Curve detail
Definition
| Name | id-tc26-gost-3410-12-512-paramSetB |
|---|---|
| Category | gost |
| Description | RFC7836 |
| Field | Prime (0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F) |
| Field bits | 512 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C |
| Param $b$ | 0x687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116 |
| Generator $x$ | 0x02 |
| Generator $y$ | 0x1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD |
Characteristics
| Order | 0x800000000000000000000000000000000000000000000000000000000000000149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f25bd |
| Cofactor | 0x1 |
| $j$-invariant | 0x3e9dfdd823c1bd3ea7a43f8e1055baadaeef1eb792ea8d21f72aae3f1258835bb7053d66a08ce3bc8369500f64ff131eef41844a2884c299128d64acc8cf86e9 |
| Trace $t$ | -0x149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f254d |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x800000000000000000000000000000000000000000000000000000000000000149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f25bd |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x380938d2d502e97ab960eda00e8876e18010f5168dee4999515b43d4af4675d5a526195a3f506e3bfc7258387026136d56573a5bb7df6b1b45fd1661d66d38b |
| factorization | ['0x5', '0x5', '0x5', '0xb', '0x1d', '0x83', '0xe5', '0x172e0d9', '0x171f388f', '0x962805493b5db046cdf7696ee75e54708b947900cefdc3ac800c77a768b1d4708fd261413eeb74fcf96fef8316547cd278dbdaa4899'] |
| max_conductor | 0x5 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeb65e13ebda9a5aba53024884262bf305746698edefe415f139cb93abc8b0db23 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0x4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006fa8719736932b73303e588cb5e94ac63fa7e5810cc23bad0070e16603ae21e7e22df47862fd1253c2458d5627d0c481a52917b4d0b0b2e8a562a48d0720f5886d |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x2', '0x2', '0x3', '0x955', '0x1249cbc7471df7ed6d0d099bc59032dd3ec23dcb598c574c42b93d790d77568c6af66161c8d5b18726aec50671a259f025a98ba2fefacef7376e0a4341291'] |
| (-)largest_factor_bitlen | 0x1f1 |
| $\text{kn_factorization}(k=2)$ | |
| (+)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 | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x2', '0x1ff3', '0x812e7', '0xec907b', '0x524411197', '0x649b71898779', '0x660c2db896adabbb6a6795e5955197b6d4b9f565ccdb5bec4533811133c18a0f104ab49d423f262f5e392626a042b3'] |
| (-)largest_factor_bitlen | 0x177 |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=5)$ | |
| (+)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 | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x2', '0x3', '0x1d', '0xc5', '0x15b', '0x287', '0x98f', '0x2bb59', '0x14338f', '0x6713e1', '0x25ab4b2aa6cdc1ba29bc9e8ae03ec601e4e3eaf4c5474c9e84db3e795a924d620e1b11988f670910018961ebb51d7a17e1a25db'] |
| (-)largest_factor_bitlen | 0x19a |
| $\text{kn_factorization}(k=8)$ | |
| (+)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 | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x4 |
| full | 0x5 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x5 |
| full | 0xb |
| relative | 0x2 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x3 |
| full | 0xc |
| relative | 0x4 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x12 |
| full | 0x12 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f254d |
| factorization | ['0x107', '0x7091', '0x11a7d5', '0xa72813b23c72724c6865f3', '0x3f4be6fe00b00d59ed550214fb44c115'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x128719736932b73303e588cb5e94ac63fa7e5810cc23bad0070e16603ae21e7e22df47862fd1253c2458d5627d0c481a52917b4d0b0b2e8a562a48d0720f558ba |
| factorization | ['0x2', '0x7', '0xe3', '0x17e1320a84af90203dbb69952db291d28a38d4bf227eed3b2979bfb81ec83fca0b1ce04afea2e7f9bd1ab0bf61882d3e1eb2ce488dd4bc39c9c22dd65d3289'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0xd8e4861b3556d1b699c104b5abab2916040e37e9e9170d654358d733ff100f1a67a7d9f85dcaee9d87df9495cd9d906ae14e0c35eec521a3d002bd9905f4d7d6c5f456229aff6147fd1539f80e1c4c08b1af5a115720ca8cc424f132bbb3658f |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | None |
| complement_bit_length | None |
| $\text{class_number}()$ | |
| upper | 0xd0d9afe7be45fbc0ecd0b864fc4cc5c033bf54c24b8128538a394ee75e5c3db78 |
| lower | 0x3628377dd490b |
| $\text{small_prime_order}(l=2)$ | |
| order | 0x800000000000000000000000000000000000000000000000000000000000000149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f25bc |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x15555555555555555555555555555555555555555555555555555555555555558c45a758b0e64636477f9e94a44e0229c1eee68302af51ad2108bcb8b3e2864a |
| complement_bit_length | 0x3 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaac622d3ac5873231b23bfcf4a52270114e0f773418157a8d690845e5c59f14325 |
| complement_bit_length | 0x4 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0x2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab188b4eb161cc8c6c8eff3d29489c045383ddcd06055ea35a4211797167c50c94 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaac622d3ac5873231b23bfcf4a52270114e0f773418157a8d690845e5c59f14325 |
| complement_bit_length | 0x4 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaac622d3ac5873231b23bfcf4a52270114e0f773418157a8d690845e5c59f14325 |
| complement_bit_length | 0x4 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x4', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x2', '0x1'], ['0xa', '0x1']] |
| len | 0x2 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=3)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x1 |
| depth | 0x1 |
| $\text{volcano}(l=7)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=11)$ | |
| crater_degree | 0x1 |
| 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 | 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 | 0x5 |
| relative | 0x5 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x1 |
| full | 0xb |
| relative | 0xb |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0xc |
| relative | 0xc |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x9 |
| full | 0x9 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x5 |
| full | 0x5 |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | -0x149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f254d |
| trace_factorization | NO DATA (timed out) |
| number_of_factors | NO DATA (timed out) |
| $\text{trace_factorization}(deg=2)$ | |
| trace | -0x149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f254d |
| 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 | 0x1 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0xf9 |
| expected | 0x100 |
| ratio | 1.02811 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x100df |
| expected | 0xff80 |
| ratio | 0.99466 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0xa9abc0 |
| expected | 0xa9ab00 |
| ratio | 0.99998 |
| $\text{square_4p1}()$ | |
| p | 0x1 |
| order | NO DATA (timed out) |
| $\text{pow_distance}()$ | |
| distance | 0x149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f25bd |
| ratio | 4.4963366898175765e+76 |
| distance 32 | 0x3 |
| distance 64 | 0x3 |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0x2 |
| bits | 0x2 |
| difference | 0x1fe |
| ratio | 0.00391 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x8086db5b59f6f39f31c1d06dd9819e10fe21fb2836a58597bc2b03059fea488e431b10d45f233b6f752e79e6c5074d58d9e412daa480289f4d93e4cbc35be7d |
| bits | 0x1fc |
| difference | 0x4 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0x72ca4d7833fc32409ccd3ebc4f4d623a5a265fbf72450e8a07e77635d899495c147e0b809899be3796f0762cbe3eff0a60344d721337448b0fe9623f54c67150 |
| bits | 0x1ff |
| difference | 0x1 |
| ratio | 0.99805 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0x26008a52a7b04b9327f55506ac123b763c8c888af3e3a715eaa4d80c1648849434552e974c6ad7c1e201ed2db72a4e575e34dd9c1c759de2e397f1d38014dd34 |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x2a04829c42769a303d13170ebd3dc4d69e5d5e7a01723d3fadc415f0c5331076581ad6caac143e4c3a201c1a280e72c5558c17b9bd55119efbd5eb3d0bf97c28 |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0xc6f0c8b3dcdd1e59d23d1c92881c835bdfee4f59b9a11867e64b8f7b1ef6e37d82eccc1bf8e9950b46b69c8c597cf8f55af8706c8dc3274c937c7645797682c |
| bits | 0x1fc |
| difference | 0x4 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0xfbc69be4e4619117394abed209181b93b2620bc0cae90f11f3f03114e8be358db9d6cb215c86ab429b6cd750b719eb9f6b959de3215fc1e85c244031e9075eb |
| bits | 0x1fc |
| difference | 0x4 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x52e7cf1a03094b27096c5cb85dbec6573bcb73a85c0f0343ab6ac4fa515943e4f1f42079c930c317296d77a1e4a210496bec96d9fd9620eb5dd8b199b654e7e1 |
| bits | 0x1ff |
| difference | 0x1 |
| ratio | 0.99805 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0x38f8bb0557af830ea8b479c18b9a232b69b96d6aa156e775a6ed921a24efdca0c03e3a74859baf386769eb206961ec4e93e2869d15ddd3d04c325da5f6fc8412 |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 0.99609 |
| $\text{x962_invariant}()$ | |
| r | 0x1e8f28b556d2012acf5a9280e41b45b21e97ff717b6276ef2195560c958769e5087879c34f521f538ea0eab26b0a753ffe78e4dca5526aa9060b73e9c0456efc |
| $\text{brainpool_overlap}()$ | |
| o | -0x687d1b459dc841457e3e06cf6f5e2517b97c7d614af138bcbf85dc806c4b289f3e965d2db1416d217f8b2703 |
| $\text{weierstrass}()$ | |
| a | 0x8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006c |
| b | 0x687d1b459dc841457e3e06cf6f5e2517b97c7d614af138bcbf85dc806c4b289f3e965d2db1416d217f8b276fad1ab69c50f78bee1fa3106efb8ccbc7c5140116 |