Curve detail
Definition
| Name | secp224k1 |
|---|---|
| Category | secg |
| Description | A Koblitz curve. |
| Field | Prime (0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d) |
| Field bits | 224 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x00000000000000000000000000000000000000000000000000000000 |
| Param $b$ | 0x00000000000000000000000000000000000000000000000000000005 |
| Generator $x$ | 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c |
| Generator $y$ | 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5 |
Characteristics
| Order | 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 |
| Cofactor | 0x1 |
| $j$-invariant | 0x0 |
| Trace $t$ | -0x1dce8d2ec6184caf0a972769fcc89 |
| Embedding degree $k$ | 0x2aaaaaaaaaaaaaaaaaaaaaaaaaaafa26cdd21040cc7d7192e91a9da9 |
| CM discriminant | -0x3 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | NO DATA (timed out) |
| factorization | NO DATA (timed out) |
| max_conductor | NO DATA (timed out) |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffe23172d139e7b350f568c896018e5 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffffffffffffffffffffffdffffcadb7872a41e04df3da09943b0fdc1613c18185dad7d8e36f57a045b06e1 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x2', '0x3', '0x2aaaaaaaaaaaaaaaaaaaaaaaaaaafa26cdd21040cc7d7192e91a9da9'] |
| (-)largest_factor_bitlen | 0xde |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x3', '0x3', '0x3', '0x7', '0x7', '0x2b', '0x1db21', '0x13dcc17192a098a9015f7b98a48b594faabd29dca198fa587'] |
| (+)largest_factor_bitlen | 0xc1 |
| (-)factorization | ['0x13d', '0x2a1', '0x16a375', '0x8c62cd', '0x54c8a2d0d7', '0x96250715bb9fb', '0x413920244914d1c6ea5'] |
| (-)largest_factor_bitlen | 0x4b |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x2', '0x53', '0x1c9', '0x4264aac21693ce5d', '0x132db81df40dd259f', '0x85634b704bfd2024ad4b3'] |
| (+)largest_factor_bitlen | 0x54 |
| (-)factorization | ['0x2', '0x2', '0xd', '0x17', '0x164da7', '0x35dc4bb', '0x23084a16ac41290e1334d578bc6d10d058e75a1d307'] |
| (-)largest_factor_bitlen | 0xaa |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | ['0x11', '0x3c8128d195', '0xd7ee97da782d060dd', '0x12e27046a13ade2025975ea55a59ed'] |
| (+)largest_factor_bitlen | 0x75 |
| (-)factorization | ['0x3', '0x5', '0xb', '0x278b2dd3', '0x77940103', '0x93b9fdb900f732b', '0x950e443c16deced9e7e989ea5'] |
| (-)largest_factor_bitlen | 0x64 |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x2', '0x2', '0x3', '0x35', '0x23cec545283d', '0xd9f09f36e487', '0x10e6ba3f4e61c88fd65efd76f2f868c1'] |
| (+)largest_factor_bitlen | 0x7d |
| (-)factorization | ['0x2', '0x7', '0x71', '0x624f54e42a41935eb77', '0x21b5e89c0216c0bf065e6f898a14f7b8e1b9'] |
| (-)largest_factor_bitlen | 0x8e |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x5', '0x5', '0x13', '0x87170583d', '0x5389b786b5', '0x220e69e3eccd', '0x8d29165977b409ebc69e92875'] |
| (+)largest_factor_bitlen | 0x64 |
| (-)factorization | ['0x4cd', '0x1c9852d7145', '0x14a1160e4f7e57', '0x8ad994f23636fec294ef406aede131f'] |
| (-)largest_factor_bitlen | 0x7c |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x2', '0xb', '0x47', '0x1a5', '0x485dc6d03', '0x104fb7c3232159ad35', '0x26bb54167acebe3ae99c925f8df'] |
| (+)largest_factor_bitlen | 0x6a |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | - |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x3', '0x97', '0xfb', '0x60769', '0xc3caf09ef596d092755ae7f6c086d2ebe8ad6f2322655b47'] |
| (+)largest_factor_bitlen | 0xc0 |
| (-)factorization | ['0x517', '0xda3', '0x2309', '0xeaebd', '0xe2f69ff', '0x4f7437d459', '0x355d7bdd41317c234e45ab9e3d9'] |
| (-)largest_factor_bitlen | 0x6a |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x2 |
| full | 0x2 |
| 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 | 0x28 |
| full | 0x28 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x4 |
| full | 0xc |
| relative | 0x3 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x120 |
| full | 0x120 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x1dce8d2ec6184caf0a972769fcc89 |
| factorization | ['0x13', '0x1d', '0x35', '0x7f', '0x27062fb', '0x37486dea6b5d9de97'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x27872a41e04df3da09943b0fdc1613c18185dad7c8e36c0530198bbe4 |
| factorization | ['0x2', '0x2', '0x3', '0x7', '0x29', '0x47', '0x105c1d9', '0x11798a8e5d', '0x24e0bfb76bd', '0x41daca4ccf1e36ed35f6fea6a0b'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x2bd4b87362ffa224a6e57f57e1e1faafff202e204f1935c8b71f8f07d277cfb6d88f97aad5f00b39a99af |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x6 |
| complement_bit_length | 0x3 |
| $\text{class_number}()$ | |
| upper | 0x2 |
| lower | 0x0 |
| $\text{small_prime_order}(l=2)$ | |
| order | 0x8000000000000000000000000000ee74697630c2657854b8bb4fd8fb |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x5555555555555555555555555555f44d9ba4208198fae325d2353b52 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x8000000000000000000000000000ee74697630c2657854b8bb4fd8fb |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0x8000000000000000000000000000ee74697630c2657854b8bb4fd8fb |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f6 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x8000000000000000000000000000ee74697630c2657854b8bb4fd8fb |
| complement_bit_length | 0x2 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x1', '0x4']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0xc', '0x1']] |
| len | 0x1 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=3)$ | |
| crater_degree | 0x1 |
| depth | 0x4 |
| $\text{volcano}(l=5)$ | |
| 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 | 0x1 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0x6 |
| relative | 0x6 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x12 |
| full | 0x12 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | -0x1dce8d2ec6184caf0a972769fcc89 |
| trace_factorization | ['0x13', '0x1d', '0x35', '0x7f', '0x27062fb', '0x37486dea6b5d9de97'] |
| number_of_factors | 0x6 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | -0x1dce8d2ec6184caf0a972769fcc89 |
| 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 | 0x6a |
| expected | 0x70 |
| ratio | 1.0566 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x310f |
| expected | 0x3138 |
| ratio | 1.00326 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0xe4623 |
| expected | 0xe4a98 |
| ratio | 1.00122 |
| $\text{square_4p1}()$ | |
| p | 0x1 |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0x1dce8d2ec6184caf0a971769fb1f7 |
| ratio | 2.7871704878214017e+33 |
| distance 32 | 0x9 |
| distance 64 | 0x9 |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c |
| bits | 0xe0 |
| difference | 0x1 |
| ratio | 0.99556 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 |
| bits | 0xa6 |
| difference | 0x3b |
| ratio | 0.73778 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x1a3f5373f44811c006bff63b25c9a8ccda3841bb26938c1be3facd0d |
| bits | 0xdd |
| difference | 0x4 |
| ratio | 0.98222 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0xff2e8fd62f296728db63d3af31aa4eabbb6e4dfba136ae9f72f0767 |
| bits | 0xdc |
| difference | 0x5 |
| ratio | 0.97778 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0x99cef4337f5ef29c5b6ca6451c131c8070d25ebaccb5940a1cf3eaa7 |
| bits | 0xe0 |
| difference | 0x1 |
| ratio | 0.99556 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x50fbc2cae0e9f23d8f1858735af665b6dca57fdc8cdec44987290833 |
| bits | 0xdf |
| difference | 0x2 |
| ratio | 0.99111 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x53ac1a6951387c259ea330b1748cb4ae61c909d8e0d1ff597389591f |
| bits | 0xdf |
| difference | 0x2 |
| ratio | 0.99111 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x37f85a0a22420b9678175bbd41f21f96ef1dfe0290bbfe3270c51f6d |
| bits | 0xde |
| difference | 0x3 |
| ratio | 0.98667 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x4bf8de3f407c348ba91294119a849954f96b16c412de499446bce8ba |
| bits | 0xdf |
| difference | 0x2 |
| ratio | 0.99111 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0xee4f47797d70618a36be7fe4ab565699de87c6ce914ff722ad00157 |
| bits | 0xdc |
| difference | 0x5 |
| ratio | 0.97778 |
| $\text{x962_invariant}()$ | |
| r | 0x0 |
| $\text{brainpool_overlap}()$ | |
| o | 0x0 |
| $\text{weierstrass}()$ | |
| a | 0x0 |
| b | 0x5 |