Curve detail
Definition
| Name | P-256 (nist/P-256, secg/secp256r1, x962/ansix9p256r1) |
|---|---|
| Category | nist |
| Field | Prime (0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff) |
| Field bits | 256 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc |
| Param $b$ | 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b |
| Generator $x$ | 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 |
| Generator $y$ | 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 |
| Simulation seed | 0xc49d360886e704936a6678e1139d26b7819f7e90 |
Characteristics
| Order | 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 |
| Cofactor | 0x1 |
| $j$-invariant | 0x1198954424ebb0f8479de43131caece8ee0a9b13a558c21e0b2f74e3fcd36aa3 |
| Trace $t$ | 0x4319055358e8617b0c46353d039cdaaf |
| Embedding degree $k$ | 0x555555550000000055555555555555553ef7a8e48d07df81a693439654210c70 |
| CM discriminant | -0x3ee69e4c05512a2feb42c40318a014ae4c618ec481b963d8454f2455ea5e97c5b |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x3ee69e4c05512a2feb42c40318a014ae4c618ec481b963d8454f2455ea5e97c5b |
| factorization | ['0x3', '0x5', '0x6a4f513f0f', '0x12e85e4e8b36afa46fc41', '0x88b86c1479992127f04e8bd8f989855afb'] |
| max_conductor | 0x1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0xffffffff0000000100000000000000004319055458e8617b0c46353d039cdaaf |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffe00000002fffffffe0000000100000001fffffffe00000001fffffffc11961b3faaed5d024bd3bfce75feb51b39e713b7e469c27bab0dbaa15a1683a5 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x2', '0x5', '0x757', '0xa82b2cb', '0x54f36f23a5ecfa8925ac64ae11bc09513b09aa3f8eb3ce85b0e639'] |
| (+)largest_factor_bitlen | 0xd7 |
| (-)factorization | ['0x2', '0x2', '0x2', '0x2', '0x3', '0x47', '0x83', '0x175', '0xd4f', '0x4429', '0x952d', '0xb25b1dd', '0x251a76f7', '0xe95f681f97', '0x87b23e9d09d3e637b2aa341'] |
| (-)largest_factor_bitlen | 0x5c |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x3', '0x7', '0x3d', '0x137', '0x8c3', '0x2a01', '0x6b68d', '0xc97d9a354bf5', '0xb1699499589d22d4adda5bb70818c886cd157'] |
| (+)largest_factor_bitlen | 0x94 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | - |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x2', '0x2', '0xb', '0x1e4d', '0x1dbeeac3fa9', '0x395937786cb77', '0x16215b8373df9161470dfd317fd72ff822af5d'] |
| (+)largest_factor_bitlen | 0x95 |
| (-)factorization | ['0x2', '0x43', '0x36d', '0x8225', '0x534bb', '0x435282a27', '0x2675c37c99adb759dfea42c9f841fde1e2142545978f'] |
| (-)largest_factor_bitlen | 0xae |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x3', '0x3', '0x3', '0x3', '0x5', '0x5', '0x11', '0x268c9', '0x4b280255', '0xac40c13db08da198c5f74d4d58c180d335548adbb10102637'] |
| (-)largest_factor_bitlen | 0xc4 |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x2', '0x2', '0x7', '0x2db6db6d8924924952492492492492491896f5e826fb132a06f3767e3f5ad8f3'] |
| (-)largest_factor_bitlen | 0xfe |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x335', '0x9ef', '0x4f09', '0xc7fd', '0xd780f55', '0xed7a2704e1d77c42c238a35e316b21a110a5e9c8da5e7'] |
| (-)largest_factor_bitlen | 0xb4 |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | - |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x3', '0x87526b57548f5f', '0x50b75584a2b6152ec0ef7287c0c464bc74fa0b9c1250b88725d'] |
| (+)largest_factor_bitlen | 0xcb |
| (-)factorization | ['0xb', '0xd', '0x5cfc4c1', '0x24b4522f791', '0x1130146b9f096f028c8e2f533f878df891ba22c278aa0b9'] |
| (-)largest_factor_bitlen | 0xb9 |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x2 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x2 |
| full | 0x5 |
| relative | 0x2 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x10 |
| full | 0x10 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0xa |
| full | 0xa |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x2 |
| full | 0x4 |
| relative | 0x2 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x4319055358e8617b0c46353d039cdaaf |
| factorization | ['0x71', '0x9d9', '0x31a9', '0x34a4df', '0x182f43483a7c4142681'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0xee69e4c35512a2fbb42c40318a014ae4c618ec451b963d8454f2455ea5e97c5e |
| factorization | ['0x2', '0x3', '0x3', '0x3', '0x46a41ddb0fb9ab8cf303a13e15ed6b8627bb8860540696f7cd5143f61e3237d'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x8196097f3cc05902e1ad8f9771e9338bde532980b8ab04f543f5b04840e607ddfeb160257f0ec580ff1ebee21e2f3593 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x3 |
| complement_bit_length | 0x2 |
| $\text{class_number}()$ | |
| upper | NO DATA (timed out) |
| lower | NO DATA (timed out) |
| $\text{small_prime_order}(l=2)$ | |
| order | 0x7fffffff800000007fffffffffffffffde737d56d38bcf4279dce5617e3192a8 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x7fffffff800000007fffffffffffffffde737d56d38bcf4279dce5617e3192a8 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x3fffffffc00000003fffffffffffffffef39beab69c5e7a13cee72b0bf18c954 |
| complement_bit_length | 0x3 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x1f44659e2afe0bb9c55fc17734c36b7b151e2a57a6f91d21d3822c4e885a470 |
| complement_bit_length | 0x8 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550 |
| complement_bit_length | 0x1 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x1', '0x1'], ['0x3', '0x1']] |
| len | 0x2 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x1', '0x2'], ['0x5', '0x2']] |
| len | 0x2 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=3)$ | |
| crater_degree | 0x1 |
| depth | 0x0 |
| $\text{volcano}(l=5)$ | |
| crater_degree | 0x1 |
| depth | 0x0 |
| $\text{volcano}(l=7)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=11)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=13)$ | |
| crater_degree | 0x2 |
| 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 | 0x1 |
| full | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x1 |
| full | 0x5 |
| relative | 0x5 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x1 |
| full | 0x5 |
| relative | 0x5 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x1 |
| full | 0x4 |
| relative | 0x4 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x1 |
| full | 0x4 |
| relative | 0x4 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0xa |
| full | 0xa |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x4319055358e8617b0c46353d039cdaaf |
| trace_factorization | ['0x71', '0x9d9', '0x31a9', '0x34a4df', '0x182f43483a7c4142681'] |
| number_of_factors | 0x5 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x4319055358e8617b0c46353d039cdaaf |
| trace_factorization | ['0xd', '0xd', '0x11', '0x22d', '0x347', '0x63ba7d8447f3c5a242d', '0xfdbed80940504f03ce2dea3c81c3d52f70949b'] |
| number_of_factors | 0x6 |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x1 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x1 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0x6f |
| expected | 0x80 |
| ratio | 1.15315 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x3fb0 |
| expected | 0x3fc0 |
| ratio | 1.00098 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x151a1e |
| expected | 0x151580 |
| ratio | 0.99915 |
| $\text{square_4p1}()$ | |
| p | 0x1 |
| order | 0x2d |
| $\text{pow_distance}()$ | |
| distance | 0xffffffff00000000000000004319055258e8617b0c46353d039cdaaf |
| ratio | 4294967296.0 |
| distance 32 | 0xf |
| distance 64 | 0x11 |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x2afa386b3f2bdcdb83f4d83f8fa3874d7b74dcb454bd644fdd6bf3d1f2da8db6 |
| bits | 0xfe |
| difference | 0x2 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x517d3f033d9b7d1994d200de245f8952bf5ac043d4014ca9af9ec20fee5119c8 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0x7469a88fab79ae982fa880b0b940b96c6108eaec0473e2f530a861fa608f682 |
| bits | 0xfb |
| difference | 0x5 |
| ratio | 0.98047 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0xdd93b1e4509ea37ed90a5b197bca89a5c65da7ba0e3c2c23e7ac3eb46d52152f |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x6001ec1f28982a022b84f8c54c387ae3bcc973841387f970c6423a040af826c0 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x304ff48b33b91e996e61e2c08fd7860b9f2dc7bb53d8648180a1ae4e51b6af92 |
| bits | 0xfe |
| difference | 0x2 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x55998956742784829dca12de6a988ea385db1548366a5131359ae2fd09295726 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x49117e29c86afaf76eedac66f8aaa4da7cdc6028abcfd5b80cb3eaa85e14dd32 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0xcdff6117e7a67ec6c45ece48e0dc99135bd0e5ec02df5f70964157c41eb6773d |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{x962_invariant}()$ | |
| r | 0x7efba1662985be9403cb055c75d4f7e0ce8d84a9c5114abcaf3177680104fa0d |
| $\text{brainpool_overlap}()$ | |
| o | 0x2539ca2755c56c184c1442a7 |
| $\text{weierstrass}()$ | |
| a | 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc |
| b | 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b |