Curve detail
Definition
| Name | sect283r1 (nist/B-283, secg/sect283r1, x962/ansit283r1) |
|---|---|
| Category | secg |
| Field | Binary |
| Field polynomial | $x^{283} + x^{12} + x^{7} + x^{5} + 1$ |
| Field bits | 283 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x000000000000000000000000000000000000000000000000000000000000000000000001 |
| Param $b$ | 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5 |
| Generator $x$ | 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053 |
| Generator $y$ | 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4 |
| Simulation seed | 0x77e2b07370eb0f832a6dd5b62dfc88cd06bb84be |
Characteristics
| Order | 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 |
| Cofactor | 0x2 |
| $j$-invariant | 0x52b93729f30766131413473e14639b58a99eace4f5c4cf1e3cc939dab79766b75e0c63 |
| Trace $t$ | 0x20df8cd33e06d8eadfd349f7ab0620a499f3 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 |
| cofactor | 0x2 |
| $\text{discriminant}()$ | |
| cm_disc | -0x1bc759948b007fb09347722a8155aae96db74435b143dbcaf586d23ee58a9649a413a357 |
| factorization | ['0x125c05fc429', '0x63871fd9057da87', '0x1437c8a1be4c00e112b461', '0x31471d9e807ea9baa3c54111e9'] |
| max_conductor | 0x1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x8000000000000000000000000000000000020df8cd33e06d8eadfd349f7ab0620a499f4 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff438a66b74ff804f6cb88dd57eaa55169248bbca4ebc24350a792dc11a7569b65bec5caa |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x3', '0x3', '0x7', '0x7', '0x3b7b', '0x29f85d', '0xb24365', '0xf13592b8fd7b3c6f', '0xb9d0963b731e11192d4da5797da1f427c93b5b'] |
| (+)largest_factor_bitlen | 0x98 |
| (-)factorization | ['0x4ad8b7', '0x38438e7', '0x7c7fee2f7ca3302a307996fd961bc0e74398fb79df17b767e9efa5f076d'] |
| (-)largest_factor_bitlen | 0xeb |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x5', '0xdf', '0xfe4e741', '0x130f6afd2a7c6bd', '0x365dd38a0fb3ed4851377', '0xe9e097494ad14e31edd6018f1a5'] |
| (+)largest_factor_bitlen | 0x6c |
| (-)factorization | ['0x3', '0xd', '0x17', '0x67', '0x27137b', '0x9b12b85', '0xc202cf8fd859', '0xcc5f70f312b75b8a7317', '0xcae087af3ac61aeb0de2eb5'] |
| (-)largest_factor_bitlen | 0x5c |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x4859', '0x1f0bef', '0x9d65c62b8b', '0x472ec54415a0744630c544cbe990c839f930626a583955c605cc7'] |
| (+)largest_factor_bitlen | 0xd3 |
| (-)factorization | ['0x5', '0x5', '0x47', '0xb7b', '0xce5', '0x1c35ff88f', '0x36519d12a544704edae148a5794f3b062d1522d9176b404e81b5ecf'] |
| (-)largest_factor_bitlen | 0xda |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x33a3', '0x74e1', '0x1065381d818b0b635ce87', '0x1531aba36baec72931fbff70803525a6395d4cebf415b'] |
| (-)largest_factor_bitlen | 0xb1 |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x2dd', '0xdf85106a2c0165a1b3dd13356f691fc81eb84efac22d9e2949340ea8a5c15432eb973'] |
| (+)largest_factor_bitlen | 0x114 |
| (-)factorization | ['0x3', '0xad', '0x1d9e1', '0xb64c13120d7fb', '0xef7d22587ed97008a08eaf08f2e6ec8d305ddafa5e55e0620aa9'] |
| (-)largest_factor_bitlen | 0xd0 |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x7', '0x3d', '0x11adf719fd247', '0x1a0b2d79ee58dbec5466d6c611fd6f5f065cf1ddd00c39a6086f86abbf'] |
| (-)largest_factor_bitlen | 0xe5 |
| $\text{kn_factorization}(k=7)$ | |
| (+)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 | ['0x7', '0x8ef', '0x9e3', '0x99ab5b5f257', '0x74517ea73af69', '0x6128fc8a3759b914ff5d19cd1699bd4bd20e7a3fed'] |
| (+)largest_factor_bitlen | 0xa7 |
| (-)factorization | ['0x3', '0x3', '0x5', '0x1d', '0xc8e06ab738b1561e35c00c8e06ab738b155ea9ed163dca5ce4d7cd754fdf8820e4ac7'] |
| (-)largest_factor_bitlen | 0x114 |
| $\text{torsion_extension}(l=2)$ | |
| least | None |
| full | None |
| relative | None |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x2 |
| full | 0x6 |
| relative | 0x3 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x78 |
| full | 0x78 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0xa8 |
| full | 0xa8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x30 |
| full | 0x30 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x20df8cd33e06d8eadfd349f7ab0620a499f3 |
| factorization | ['0x9e3b', '0x20e4245', '0xd4eb9e3', '0x1f1b58c676a614a2fa7'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x3c759948b007fb09347722a8155aae96db74435b143dbcaf586d23ee58a9649a413a357 |
| factorization | ['0x7', '0x11', '0xde41', '0x31d55dd24fcd6a7', '0x3019a109d9a765e0ce6f1a03a945b9b961e92cfa1da3abee837'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x183345456ebcf3139b60053edc9675a83200d4047e5672b134bdd5711de7af52ed2078d41afd2d777d83115910390902cfffeff0a95 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x2 |
| complement_bit_length | 0x2 |
| $\text{class_number}()$ | |
| upper | 0x14b2e541a08d75299ea200d5214e2ffdf22ea6 |
| lower | 0x2225a |
| $\text{small_prime_order}(l=2)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb306 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x1fffffffffffffffffffffffffffffffffff7c81ccb307e49c5480b2d82153e77d6d983 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0x666666666666666666666666666666666664c19f5bd67fa85aa8023c4d3772e4c491e7 |
| complement_bit_length | 0x4 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb306 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x22222222222222222222222222222222222195dfc9477fe2c8e2ab696f127ba196db4d |
| complement_bit_length | 0x5 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x1', '0x2']] |
| 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 | 0x2 |
| 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 | 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 | 0x2 |
| depth | 0x0 |
| $\text{isogeny_extension}(l=2)$ | |
| least | None |
| full | None |
| relative | None |
| $\text{isogeny_extension}(l=3)$ | |
| 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 | 0x3 |
| relative | 0x3 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0xe |
| full | 0xe |
| relative | 0x1 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x1 |
| full | 0x12 |
| relative | 0x12 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x20df8cd33e06d8eadfd349f7ab0620a499f3 |
| trace_factorization | ['0x9e3b', '0x20e4245', '0xd4eb9e3', '0x1f1b58c676a614a2fa7'] |
| number_of_factors | 0x4 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x20df8cd33e06d8eadfd349f7ab0620a499f3 |
| trace_factorization | NO DATA (timed out) |
| number_of_factors | NO DATA (timed out) |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x3 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x0 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0x11a |
| expected | 0x8d |
| ratio | 0.5 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x9ac5 |
| expected | 0x4def |
| ratio | 0.50355 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x386d28 |
| expected | 0x1c83f6 |
| ratio | 0.50536 |
| $\text{square_4p1}()$ | |
| p | 0x1 |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0x20df8cd33e06d8eadfd349f7ab0620a499f2 |
| ratio | 5.4270874313740014e+42 |
| distance 32 | 0xe |
| distance 64 | 0xe |
| $\text{multiples_x}(k=1)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=2)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=3)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=4)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=5)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=6)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=7)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=8)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=9)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{multiples_x}(k=10)$ | |
| Hx | None |
| bits | None |
| difference | None |
| ratio | None |
| $\text{brainpool_overlap}()$ | |
| o | None |
| $\text{weierstrass}()$ | |
| a | None |
| b | None |