Curve detail
Definition
| Name | w-383-mers |
|---|---|
| Category | nums |
| Description | Original nums curve from https://eprint.iacr.org/2014/130.pdf |
| Field | Prime (0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe5b) |
| Field bits | 383 |
| Form | Weierstrass $y^2 = x^3 + ax + b$ |
| Param $a$ | 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe58 |
| Param $b$ | 0x17dbc |
Characteristics
| Order | 0x7fffffffffffffffffffffffffffffffffffffffffffffffa9caf814a8a116ad9fb0b4035417aaf319297fc0bb7a439f |
| Cofactor | 0x1 |
| $j$-invariant | 0x4c6dafb9b071be8dcf501e229ccf718a7db00cdffe463355a1709a1538edae59f50e16fd89261cfb138db23400f32fbd |
| Trace $t$ | 0x563507eb575ee952604f4bfcabe8550ce6d6803f4485babd |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x7fffffffffffffffffffffffffffffffffffffffffffffffa9caf814a8a116ad9fb0b4035417aaf319297fc0bb7a439f |
| cofactor | 0x1 |
| $\text{discriminant}()$ | |
| cm_disc | -0x1e2f853b1999b56cf545a53d57387b7aa129d19ef177b34cfdc57bae8d3b3a991df04987177beccffa91dc5ea0766c9e3 |
| factorization | ['0x3b', '0x1fc40ae6e7b9', '0x41f865883131524e509b097a6c79d4c148d82738e753288d95fda8d4a6cf5f99a37059150f86ab9238c1'] |
| max_conductor | 0x1 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x800000000000000000000000000000000000000000000000563507eb575ee952604f4bfcabe8550ce6d6803f4485b919 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe5a1d07ac4e6664a930aba5ac2a8c784855ed62e610e884cb3023a845172c4c566e20fb678e8841330056e23a15f89be72d |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x2', '0x2', '0x2', '0x2', '0x2', '0x3', '0xb', '0x53', '0x5fb53a6a5ce76b343f2ea3903754c5c57db5c9fa3486f68f1f879820a4f7ef4f41d91569c470487db0ad189557ef'] |
| (+)largest_factor_bitlen | 0x16f |
| (-)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', '0x2', '0x805', '0x33c1', '0x3cfcbf9', '0xf88da98377565a240ad0af76209411d57789b95e93f2b28446caeaf3e8f57e0ca89252aa3a3742f1e63'] |
| (-)largest_factor_bitlen | 0x14c |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x7', '0x7', '0x13', '0x306689', '0x15110abd5197a2f', '0x2358e8d3878b9158c4d14ddfa8cc0ea4ee87375be53a8329582621c2dca4d46d61485c9ae0f'] |
| (-)largest_factor_bitlen | 0x12a |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x2', '0x2', '0xbf', '0x277', '0x8c17', '0x199145', '0x146c209', '0x30c8f25d1', '0x7b76efcb47', '0x86e70525112b', '0x906f5e31121017a7', '0xb24b3081209d9c0a2d11815a5a4c447'] |
| (+)largest_factor_bitlen | 0x7c |
| (-)factorization | ['0x2', '0x3', '0x1d', '0x421f', '0x36c043', '0x3b796571', '0x11e9be2f6bc9f10113317c63cc6cb62f2a127c29d00b9860e8465798df611c635ab04ea01ca6327'] |
| (-)largest_factor_bitlen | 0x139 |
| $\text{kn_factorization}(k=6)$ | |
| (+)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 | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)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 | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x30 |
| full | 0x30 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0xf |
| full | 0xf |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0xa8 |
| full | 0xa8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x10 |
| full | 0x10 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x563507eb575ee952604f4bfcabe8550ce6d6803f4485babd |
| factorization | ['0x3', '0x5', '0x5bf44cb6c3987057de32732fa64d27853a7e66a9e2b0c73'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x62f853b1999b56cf545a53d57387b7aa129d19ef177b34cfdc57bae8d3b3a991df04987177beccffa91dc5ea0766ced2 |
| factorization | NO DATA (timed out) |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x4c6e708c6f14360b03c03d1d15906a6a198bca53f8e9a0c0cfcaaf8f05b145c10480e1e61e18f51e3190f6080071ac1e9b528d5259cd9305595aca7822d8b256a3d54c23b4592c39 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x1 |
| complement_bit_length | 0x1 |
| $\text{class_number}()$ | |
| upper | 0x74a62bf1dbc265507e30ff3043ad35d04734491b1dc3f66ec9 |
| lower | 0x3ca |
| $\text{small_prime_order}(l=2)$ | |
| 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 | [['0x2', '0x2']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x4', '0x3']] |
| 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 | 0x0 |
| 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 | 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 | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0xe |
| full | 0xe |
| relative | 0x1 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x1 |
| full | 0x8 |
| relative | 0x8 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x14 |
| full | 0x14 |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x563507eb575ee952604f4bfcabe8550ce6d6803f4485babd |
| trace_factorization | ['0x3', '0x5', '0x5bf44cb6c3987057de32732fa64d27853a7e66a9e2b0c73'] |
| number_of_factors | 0x3 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x563507eb575ee952604f4bfcabe8550ce6d6803f4485babd |
| trace_factorization | ['0x11b', '0x11bd061ba016cbd', '0xb931ce1293c9a3690e0311a7716fa5cc5c6edb5511390270659c4dc73922bd2530bfc8190bff77a3'] |
| 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 | 0xb9 |
| expected | 0xbf |
| ratio | 1.03243 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x8ec1 |
| expected | 0x8ee0 |
| ratio | 1.00085 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x46e309 |
| expected | 0x46e15f |
| ratio | 0.99991 |
| $\text{square_4p1}()$ | |
| p | 0x3 |
| order | 0x7 |
| $\text{pow_distance}()$ | |
| distance | 0x563507eb575ee952604f4bfcabe8550ce6d6803f4485bc61 |
| ratio | 9.320213029429296e+57 |
| distance 32 | 0x1 |
| distance 64 | 0x1f |
| $\text{multiples_x}(k=1)$ | |
| 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 |
| $\text{x962_invariant}()$ | |
| r | 0x3f894ee0d5a7a779f781ad0cf28408cf9095ae56f3e92a6815dfe6afb4868bf5f5c24d42df06221e6fb78abfffb5436d |
| $\text{brainpool_overlap}()$ | |
| o | 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffe58 |
| $\text{weierstrass}()$ | |
| a | 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe58 |
| b | 0x17dbc |