Curve detail
Definition
| Name | ed-384-mont |
|---|---|
| Category | nums |
| Description | Original nums curve from https://eprint.iacr.org/2014/130.pdf |
| Field | Prime (0xb0ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff) |
| Field bits | 384 |
| Form | Twisted Edwards $ax^2 + y^2 = 1 + dx^2y^2$ |
| Param $a$ | 0xb0fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe |
| Param $d$ | 0x6f17 |
Characteristics
| Order | 0x2c3ffffffffffffffffffffffffffffffffffffffffffffff56d07e24e2749cd9f6b769aec80f6fe06fe4e3a6332489b |
| Cofactor | 0x4 |
| $j$-invariant | 0x537206bf00c21d5baee862c54cc66fe15e4e59b2eaed1e5d90aaa82d7ff2aefbc763a4d8773187650d9a1bb40c0374c |
| Trace $t$ | 0x2a4be076c762d8c9825225944dfc2407e406c7167336dd94 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x2c3ffffffffffffffffffffffffffffffffffffffffffffff56d07e24e2749cd9f6b769aec80f6fe06fe4e3a6332489b |
| cofactor | 0x4 |
| $\text{discriminant}()$ | |
| cm_disc | None |
| factorization | None |
| max_conductor | None |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0xb100000000000000000000000000000000000000000000002a4be076c762d8c9825225944dfc2407e406c7167336dd94 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0x7a60fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd42fcfc2443d557168aa0a17e8e72c29ab47b5fb09ca197a5b453d832e7f12356f74816deebccc87150b484453238dd94 |
| 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 | ['0x5', '0x7', '0xbf', '0x4c7', '0x8be914f', '0x5312f09e0327d3ef2dc224278e8f808408855016be54255fab956eeecbfe338e5f99a894d8426960f3e5'] |
| (+)largest_factor_bitlen | 0x14f |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x5', '0x5', '0x3b', '0x7f', '0x133', '0xb9b', '0x27239', '0xba89b', '0x7710ea19', '0x1019dd5869815b410766fb0bad533cebcb1d13c8b9d0acc09ecb98c550e80465af9babd'] |
| (-)largest_factor_bitlen | 0x119 |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0xd', '0x11', '0x17', '0x301', '0xbded503f4059ab6a3574b4191dafb66766e8a49197a1e41b7c6ff1c1ccbc0dd42162169a2d1f17bfd7fae91bcbd'] |
| (-)largest_factor_bitlen | 0x16c |
| $\text{kn_factorization}(k=5)$ | |
| (+)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 | ['0x35', '0x59', '0x61', '0x17f49a6ab33d9', '0x71b69aee593f41', '0x23f8b7e1b66e8aed', '0x65bc381fa6dea69af988e6d08519ad68f1ce8823774cef21969'] |
| (+)largest_factor_bitlen | 0xcb |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x13', '0x3b9', '0x1d4c26c33', '0x99108783f70a5a16eb57fe3094343e431b754c75dec526c639407c3d1b96ea736719d9560c215adc62333'] |
| (-)largest_factor_bitlen | 0x154 |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x30 |
| full | 0x30 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x78 |
| full | 0x78 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0xc |
| full | 0xd |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x120 |
| full | 0x120 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x2a4be076c762d8c9825225944dfc2407e406c7167336dd94 |
| factorization | ['0x2', '0x2', '0x5', '0x13', '0x371b', '0x16ed7', '0x16cf36d6c5e221', '0x40ccc2c379c1e40d23dbf9c27'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0xaa0303dbbc2aa8e9755f5e81718d3d654b84a04f635e685a4bac27cd180edca908b7e9211433378eaf4b7bbacdc7226f |
| factorization | ['0x17d371', '0x722b4f9116dc2c77b2a5a1c46d030d6398b72898001e2839a11c2e253c96db5b07b1c4818316255ce87b735a3df'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x395558c7d3488126d3c6ac8ba1c68b6b9267da4644440520c771fba9d6b544a10d97e4b47283f91ceeedce2e578433c03a932a8b3c350a70cc438ad5544c9cacc6c01f908d0cdd98 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | None |
| complement_bit_length | None |
| $\text{class_number}()$ | |
| 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 | 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 | [['0x1', '0x1'], ['0x2', '0x1']] |
| len | 0x2 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x4', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x2', '0x6']] |
| 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 | 0x2 |
| 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 | 0x1 |
| 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 | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0xd |
| relative | 0xd |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x12 |
| full | 0x12 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x2a4be076c762d8c9825225944dfc2407e406c7167336dd94 |
| trace_factorization | ['0x2', '0x2', '0x5', '0x13', '0x371b', '0x16ed7', '0x16cf36d6c5e221', '0x40ccc2c379c1e40d23dbf9c27'] |
| number_of_factors | 0x7 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x2a4be076c762d8c9825225944dfc2407e406c7167336dd94 |
| trace_factorization | NO DATA (timed out) |
| number_of_factors | NO DATA (timed out) |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x1 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x2 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0xc7 |
| expected | 0xc0 |
| ratio | 0.96482 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x8f45 |
| expected | 0x8fa0 |
| ratio | 1.00248 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x476deb |
| expected | 0x477040 |
| ratio | 1.00013 |
| $\text{square_4p1}()$ | |
| p | NO DATA (timed out) |
| order | NO DATA (timed out) |
| $\text{pow_distance}()$ | |
| distance | 0x30ffffffffffffffffffffffffffffffffffffffffffffffd5b41f89389d27367dadda6bb203dbf81bf938e98cc9226c |
| ratio | 3.61224 |
| distance 32 | 0xc |
| distance 64 | 0x14 |
| $\text{multiples_x}(k=1)$ | |
| 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 | 0x77dbfcdd7e0a2d47eae442f4ac6111807897694b642e3959decb3dbd505935a955d3d9fda1af593399edb1887ceb9d06 |
| $\text{brainpool_overlap}()$ | |
| o | -0x2d4caff1f3ec0b8f825772b1b372ec1dbfa4e804430f4724ee302f2 |
| $\text{weierstrass}()$ | |
| a | 0x91530664469d777cfe9a0ab41ce87b5827b8ab707a33105b99df8884ce0c1c1943b1426f8b2b1582335ba72c9e79939a |
| b | 0x7d07db5ab91e493dc63193445ee8713167256402778c9b9eed5c968c7d2ce660a2189580ef947ab4526ef98bbc6c3b0f |