Curve detail
Definition
| Name | secp256k1 |
|---|---|
| Category | secg |
| Description | A Koblitz curve. |
| Field | Prime (0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f) |
| Field bits | 256 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x0000000000000000000000000000000000000000000000000000000000000000 |
| Param $b$ | 0x0000000000000000000000000000000000000000000000000000000000000007 |
| Generator $x$ | 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 |
| Generator $y$ | 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8 |
Characteristics
| Order | 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 |
| Cofactor | 0x1 |
| $j$-invariant | 0x0 |
| Trace $t$ | 0x14551231950b75fc4402da1722fc9baef |
| Embedding degree $k$ | 0x2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa74727a26728c1ab49ff8651778090ae0 |
| CM discriminant | -0x3 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x3 |
| factorization | ['0x3', '0x3', '0x3', '0x4f', '0x4f', '0x15d', '0x15d', '0x292b71', '0x292b71', '0x4649e5c33cf48540a57d66b', '0x4649e5c33cf48540a57d66b'] |
| max_conductor | 0xe4437ed6010e88286f547fa90abfe4c3 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x1000000000000000000000000000000014551231950b75fc4402da1712fc9b71f |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffdfffff85d9d671cd581c69bc5e697f5e1d12ab7e202a91318c7301d668dbcd41ad5dcc365 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x2', '0xd', '0x53', '0xb2b7', '0x7c7b7', '0x597660d4cfa74f61a5ae7dcc4ca77c896e38fbee15d8add64c237'] |
| (+)largest_factor_bitlen | 0xd3 |
| (-)factorization | ['0x2', '0x2', '0x2', '0x2', '0x2', '0x2', '0x3', '0x95', '0x277', '0x17d6cfb8ee30c51', '0x978c6f353c3889a79', '0x10dbff26eab8198050172ee03275'] |
| (-)largest_factor_bitlen | 0x6d |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x1e6354fd', '0x3927d2df', '0x4b77324461ee2e7c353b7c8513203d859582d612d138593acb'] |
| (-)largest_factor_bitlen | 0xc7 |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x2', '0x5', '0x17', '0x2b', '0x97', '0xf3a2e3', '0x10c2ca9', '0x8d55ec35b6704955', '0x3d3b54e9734cf42ec4daaca05a6541a1'] |
| (-)largest_factor_bitlen | 0x7e |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x3', '0x3', '0xb', '0x7901', '0x7a1b', '0x8df5ab', '0x419958f8c40cf26b', '0x142dec32810085788587eff071301d6268b'] |
| (-)largest_factor_bitlen | 0x89 |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x2', '0x3', '0x3', '0x293', '0xa63', '0xe1d', '0x2ba5', '0x491a39d', '0x537a3d57c23db9', '0xbdee2b5096c10674be338ca12fe86a07'] |
| (+)largest_factor_bitlen | 0x80 |
| (-)factorization | ['0x2', '0x2', '0x7', '0x11', '0x411bf', '0x51fd372907c1fea5', '0x2103530e7c94c2db72eb05d06bb131da01a1f104415'] |
| (-)largest_factor_bitlen | 0xaa |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x1d', '0xc1', '0x119', '0x16055', '0x2c68f', '0x10c135f76aa6952586fb084c54b224a5899410fca1a73c0ec391'] |
| (+)largest_factor_bitlen | 0xcd |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | - |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x2', '0x2', '0x2', '0x5', '0xb', '0x13', '0x2bd', '0x1e1be9bf', '0xd94c2efaa2f', '0x688e4ee4ab299', '0x1eb7d07bfcf31a6a78d79a0193df1'] |
| (+)largest_factor_bitlen | 0x71 |
| (-)factorization | ['0x2', '0x3', '0x1f', '0x4d5', '0x5ee08b', '0x11064e589cd', '0x50e5cd9025c4ded34fa881eac6a3a6b654fce679d51cd'] |
| (-)largest_factor_bitlen | 0xb3 |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x3', '0x13df', '0xa4b85', '0x25d0e731349', '0x169727245f10d0477f83440599fc9d05fccb75844313e31'] |
| (+)largest_factor_bitlen | 0xb9 |
| (-)factorization | ['0x5', '0x9a0454a1', '0x5f0bf78d071269232374d', '0x729b998516ad72a0e60b8d1683dfde269627'] |
| (-)largest_factor_bitlen | 0x8f |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x28 |
| full | 0x28 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x2 |
| full | 0x4 |
| relative | 0x2 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x30 |
| full | 0x30 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x14551231950b75fc4402da1722fc9baef |
| factorization | ['0x2a1', '0x7bbf018f252b819f7a2bfbfc44638f'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x9d671cd581c69bc5e697f5e1d12ab7e202a91318c7301d658dbccc77d5ce2ef2 |
| factorization | ['0x2', '0x3', '0x7', '0x11', '0xbdd', '0x20885', '0x450d57', '0xc72ba1', '0x1438b013', '0x228d1011', '0xbab873df5893', '0x599ca070b13f0320b'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x7d4b584979c431f8a1d6817aa688db0716e5f9d306371e9b876f0401e26d6ec56aa89623e98069ed360657caeb81edf3 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x6 |
| complement_bit_length | 0x3 |
| $\text{class_number}()$ | |
| upper | 0x2 |
| lower | 0x0 |
| $\text{small_prime_order}(l=2)$ | |
| order | 0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d905 |
| complement_bit_length | 0x7 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x55555555555555555555555555555554e8e4f44ce51835693ff0ca2ef01215c0 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d9050 |
| complement_bit_length | 0x3 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x1', '0x4']] |
| 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 | 0x1 |
| depth | 0x1 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x0 |
| 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 | 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 | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=3)$ | |
| least | 0x1 |
| full | 0x1 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0x4 |
| relative | 0x4 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x6 |
| relative | 0x6 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x14551231950b75fc4402da1722fc9baef |
| trace_factorization | ['0x2a1', '0x7bbf018f252b819f7a2bfbfc44638f'] |
| number_of_factors | 0x2 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x14551231950b75fc4402da1722fc9baef |
| trace_factorization | ['0xb', '0xd', '0x43bd', '0x29b1315e5e7892dadf75c7af437e685a55c7a3ba735d59263e249e9deef'] |
| number_of_factors | 0x4 |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x3 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x4 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x0 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0x82 |
| expected | 0x80 |
| ratio | 0.98462 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x3f44 |
| expected | 0x3fc0 |
| ratio | 1.00766 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x151720 |
| expected | 0x151580 |
| ratio | 0.9997 |
| $\text{square_4p1}()$ | |
| p | 0x3 |
| order | 0x3 |
| $\text{pow_distance}()$ | |
| distance | 0x14551231950b75fc4402da1732fc9bebf |
| ratio | 2.677766655660072e+38 |
| distance 32 | 0x1 |
| distance 64 | 0x1 |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 |
| bits | 0xa6 |
| difference | 0x5a |
| ratio | 0.64844 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x4c7ff4f2ba8603998339c8e42675ceac23ef2e9623fdb260b24b1c944a2ea1a9 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0xa6b594b38fb3e77c6edf78161fade2041f4e09fd8497db776e546c41567feb3c |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0xa3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8 |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x9d7b3f1498794e639b6745573b33373f2661e89fd00646045ff0b6d91c8c86ee |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x611a3775ff4f3e5acf0c371b5abe17d8d57b398710bd8b102597f5732b69d485 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x16f9a89d6da61f39bdbd7aa1d99d6c4fe7d35c91ae777df739678098dcdf2247 |
| bits | 0xfd |
| difference | 0x3 |
| ratio | 0.98828 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0xc2c5baf2beef370aaceba85af829a907a78ee9fe4b4e348c06ea5504bff5c57b |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0x8c6154856794fcd5ee79ba8c96b7dd980e289a6b93a52d50dbdb9388a4c75604 |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{x962_invariant}()$ | |
| r | 0x0 |
| $\text{brainpool_overlap}()$ | |
| o | 0x0 |
| $\text{weierstrass}()$ | |
| a | 0x0 |
| b | 0x7 |