Curve detail
Definition
| Name | FRP256v1 |
|---|---|
| Category | anssi |
| Field | Prime (0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03) |
| Field bits | 256 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00 |
| Param $b$ | 0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f |
| Generator $x$ | 0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff |
| Generator $y$ | 0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb |
| Simulation seed | 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 |
Characteristics
| Order | 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1 |
| Cofactor | 0x1 |
| $j$-invariant | 0x5a6aa07dbd5b82f95fa8af9893561168a1a30f364407907db8a8cd296ebe55e9 |
| Trace $t$ | -0x1a7aba249509f5263700e105ee67b9dd |
| Embedding degree $k$ | 0x2854d94201df2397d803125177b5b5e48dfa1150357875435aaa4e0ef6790e50 |
| CM discriminant | -0x3c537358acc6e15261ae40aa9283fc9b84ae8425db8d0fb092b2b090f5ef34743 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1 |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x3c537358acc6e15261ae40aa9283fc9b84ae8425db8d0fb092b2b090f5ef34743 |
| factorization | ['0x1a768d1', '0x973d677d15', '0x17a415cd01d', '0x13c67b49d4c14725', '0x21cea32dcc781645fbdf8ff7'] |
| max_conductor | 0x1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0xf1fd178c0b3ad58f10126de8ce42435b1ee6f39816bed547b1fc124dea06e227 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xe4be808d3a1d6f02543fdc9a38c4bbf9d4a30c76be8054ec6809d66d20b8194a29b09dcc1ed4604fbe958fe70f7ccf44bb0b36b02e790d4147989099d39198cd |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x2', '0x1d', '0x1a7c8cdb', '0x99f61dcb8948d', '0x430d3f7a465259c0eb138a4de510cfe38d28fe2e6fb'] |
| (+)largest_factor_bitlen | 0xab |
| (-)factorization | ['0x2', '0x2', '0x2', '0x2', '0x2', '0x3', '0x11', '0x1353c30b', '0x4ca56721', '0x68f543e235db91c6c1652aace346e97005e0070435d3aff'] |
| (-)largest_factor_bitlen | 0xbb |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x5', '0x9fd', '0x9b0def69219b417e91896031daa4522a2397bccdec62462c2bf75219c46d1'] |
| (-)largest_factor_bitlen | 0xf4 |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x2', '0x2', '0x5', '0x5', '0x1f7', '0x22e9b3', '0x1e3e4eea509', '0xe55343ccae11bc96b7b645b9bdf2f826c7af2a4cc9205'] |
| (+)largest_factor_bitlen | 0xb4 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | - |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | ['0x7', '0xb', '0x534d3', '0x12877353f1', '0x215bfae7c05575fb69e50cb9f5d6996ba4c2b4515eb7b31913'] |
| (+)largest_factor_bitlen | 0xc6 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | - |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x2', '0x2', '0x520a9', '0xe96bc7', '0x12f3a60853', '0x369f17f4530930ea691420c243490bad73ba60cd01cbd'] |
| (-)largest_factor_bitlen | 0xb2 |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x13', '0x2b280d659', '0x58384a93407a8b1', '0x523684f57000c9fc723368ec68f3381922beab34f'] |
| (-)largest_factor_bitlen | 0xa3 |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x2', '0x2', '0x2', '0x29', '0x4c781def862d', '0x114a02e699102ae0d0a5076d9fd1cb1292e4a8ff496c081fc431'] |
| (+)largest_factor_bitlen | 0xcd |
| (-)factorization | ['0x2', '0x3', '0x5', '0xb', '0x95', '0x26c02e1', '0x5e5140ff974c14337', '0x9e23ccf58bee2699156cd0f17a40608977833d'] |
| (-)largest_factor_bitlen | 0x98 |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | - |
| (-)factorization | ['0x133', '0x4cf', '0x61f', '0x36d865c21a12f89942707cbe4d53bd146653fecaf52eeeb691fb212f0d'] |
| (-)largest_factor_bitlen | 0xe6 |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x2 |
| full | 0x6 |
| relative | 0x3 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0xa |
| full | 0xa |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0xa8 |
| full | 0xa8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x8 |
| full | 0x10 |
| relative | 0x2 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x1a7aba249509f5263700e105ee67b9dd |
| factorization | ['0x2b', '0x1ee3', '0x7b0a1', '0x2fd5e117', '0x38d506ca638a0eb'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0xef3feee6aabd9478eaacc0eebd78ffa69ec33927b5769bbf70342f13d5a7733a |
| factorization | ['0x2', '0x5', '0x1f', '0x83', '0x15fb47', '0xb33a51a63', '0x337fdf8b577f', '0x281b869e94570af', '0x31c05e9914aee6db36869'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x31c6e7a7d495703ca6d01b30ef854eeb808c714cbfc77e280d6a59109d04fa25a0a598d23b56b8b7a1aa168b11993ca9 |
| factorization | ['0x3', '0x3', '0x3', '0x25', '0x2b', '0x4eb', '0x1ee3', '0x7b0a1', '0x2fd5e117', '0x1568413e3d', '0x38d506ca638a0eb', '0x47210f7c4b960ea7', '0x4373f0819be0400425e79d9b14be170c0b3'] |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x6 |
| complement_bit_length | 0x3 |
| $\text{class_number}()$ | |
| upper | 0x6e7ecd75285bbd592238abf2b19f1386e0 |
| lower | 0x11b4484 |
| $\text{small_prime_order}(l=2)$ | |
| order | 0x2854d94201df2397d803125177b5b5e48dfa1150357875435aaa4e0ef6790e50 |
| complement_bit_length | 0x3 |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x3c7f45e302ceb563c4049b7a339090d6d4f719f85034afe507ff751671b59578 |
| complement_bit_length | 0x3 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x50a9b28403be472fb00624a2ef6b6bc91bf422a06af0ea86b5549c1decf21ca0 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e0 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e0 |
| complement_bit_length | 0x1 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e0 |
| complement_bit_length | 0x1 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x3', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x4', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x6', '0x2']] |
| 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 | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=11)$ | |
| crater_degree | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=13)$ | |
| crater_degree | 0x0 |
| 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 | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x1 |
| full | 0x6 |
| relative | 0x6 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x1 |
| full | 0x5 |
| relative | 0x5 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0xe |
| full | 0xe |
| relative | 0x1 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x1 |
| full | 0x10 |
| relative | 0x10 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x14 |
| full | 0x14 |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | -0x1a7aba249509f5263700e105ee67b9dd |
| trace_factorization | ['0x2b', '0x1ee3', '0x7b0a1', '0x2fd5e117', '0x38d506ca638a0eb'] |
| number_of_factors | 0x5 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | -0x1a7aba249509f5263700e105ee67b9dd |
| trace_factorization | ['0x3', '0x3', '0x3', '0x25', '0x4eb', '0x1568413e3d', '0x47210f7c4b960ea7', '0x4373f0819be0400425e79d9b14be170c0b3'] |
| number_of_factors | 0x6 |
| $\text{isogeny_neighbors}(l=2)$ | |
| 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 | 0x82 |
| expected | 0x80 |
| ratio | 0.98462 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x3f65 |
| expected | 0x3fc0 |
| ratio | 1.00561 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x1514d0 |
| expected | 0x151580 |
| ratio | 1.00013 |
| $\text{square_4p1}()$ | |
| p | 0x1 |
| order | 0x3 |
| $\text{pow_distance}()$ | |
| distance | 0xe02e873f4c52a70efed921731bdbca4ac23981ebf2d406be0022ba63929aa1f |
| ratio | 17.27089 |
| distance 32 | 0x1 |
| distance 64 | 0x1f |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0xa847235b97b15db6ca85669c3e5029dfa100c7b0c1cabc0cdd3794d2770a1946 |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x45b1f819e6d5ebf6c19feb017cbbf059ec5cfb3611c8446ea48c84292f0ebbd |
| bits | 0xfb |
| difference | 0x5 |
| ratio | 0.98047 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0x78cebe10de3aeecd0154ac0ea69292a7190b9847a81413715a566574a5aa3397 |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0xaeede4ac83cb4bdaea5b23318c30b66a5c105196521f14c51930497f49c8d953 |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x308016159cb9fa285c56b7b65181f8ad4adc670b74270d8710ea4783031fe0a6 |
| bits | 0xfe |
| difference | 0x2 |
| ratio | 0.99219 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0xeb9d52556a3e18330c261da3ca87ae3f2937d6b3acf35b577de124841b0b5c43 |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x1e09237b8257b9667e70c774f31e03d2ba4b2c5b0ddfc0c495b4b7310e2842b2 |
| bits | 0xfd |
| difference | 0x3 |
| ratio | 0.98828 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x6a61e5cd1a646506fced8d8328bce5b756aafe621ecfb9cc7ccf5f4a493267ba |
| bits | 0xff |
| difference | 0x1 |
| ratio | 0.99609 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0xefa9c112b762451aa4a4ffbb01a22a297f8631c1ebdd0ab38806fa0dc25bd348 |
| bits | 0x100 |
| difference | 0x0 |
| ratio | 1.0 |
| $\text{x962_invariant}()$ | |
| r | 0xed7449cb1194b8a5907fcc4a3eb534b5f1b735292887cf13a73bdfb73875540 |
| $\text{brainpool_overlap}()$ | |
| o | -0xc26c755c6b2bb5dc34dc1e75 |
| $\text{weierstrass}()$ | |
| a | 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00 |
| b | 0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f |