Curve detail
Definition
| Name | id-GostR3410-2001-CryptoPro-B-ParamSet |
|---|---|
| Category | gost |
| Description | RFC4357 |
| Field | Prime (0x8000000000000000000000000000000000000000000000000000000000000c99) |
| Field bits | 256 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x8000000000000000000000000000000000000000000000000000000000000c96 |
| Param $b$ | 0x3e1af419a269a5f866a7d3c25c3df80ae979259373ff2b182f49d4ce7e1bbc8b |
| Generator $x$ | 0x01 |
| Generator $y$ | 0x3fa8124359f96680b83d1c3eb2c070e5c545c9858d03ecfb744bf8d717717efc |
Characteristics
| Order | 0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198f |
| Cofactor | 0x1 |
| $j$-invariant | 0xeb55211d5ce06b7a7f1cc637dd93b32cf6ae9e3f7de2a17453a9c240919033b |
| Trace $t$ | -0x15f700cfff1a624e5e497161bcc8a0cf5 |
| Embedding degree $k$ | 0x40000000000000000000000000000000afb8067ff8d31272f24b8b0de6450cc7 |
| CM discriminant | -0x26b |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198f |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x26b |
| factorization | ['0x67', '0x67', '0x26b', '0x1849', '0x1849', '0x106f645', '0x106f645', '0xedcd144d', '0xedcd144d', '0x5ffb8817411f', '0x5ffb8817411f'] |
| max_conductor | 0x37edd5497379ce4edff2a11e9b89c41 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x7ffffffffffffffffffffffffffffffea08ff3000e59db1a1b68e9e43375ffa5 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0x4000000000000000000000000000000000000000000000000000000000000c99e27474b139420919928b9f8bda20912fdc68cf537566126e33cb26c6716a7cb9 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x2', '0x2', '0x2', '0x2', '0x3', '0x1f', '0xc5', '0xc0a03a415d', '0x1ca34c7494c4adf06ff2e07', '0x153f9378dd215a0bd84b16f871bb'] |
| (+)largest_factor_bitlen | 0x6d |
| (-)factorization | ['0x2', '0x290ed7fe8767c7eb5', '0x18f0ba055a2b64e61c5c38527b065ce594317c9f25e30f0b'] |
| (-)largest_factor_bitlen | 0xbd |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x313', '0xe35', '0x365f4d', '0x40edd9', '0x6ccf1db4858dbda85678e8d3882c8ab779ee95c311b8a81d'] |
| (+)largest_factor_bitlen | 0xbf |
| (-)factorization | ['0x3', '0x5', '0x25', '0x977', '0x35c3', '0x2850bf', '0x127e224b1', '0x146623f17a41c0753e8d779578847df9ccfeae67285'] |
| (-)largest_factor_bitlen | 0xa9 |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x2', '0x5', '0xb', '0x5815', '0x169d86df47', '0x72d96657350d59459aed6c861bc826762807d7f706178eecfb'] |
| (+)largest_factor_bitlen | 0xc7 |
| (-)factorization | ['0x2', '0x2', '0x7', '0xe5', '0x67f', '0x1a9ceeb', '0x16b3ceae9a7e2adb98d5f92ab4b4d84990a30d34c0679bf288dd5'] |
| (-)largest_factor_bitlen | 0xd1 |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | ['0x3', '0x3', '0x7', '0x557', '0x1859e9ff41c18be5ce47eb0ca46e23ad7e3f6a1674b9a5650e3f2ef14acb5'] |
| (+)largest_factor_bitlen | 0xf1 |
| (-)factorization | ['0x3e0910d651', '0x25e0b7d549fcd943e521c7e1', '0x37c7e86f3085a0aa538347d357e5e22b'] |
| (-)largest_factor_bitlen | 0x7e |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x2', '0x3', '0x3', '0x3', '0xd', '0x3b', '0x2fa5', '0x1a7c031', '0xc0f9969eb12b4c5b3', '0x1108ccdce9b3231f87d8bdf237c7dd008cf'] |
| (-)largest_factor_bitlen | 0x89 |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x32e4b1a29d7', '0x4cd86d8ae7f5d', '0x26a2d0d2f27c5c05cf', '0x14d18b570d0a61cfd46de496f'] |
| (+)largest_factor_bitlen | 0x61 |
| (-)factorization | ['0x11', '0x13', '0x22c15', '0x2c5ff', '0x6509ab99bd0388a9da69a5a2e55fcb4d9e482b811dc1de9a7b49d9'] |
| (-)largest_factor_bitlen | 0xd7 |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x2', '0x3', '0x253c0b13fdb3283', '0x402b782b8480d65fe9ae86a10f21555d42a35e5ea351b00b8d'] |
| (+)largest_factor_bitlen | 0xc7 |
| (-)factorization | ['0x2', '0x2', '0x2', '0x5', '0x125', '0x2a1', '0x771d5aed037f279b2bbeb4dca48c5151e52fee78f0d8993ee6c3e77f6a5'] |
| (-)largest_factor_bitlen | 0xeb |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x5', '0x5', '0x5', '0xd', '0x59', '0x6d', '0x2a5', '0x3e2f', '0xa47bdfed82889', '0x5501df06acaa577', '0x1f0fce1fc63bee7bdafaa73aa9'] |
| (+)largest_factor_bitlen | 0x65 |
| (-)factorization | ['0x3', '0xb', '0x1f07c1f07c1f07c1f07c1f07c1f07c1f5cf4603e0c093f3f7d3be654509d9997'] |
| (-)largest_factor_bitlen | 0xfd |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x2 |
| full | 0x4 |
| relative | 0x2 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x3 |
| full | 0x6 |
| relative | 0x2 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x2a |
| full | 0x2a |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x15f700cfff1a624e5e497161bcc8a0cf5 |
| factorization | ['0x3e0f', '0x3379a9', '0x237b4965', '0xcb3359788e99c407'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x1627474b139420919928b9f8bda20912fdc68cf537566126e33cb26c670cbd5e0 |
| factorization | ['0x2', '0x2', '0x2', '0x2', '0x2', '0x11', '0xfb', '0x1c1', '0x83f', '0x9311', '0xf2d1da4f87311289', '0x1596521c929069ed5aee7278583975e0856b'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x136e0ca71e845bc976aeec853d17acef4f32ee794cb0f9d451b11b2b9c8d5388976933f3e5521d0e77dc3efef94bcf4f3 |
| factorization | ['0x3', '0x5', '0x269', '0x3e0f', '0x650b', '0x3379a9', '0x3f81a7', '0x3a9cb35', '0x237b4965', '0x24e0170f', '0xcb3359788e99c407', '0x43dd4bfa4963187eb4b', '0x1c95600fec2ce70883bd'] |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x2 |
| complement_bit_length | 0x2 |
| $\text{class_number}()$ | |
| upper | 0x33 |
| lower | 0x0 |
| $\text{small_prime_order}(l=2)$ | |
| order | 0x40000000000000000000000000000000afb8067ff8d31272f24b8b0de6450cc7 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x40000000000000000000000000000000afb8067ff8d31272f24b8b0de6450cc7 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198e |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0x40000000000000000000000000000000afb8067ff8d31272f24b8b0de6450cc7 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x40000000000000000000000000000000afb8067ff8d31272f24b8b0de6450cc7 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198e |
| complement_bit_length | 0x1 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x4', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x1', '0x2'], ['0x2', '0x1'], ['0x4', '0x2']] |
| len | 0x3 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=3)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x2 |
| 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 | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=17)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=19)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{isogeny_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=3)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x1 |
| full | 0x4 |
| relative | 0x4 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x6 |
| relative | 0x6 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x7 |
| full | 0x7 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x14 |
| full | 0x14 |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | -0x15f700cfff1a624e5e497161bcc8a0cf5 |
| trace_factorization | ['0x3e0f', '0x3379a9', '0x237b4965', '0xcb3359788e99c407'] |
| number_of_factors | 0x4 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | -0x15f700cfff1a624e5e497161bcc8a0cf5 |
| trace_factorization | ['0x3', '0x5', '0x269', '0x650b', '0x3f81a7', '0x3a9cb35', '0x24e0170f', '0x43dd4bfa4963187eb4b', '0x1c95600fec2ce70883bd'] |
| number_of_factors | 0x9 |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x2 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0x7f |
| expected | 0x80 |
| ratio | 1.00787 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x3f61 |
| expected | 0x3fc0 |
| ratio | 1.00586 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x151363 |
| expected | 0x151580 |
| ratio | 1.00039 |
| $\text{square_4p1}()$ | |
| p | 0x1 |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0x15f700cfff1a624e5e497161bcc8a198f |
| ratio | 1.2393702545009617e+38 |
| distance 32 | 0xf |
| distance 64 | 0xf |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0x1 |
| bits | 0x1 |
| difference | 0xff |
| ratio | 0.00391 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x623a1dbebbd0496d05e6702dd0f381ada3183b305dd5b1403e9014bd08622b03 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0xd7dbd1df0fa255075f641220ad54b084cdb213cdbc02fa16c4360c09f5009b2 |
| bits | 0xfc |
| difference | 0x4 |
| ratio | 0.98438 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0x33e6f7d9b9893a117bfd65d8fae7c0e826422954dbf5a3f63040af9c481ca24f |
| bits | 0xfe |
| difference | 0x2 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0x45f578a8582812acdd6526a44ae3cbb43008d949309f00604ad0f4b83e2c5106 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x334d6d60ba419517dfb14582f98da3fd85057257902aa4ac5447c65883cf8efb |
| bits | 0xfe |
| difference | 0x2 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x6164f72b4c451fb9bbbc496768bb03da404c155b48d0d476d7ba6759403252e7 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x7ae58dcdc464bc8d6e87960189d77397e277de2719b95fc8033fb539ea914b19 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x1cf5a8d087f362656c752b1df559a37ff5f7eefdb15a925ff6a448a220af3f3c |
| bits | 0xfd |
| difference | 0x3 |
| ratio | 0.98828 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0x2340170e096261620d94468913d4b828abd65cdef63895ff6e9827ab0f7ec3dc |
| bits | 0xfe |
| difference | 0x2 |
| ratio | 0.99219 |
| $\text{x962_invariant}()$ | |
| r | 0x15d29bff7b119c4987be7021c2ce9511594bec70fd08577bdcc17a42e59d762f |
| $\text{brainpool_overlap}()$ | |
| o | -0x3e1af419a269a5f866a7c72c |
| $\text{weierstrass}()$ | |
| a | 0x8000000000000000000000000000000000000000000000000000000000000c96 |
| b | 0x3e1af419a269a5f866a7d3c25c3df80ae979259373ff2b182f49d4ce7e1bbc8b |