Curve detail
Definition
| Name | ed-382-mont |
|---|---|
| Category | nums |
| Description | Original nums curve from https://eprint.iacr.org/2014/130.pdf |
| Field | Prime (0x3ffaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff) |
| Field bits | 382 |
| Form | Twisted Edwards $ax^2 + y^2 = 1 + dx^2y^2$ |
| Param $a$ | 0x3ffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe |
| Param $d$ | 0xaf381 |
Characteristics
| Order | 0xffebfffffffffffffffffffffffffffffffffffffffffffd31afaa1520dc177d8c1605c481e068269880369e5f3fa61 |
| Cofactor | 0x4 |
| $j$-invariant | 0xca7a7e821e9e780fec8f382519f34ac2d92b9c4ef1a36566c23ecad8a420be99872735008cbd0065cda4b356be6cc11 |
| Trace $t$ | 0xb394157ab7c8fa209cfa7e8edf87e5f659dff2586830167c |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0xffebfffffffffffffffffffffffffffffffffffffffffffd31afaa1520dc177d8c1605c481e068269880369e5f3fa61 |
| cofactor | 0x4 |
| $\text{discriminant}()$ | |
| cm_disc | None |
| factorization | None |
| max_conductor | None |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x3ffb00000000000000000000000000000000000000000000b394157ab7c8fa209cfa7e8edf87e5f659dff2586830167c |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xffd8018ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7e0c6bb274b4eb2579c482d74115b0a8a0ab3028a1b59d636c4eb45d254f653915f2122b974f453c1a01008d30798c14 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x3', '0x200f5', '0x3e8bd', '0x2b904d70f7ca2ba9d1d58bbd04b1399607122d296b75a7658544cedf5268e6d84a8e2ff5c13f1ff879569b7'] |
| (+)largest_factor_bitlen | 0x15a |
| (-)factorization | ['0x7', '0x7', '0x17', '0x8b', '0x143b', '0x187d', '0x28d8f87', '0x2e5108805e3e9', '0x1df1e270e35487147ab05edb2115497bdf18e863b3b34cf92ec8488cbc55b4f737f'] |
| (-)largest_factor_bitlen | 0x109 |
| $\text{kn_factorization}(k=2)$ | |
| (+)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 | ['0xd', '0x1e31e02ee688b8b1e3', '0x7d2deac67aa6431cca234af3b23e947d4884ac98678a2de018f7e34c6bf08aea4e9f463e041b4b'] |
| (+)largest_factor_bitlen | 0x137 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x11', '0x4b75f5', '0x4d2e7b93149', '0xa9656ac168d9f084e2ec811cfd0183021cd3fb6882620591f9d6ddaacb0fe2d7bc9e6336869ba2b'] |
| (-)largest_factor_bitlen | 0x13c |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x3', '0x5', '0x10d', '0xa7ab', '0xb60bc2ebbd', '0x8ce744ba9b39a1', '0x6ed7dec03ba837dbf1041555c625022a338ac459492d5f6eb026ee27552dfcc281'] |
| (+)largest_factor_bitlen | 0x107 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x1421', '0x3c11', '0x5419', '0x98efb1f', '0x22837f1c22678672bc6ec74255fcd0ce1a088d30a78b5399c35f72b716007327cc116176ad60cb47'] |
| (+)largest_factor_bitlen | 0x13e |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x120 |
| full | 0x120 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0xb394157ab7c8fa209cfa7e8edf87e5f659dff2586830167c |
| factorization | ['0x2', '0x2', '0x3', '0xd', '0x13', '0x21411ecf9', '0x7766993e85bc4a197458b969cd01b811a978b'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x3dfd6bb274b4eb2579c482d74115b0a8a0ab3028a1b59d636c4eb45d254f653915f2122b974f453c1a01008d30798c11 |
| factorization | ['0x377', '0x935', '0x33346c489951c0fd', '0x9b710dbfb9e722f6bf564f5f976bc3166dc1b3d463436c979481f2de7932fdf7ed436ebd717'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x1657576b6aae56f93954b55ef16c1a932af91f9f6ed86534e28189eefec726c747f27ad4b5003b5b0fa3e5e890a2c15a0bb1fa8da849f0caa5f707431862d03056df7907fb69b48 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x2 |
| complement_bit_length | 0x2 |
| $\text{class_number}()$ | |
| upper | NO DATA (timed out) |
| lower | NO DATA (timed out) |
| $\text{small_prime_order}(l=2)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=3)$ | |
| order | 0xffebfffffffffffffffffffffffffffffffffffffffffffd31afaa1520dc177d8c1605c481e068269880369e5f3fa60 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0xffebfffffffffffffffffffffffffffffffffffffffffffd31afaa1520dc177d8c1605c481e068269880369e5f3fa60 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0x3ffaffffffffffffffffffffffffffffffffffffffffffff4c6bea85483705df6305817120781a09a6200da797cfe98 |
| complement_bit_length | 0x4 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x7ff5fffffffffffffffffffffffffffffffffffffffffffe98d7d50a906e0bbec60b02e240f034134c401b4f2f9fd30 |
| complement_bit_length | 0x3 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x3ffaffffffffffffffffffffffffffffffffffffffffffff4c6bea85483705df6305817120781a09a6200da797cfe98 |
| complement_bit_length | 0x4 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x1', '0x1'], ['0x2', '0x1']] |
| len | 0x2 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x2', '0x2']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0xc', '0x1']] |
| len | 0x1 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x1 |
| $\text{volcano}(l=3)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=7)$ | |
| crater_degree | 0x0 |
| 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 | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{isogeny_extension}(l=3)$ | |
| least | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x12 |
| full | 0x12 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0xb394157ab7c8fa209cfa7e8edf87e5f659dff2586830167c |
| trace_factorization | ['0x2', '0x2', '0x3', '0xd', '0x13', '0x21411ecf9', '0x7766993e85bc4a197458b969cd01b811a978b'] |
| number_of_factors | 0x6 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0xb394157ab7c8fa209cfa7e8edf87e5f659dff2586830167c |
| trace_factorization | ['0x2', '0x7', '0x2b3', '0x33ad', '0x2d65bcbd', '0x4b91803728b', '0x4fc2aad9bc1d1d63ac63aea614ff695317ad323e5dab991e30f6f6ab5e58d6b62cc9e9'] |
| number_of_factors | 0x7 |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x1 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x0 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0xba |
| expected | 0xbf |
| ratio | 1.02688 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x8db7 |
| expected | 0x8e21 |
| ratio | 1.00292 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x464d39 |
| expected | 0x46533e |
| ratio | 1.00033 |
| $\text{square_4p1}()$ | |
| p | NO DATA (timed out) |
| order | 0x7 |
| $\text{pow_distance}()$ | |
| distance | 0x500000000000000000000000000000000000000000000b394157ab7c8fa209cfa7e8edf87e5f659dff2586830167c |
| ratio | 3275.8 |
| distance 32 | 0x4 |
| distance 64 | 0x4 |
| $\text{multiples_x}(k=1)$ | |
| 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 | 0x116c8aa74dcdaa371ede1d3f81718197762145173b08ad4bdd1a56d09835d2bcc020b41cd1462a0daec7c30adf9cdbd8 |
| $\text{brainpool_overlap}()$ | |
| o | 0x1c4a5ad155e2299428c6b167e6fe42b29aff45c99a63e17ec456bfcb |
| $\text{weierstrass}()$ | |
| a | 0x1c91cabc91750134dc649eab481e7be3c0af2f189cacfc7d19db091c214137d9763b53c668ed610857dff998c3aab8a4 |
| b | 0x62a1abc3f8df87f87a86718f3d1113cdee1b3ebd7c1819ff53f8d93bf6688bdbb0a6c618d9fbc2b1fd0dd232ed3140 |