Curve detail
Definition
| Name | w-382-mont |
|---|---|
| Category | nums |
| Description | Original nums curve from https://eprint.iacr.org/2014/130.pdf |
| Field | Prime (0x3ffaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff) |
| Field bits | 382 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x3ffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc |
| Param $b$ | -0x20a72 |
Characteristics
| Order | 0x3ffaffffffffffffffffffffffffffffffffffffffffffffa6eb1cff4bde214d73b321ffd8e82cd160ab86803ebb301d |
| Cofactor | 0x1 |
| $j$-invariant | 0x7c1c7dcbbb7ac08a19e2c0907ee9189c5968fb6b296fa9dbd654c012f15a4f2649518c3caf514201d2d8887faad1f64 |
| Trace $t$ | 0x5914e300b421deb28c4cde002717d32e9f54797fc144cfe3 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x3ffaffffffffffffffffffffffffffffffffffffffffffffa6eb1cff4bde214d73b321ffd8e82cd160ab86803ebb301d |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0xe0ec7875415a0e687edc572aa208a23e2994f4bbf3577336dcc02d1cdc215b8f49044cfdf036c493385452d2a0971cb3 |
| factorization | ['0x7', '0x101', '0x2001c64a75bbb411b743a43d479514623603d5fbb9532b01674676d66d972cc322b951ae0693888c7b907b5998c5f5'] |
| max_conductor | 0x1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x3ffb000000000000000000000000000000000000000000005914e300b421deb28c4cde002717d32e9f54797fc144cfe3 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xffd8018ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff1f13878abea5f1978123a8d55df75dc1d66b0b440ca88cc9233fd2e323dea470b6fbb3020fc93b6cc7abad2d5f68e34d |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x2', '0x2', '0x2', '0x68926e50643ef0c9', '0x3abc60a13cb0f140c21ba761d1548367ff50bfbdda2c605d4bb173b1a4013e8d3f3bcac3ea816a33'] |
| (+)largest_factor_bitlen | 0x13e |
| (-)factorization | ['0x2', '0x5', '0x5', '0xb', '0x11', '0x107a1', '0x319c3c4c154561355', '0x1a556e4ce1c44772c30edc6428d2f022d6ff3017c5229ec1f6dd54bb904dfac6cd4500df5'] |
| (-)largest_factor_bitlen | 0x121 |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0xffebfffffffffffffffffffffffffffffffffffffffffffe9bac73fd2f788535cecc87ff63a0b34582ae1a00faecc073'] |
| (-)largest_factor_bitlen | 0x180 |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x2', '0x7', '0xd', '0x13', '0xe3', '0x259', '0x2c87', '0x41683a7f17811b6c3a4bd5b00012f9f9caa0f1f9646e093e6e8e3cdf8a586777f37e1db10a0be43f17128d'] |
| (+)largest_factor_bitlen | 0x157 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x397', '0x2c81', '0xa4f3', '0x2bb07', '0x103c6600d', '0x1588af7b95f34b724443d79c2b94bb298614cd84f928e001a4676882ade10cbf33319c689bb'] |
| (-)largest_factor_bitlen | 0x129 |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x2', '0x5a7', '0x7277', '0x4e0f5', '0x12294bb776c590d2e94629082b0504061ffeec2b7ff8253feb7fbb75b9100199be6ec30c291eb265e3fb11'] |
| (-)largest_factor_bitlen | 0x155 |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x3', '0x5', '0xd', '0xd', '0x443', '0x1f01', '0x6425a539959bdaab15223b68c64d8829eb4275482e98f4c13647f67a7fd8d9d284fb40bfa5c807dc523a2e6b'] |
| (-)largest_factor_bitlen | 0x15f |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x6 |
| full | 0x7 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x5 |
| full | 0xa |
| relative | 0x2 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x15 |
| full | 0x15 |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x60 |
| full | 0x60 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x5914e300b421deb28c4cde002717d32e9f54797fc144cfe3 |
| factorization | ['0x3', '0x3', '0x3', '0x1a305', '0x33f8b9', '0xb5142b', '0xe097d45b4d56a55a142ee73fd7c8ec7'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x20fb7875415a0e687edc572aa208a23e2994f4bbf3577336dcc02d1cdc215b8f49044cfdf036c493385452d2a0971cb6 |
| factorization | ['0x2', '0x2234cf8ecfb9', '0xde4986f4a1992a5', '0x8e2359e51e3096ed29691106701c7f12dad36bb2f10d12791e81d5d7de5ab51662e77'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x21bd991cfdeb83cfa51542148e8d48e372b36cf60158cc051118ff17da21879ef6e81a31ae6add6602cbf2e5ed6400febe6efd56b5e8339bd06d8e14d8fe6a42daaf2031ab48cf7f |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x4 |
| complement_bit_length | 0x3 |
| $\text{class_number}()$ | |
| upper | 0x4f6071cb969756421f35bd0f1c4365a1ab6098a6066a1c2686 |
| lower | 0x1a6 |
| $\text{small_prime_order}(l=2)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=3)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=5)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=7)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=11)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=13)$ | |
| order | None |
| complement_bit_length | None |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x2', '0x2']] |
| 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 | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=7)$ | |
| crater_degree | 0x1 |
| depth | 0x0 |
| $\text{volcano}(l=11)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=13)$ | |
| crater_degree | 0x0 |
| 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 | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x7 |
| relative | 0x7 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x1 |
| full | 0xa |
| relative | 0xa |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x7 |
| full | 0x7 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x12 |
| relative | 0x12 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x5914e300b421deb28c4cde002717d32e9f54797fc144cfe3 |
| trace_factorization | ['0x3', '0x3', '0x3', '0x1a305', '0x33f8b9', '0xb5142b', '0xe097d45b4d56a55a142ee73fd7c8ec7'] |
| number_of_factors | 0x5 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x5914e300b421deb28c4cde002717d32e9f54797fc144cfe3 |
| trace_factorization | NO DATA (timed out) |
| number_of_factors | NO DATA (timed out) |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x0 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0xc1 |
| expected | 0xbf |
| ratio | 0.98964 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x8dc5 |
| expected | 0x8e21 |
| ratio | 1.00253 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x465667 |
| expected | 0x46533e |
| ratio | 0.99982 |
| $\text{square_4p1}()$ | |
| p | NO DATA (timed out) |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0x5000000000000000000000000000000000000000000005914e300b421deb28c4cde002717d32e9f54797fc144cfe3 |
| ratio | 3275.8 |
| distance 32 | 0x3 |
| distance 64 | 0x1d |
| $\text{multiples_x}(k=1)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=2)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=3)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=4)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=5)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=6)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=7)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=8)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=9)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=10)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{x962_invariant}()$ | |
| r | 0x372b04bd7be47f49dddc010c62ea41cb5f4e58b5b93f771808019d2ac978f149d93de85d3ed8c3536f69a5350468c1dd |
| $\text{brainpool_overlap}()$ | |
| o | 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd |
| $\text{weierstrass}()$ | |
| a | 0x3ffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc |
| b | -0x20a72 |