf', '0x751', '0x9ad', '0xcb3', '0x2905', '0x808f', '0x34b5c3', '0x25e6e9ec284d', '0x6091707d7a6361'] |
| (+)largest_factor_bitlen | 0x37 |
| (-)factorization | ['0x3', '0x61', '0x68ff', '0x12077b', '0x178fbd369907a8f', '0x52ba73276ce1fc3c6f7fc173'] |
| (-)largest_factor_bitlen | 0x5f |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x2', '0x3', '0xb', '0x4813', '0x28875301', '0x1b31d814ca1f5ace6fd89be550c4797b5b05b'] |
| (+)largest_factor_bitlen | 0x91 |
| (-)factorization | ['0x2', '0x2', '0x2', '0x2', '0x2', '0x2', '0x7', '0x35', '0x4f', '0x90149', '0x46acedb918ed3', '0x11fd0f477aab1e427aa0c636831'] |
| (-)largest_factor_bitlen | 0x69 |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x49a71', '0x14dacb48a47ec7f0bb7d02916c50797ba8ae4b13ba7bf'] |
| (+)largest_factor_bitlen | 0xb1 |
| (-)factorization | ['0xb', '0xb03', '0x17bf', '0x1708f', '0xf239e63', '0x645b25bd023b544137376b6c2e57d5f'] |
| (-)largest_factor_bitlen | 0x7b |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x2', '0x2', '0x5', '0x17', '0x1d', '0x2f', '0x246515f5afe91', '0x5258a7450ffebaf3e10b02acff491d8f'] |
| (+)largest_factor_bitlen | 0x7f |
| (-)factorization | ['0x2', '0x3', '0x3', '0x29a7', '0xaa26df', '0x39898b69a856ac42eb18095b0f087377edebe2d'] |
| (-)largest_factor_bitlen | 0x9a |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x3', '0x78b', '0x5a80f33a8dad5cc1e94922f3e6b46222eeb098df3d28c9'] |
| (+)largest_factor_bitlen | 0xb7 |
| (-)factorization | ['0x5', '0x3d25133fcfd872cb9', '0x6b2e7d27375298d83ecfe3b90691b6d3'] |
| (-)largest_factor_bitlen | 0x7f |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x2 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x3 |
| full | 0xc |
| relative | 0x4 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x60 |
| full | 0x60 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x1d90d03e8f096b9948b20f0ab |
| factorization | ['0xb', '0x44b183', '0xa043f8140dea19f1cb'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x26a21191c2ec4b2ae3edaa7e3ce2f0d116dee354fbf012402 |
| factorization | ['0x2', '0x3', '0x3', '0x7', '0x648d', '0x2933c9', '0x117cfaed', '0x15509106a663', '0x354bdb9b30d9a6831125'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x29d29909b3e7621aae2c76c058d141a59271da7042a4f1d627c34813f636ba4b8aa9d3e99 |
| factorization | ['0xb', '0xd', '0x44b183', '0xa043f8140dea19f1cb', '0x8b9f50c2db6336ec669', '0x33131c3dc9949d2fb6e77bfe8649f'] |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x2 |
| complement_bit_length | 0x2 |
| $\text{class_number}()$ | |
| upper | 0x2 |
| lower | 0x0 |
| $\text{small_prime_order}(l=2)$ | |
| order | 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8c |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x3fffffffffffffffffffffff89bcbf05c3da519a9d37bf63 |
| complement_bit_length | 0x3 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x555555555555555555555554b7a65407afcdc2237c4a5484 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8c |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8c |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x7fffffffffffffffffffffff13797e0b87b4a3353a6f7ec6 |
| complement_bit_length | 0x2 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x1', '0x1'], ['0x3', '0x1']] |
| len | 0x2 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0xc', '0x1']] |
| len | 0x1 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=3)$ | |
| crater_degree | 0x1 |
| depth | 0x0 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=7)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=11)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=13)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=17)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=19)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{isogeny_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=3)$ | |
| least | 0x1 |
| full | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0x4 |
| relative | 0x4 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x12 |
| relative | 0x12 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x1d90d03e8f096b9948b20f0ab |
| trace_factorization | ['0xb', '0x44b183', '0xa043f8140dea19f1cb'] |
| number_of_factors | 0x3 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x1d90d03e8f096b9948b20f0ab |
| trace_factorization | NO DATA (timed out) |
| number_of_factors | NO DATA (timed out) |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x3 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x4 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x0 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0x67 |
| expected | 0x60 |
| ratio | 0.93204 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x2412 |
| expected | 0x23d0 |
| ratio | 0.99285 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x8dbd3 |
| expected | 0x8dc20 |
| ratio | 1.00013 |
| $\text{square_4p1}()$ | |
| p | 0x3 |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0x1d90d03e8f096b9958b210273 |
| ratio | 4.287575002426037e+28 |
| distance 32 | 0xd |
| distance 64 | 0xd |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d |
| bits | 0xc0 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x554123b78ce563f89a0ed9414f5aa28ad0d96d6795f9c66 |
| bits | 0xbb |
| difference | 0x5 |
| ratio | 0.97396 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x60bba5021df10b44d6e31f9b901b83bddbe7ce07ae94681f |
| bits | 0xbf |
| difference | 0x1 |
| ratio | 0.99479 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0x1be5434c72cf928dc1a105905e8ca6daf4c85cab9145aab6 |
| bits | 0xbd |
| difference | 0x3 |
| ratio | 0.98438 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0x577ab451b17027eea6e643c7714762f48c81530320673802 |
| bits | 0xbf |
| difference | 0x1 |
| ratio | 0.99479 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0xe188a41a9c084bcee05b396c5be3b3209b5106b78b185aef |
| bits | 0xc0 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x4f43d867993d35d35502791626508ecee847f874e18610a4 |
| bits | 0xbf |
| difference | 0x1 |
| ratio | 0.99479 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0xed9521f70f3a50c67fc27f1267aa4b49b6a1e7fd67f2808b |
| bits | 0xc0 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x984f9cb52b96c303cb6b2f1af4ff87fb951fb2a868342bc7 |
| bits | 0xc0 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0x44c396a97fd06ef50fd85799c71ddc722dfe4fe7974e0c41 |
| bits | 0xbf |
| difference | 0x1 |
| ratio | 0.99479 |
| $\text{x962_invariant}()$ | |
| r | 0x0 |
| $\text{brainpool_overlap}()$ | |
| o | 0x0 |
| $\text{weierstrass}()$ | |
| a | 0x0 |
| b | 0x3 |