Curve detail
Definition
| Name | id-tc26-gost-3410-12-512-paramSetA |
|---|---|
| Category | gost |
| Description | RFC7836 |
| Field | Prime (0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7) |
| Field bits | 512 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4 |
| Param $b$ | 0x00E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760 |
| Generator $x$ | 0x03 |
| Generator $y$ | 0x7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4 |
Characteristics
| Order | 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff27e69532f48d89116ff22b8d4e0560609b4b38abfad2b85dcacdb1411f10b275 |
| Cofactor | 0x1 |
| $j$-invariant | 0x366d06b0ea038a1f285c60d04d76a587f3877fb02b0a232ebceaeb27e3b0bc0bf27bf6d0ec8a3ee967e0b2b9c5f5709599c76c481ffea31818c23177e4db6144 |
| Trace $t$ | 0xd8196acd0b7276ee900dd472b1fa9f9f64b4c754052d47a235324ebee0ef4b53 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff27e69532f48d89116ff22b8d4e0560609b4b38abfad2b85dcacdb1411f10b275 |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x34995193ff414293c11fd74062712cceb454741a2284e9ae238bcca861c7d6e4f505e77401108c618bcae31cdde5597872cd7b19ef842cee5bad5f94d04dc3a33 |
| factorization | ['0x7', '0xd', '0x17', '0x66ef9f48094e2d6818b4b600ff466d75b29c39712885e2438b28d3aa26774eaf4fea490d187778bbf64c58c65fef122ab55ec13514754631ded54f4b9767df'] |
| max_conductor | 0x1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x10000000000000000000000000000000000000000000000000000000000000000d8196acd0b7276ee900dd472b1fa9f9f64b4c754052d47a235324ebee0ef491b |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb8cb66ae6c00bebd6c3ee028bf9d8ed3314bab8be5dd7b1651dc7433579e38291b0afa188bfeef739e74351ce3221aa6878d3284e6107bd311a452a06b2fb28b20d |
| 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 | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x2', '0x49', '0x745d', '0xb9298685d9ad5b3a8491aa4b6c6775112f428f69e492b94987f35a503b71896e782bb0225efaebf741bd8aa1dad2330d05674d23a32deab854eabcac9a3'] |
| (-)largest_factor_bitlen | 0x1ec |
| $\text{kn_factorization}(k=4)$ | |
| (+)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 | ['0x2', '0x2', '0x2', '0x3', '0x3', '0xbe9f', '0x17e00b2c3ed41b00756f9d5b3b701803db3d01325928f61fc4c744494027e105c88cbc6a63214925e0bf092f9a266d8031536e317b625baf2cfe828fd9df'] |
| (-)largest_factor_bitlen | 0x1ed |
| $\text{kn_factorization}(k=6)$ | |
| (+)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 | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x3b6eff', '0x39a4838e9', '0x11fb35116bcfbb', '0x882c80021498d90ed8aca83ad73876007c42f841cb062dc1e7510ab864cd48a34a9d7795c8ab96d5e9f0844850381e60900b4d'] |
| (+)largest_factor_bitlen | 0x198 |
| (-)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 | 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 | 0x4 |
| full | 0xd |
| relative | 0x3 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x4 |
| full | 0x10 |
| relative | 0x4 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0xd8196acd0b7276ee900dd472b1fa9f9f64b4c754052d47a235324ebee0ef4b53 |
| factorization | ['0x1286b', '0x29f10dd18b9305fd', '0x473282dea4fbd22249504914df79dede05a75a196ee6d'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x4995193ff414293c11fd74062712cceb454741a2284e9ae238bcca861c7d6e4f505e77401108c618bcae31cdde5597872cd7b19ef842cee5bad5f94d04dc40de |
| factorization | NO DATA (timed out) |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x11636865d24c651a25cf1af326ad3c039094f94f28bc2939339c1e03bca6e35a149c2d86fa3771cdf89a721a7322b783e8f29b4085abbc1e69a9a79477efd2cbf71d9bdc13235ad9fd7a513ae13cf15cc70f1d4ae20cc7c2a82586949f5cda67f |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | None |
| complement_bit_length | None |
| $\text{class_number}()$ | |
| upper | 0xcd81f08082b5554c90ce4dd9f7fb5b10c1a6295fe59c3a81a295bc6b3316cb0955 |
| lower | 0x177c6 |
| $\text{small_prime_order}(l=2)$ | |
| 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 | [['0x4', '0x1']] |
| 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 | 0x1 |
| depth | 0x0 |
| $\text{volcano}(l=17)$ | |
| crater_degree | 0x2 |
| 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 | 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 | 0x1 |
| full | 0xd |
| relative | 0xd |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x1 |
| full | 0x10 |
| relative | 0x10 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x14 |
| full | 0x14 |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0xd8196acd0b7276ee900dd472b1fa9f9f64b4c754052d47a235324ebee0ef4b53 |
| trace_factorization | ['0x1286b', '0x29f10dd18b9305fd', '0x473282dea4fbd22249504914df79dede05a75a196ee6d'] |
| number_of_factors | 0x3 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0xd8196acd0b7276ee900dd472b1fa9f9f64b4c754052d47a235324ebee0ef4b53 |
| trace_factorization | ['0x3', '0x202bdeb99f3bf7', '0x36a3472ea9a679528c379e095ea54337f9d9e3f44b2c11d81a6118c6c927d261cafe78dd76c2897276c1c0087c99ece2eee704916778f4d33c1'] |
| number_of_factors | 0x3 |
| $\text{isogeny_neighbors}(l=2)$ | |
| 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 | 0x10b |
| expected | 0x100 |
| ratio | 0.9588 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0xfe73 |
| expected | 0xff80 |
| ratio | 1.00413 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0xa9a538 |
| expected | 0xa9ab00 |
| ratio | 1.00013 |
| $\text{square_4p1}()$ | |
| p | NO DATA (timed out) |
| order | NO DATA (timed out) |
| $\text{pow_distance}()$ | |
| distance | 0xd8196acd0b7276ee900dd472b1fa9f9f64b4c754052d47a235324ebee0ef4d8b |
| ratio | 1.3717201665360076e+77 |
| distance 32 | 0xb |
| distance 64 | 0xb |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0x3 |
| bits | 0x2 |
| difference | 0x1fe |
| ratio | 0.00391 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x7fa1978e28844741c78910dc2b9a3bf8d2fe4331d92668104d9d8d9118a1304844eebf44ac73fdc217b388c445e542fedc18d723dc2e96afeaf30af03a0d542b |
| bits | 0x1ff |
| difference | 0x1 |
| ratio | 0.99805 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0xcfa47980a9f1eef6a03ae425c2974aea3abd9f9da728af1b784b672ef7615694b2f336a63fce52e719bcbbe0dfa09d3c25f1adf44df1c39a900b4b4cc80f7aed |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0xe9be0f93a35b919ba8446d83bcca27be17d727785681582c6daa7123d8bd8bfa56b0f097ffedc9f58cbb8c5962bf12963057aef53c204681515884f2ca5dac7d |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0xfe1b0bc43943e14bfd5c3560ec3c617305edddbd6a56e07e1765a4d2cba372a099ddfcd643f03e872a29534d26ea8a23aa4d63057b92e28169b54eecda85bd42 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x3234ebb205b4af2341fe12d32af5a95c61b527a444594eceb83fb0ade332a74047a225f0124e409a02d3726beb438ae3f21a2093714104167847a715a33eb360 |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x3fc485f4e24fef847b1490706499eeaf780d5ee0fb23ffed93d453cc39482f032d9a73a2dda827a9ef9d538aa1c01e9ba7495305f04216dce11ff3fcf38a4ace |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x9b2e989216d028ef9cec2fd2bc655911513539c665c329ce396d93a2ee9339fc5459b7ebaf1dd6f46128164f169e11c5615d5bd21c1219cdab5d4217be2b3aa2 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x20992351c563e8ba65a92fbdb7bf3f75b7ff5b5b66604e82afc45bbb5286b17e97841a4dff3554ee7a915c0142c15495609c65fd46cf98d71903083e84aa1ee8 |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0xac9e094bc7652180a915e9a30e7ae19b41b015935e1e26260986bf00bb368582b6ea95bd736a5f0ae9f0da9e077ff7ce3e04d4c123636c3f15b9ce63224750c7 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{x962_invariant}()$ | |
| r | 0x2ff1c3cffda61b1f39d9d0f6219db0682b5743ad4df80d380019ace07e959a7931f3deb4d03b24818aad9f66e3e00919fac675f6235d9dfe8a1a0ceca9bdec46 |
| $\text{brainpool_overlap}()$ | |
| o | -0x68c2505dedfc86ddc1bd0b2b6667f1da34b82574761cb0e879bd081cfd0b6265ee3cb090f30d27614cb4597c |
| $\text{weierstrass}()$ | |
| a | 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc4 |
| b | 0xe8c2505dedfc86ddc1bd0b2b6667f1da34b82574761cb0e879bd081cfd0b6265ee3cb090f30d27614cb4574010da90dd862ef9d4ebee4761503190785a71c760 |