Curve detail
Definition
| Name | ed-383-mers |
|---|---|
| Category | nums |
| Description | Original nums curve from https://eprint.iacr.org/2014/130.pdf |
| Field | Prime (0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe5b) |
| Field bits | 383 |
| Form | Twisted Edwards $ax^2 + y^2 = 1 + dx^2y^2$ |
| Param $a$ | 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe5a |
| Param $d$ | 0x7fed6 |
Characteristics
| Order | 0x1ffffffffffffffffffffffffffffffffffffffffffffffff1109704e73d9fbbbcd5687c9eaca2206ffebcec1ba7c81d |
| Cofactor | 0x4 |
| $j$-invariant | 0x1009575ea00fe1506252fd0824cafd104ba005000a1beeaf41c711e40718045b53f1e0e0739558c580abf51cc070c22f |
| Trace $t$ | 0x3bbda3ec630981110caa5e0d854d777e40050c4f9160dde8 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x1ffffffffffffffffffffffffffffffffffffffffffffffff1109704e73d9fbbbcd5687c9eaca2206ffebcec1ba7c81d |
| cofactor | 0x4 |
| $\text{discriminant}()$ | |
| cm_disc | None |
| factorization | None |
| max_conductor | None |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x8000000000000000000000000000000000000000000000003bbda3ec630981110caa5e0d854d777e40050c4f9160dc44 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe5a0df0f60a69a77deb493542a6ed5c02c48303c3a17599150239917a9245eb80b83a45a224fb9bcb78cc359537fe5d19e4 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x3b', '0x241', '0xb8d', '0x1f39', '0x33c84925b5', '0x17b3f7dc0a3', '0x247b537eebd3d42d00ac3f922f279b7a7da177170f5383e1994e2734579aff3898b'] |
| (-)largest_factor_bitlen | 0x10a |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x3', '0x3', '0x2b', '0xedaf0bd988597', '0xb664bd76315a63d5da363182279f4b0ccb863e87719efa408d40db387399b5f48ee3050ea7dc9703b'] |
| (-)largest_factor_bitlen | 0x144 |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | ['0x3', '0xd', '0x74962feb', '0x1cd3a92075f68db34a45c60019bfe741ab87121ec828f6c29aa1f73a212653e32d0e0a2527218a171b860915'] |
| (+)largest_factor_bitlen | 0x15d |
| (-)factorization | ['0x5', '0x7', '0xc7', '0x377', '0x16723c91', '0x3df1bfc90d8efd75d6456d84b5544cea432718c933b49109ddabca96cf308f3838011837552eb907ed15'] |
| (-)largest_factor_bitlen | 0x14e |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x5', '0x11', '0x6b', '0xef', '0x1f3', '0x561760fbb', '0x1f39d5904f', '0x2dd8f2168b', '0x65100260bcde3b55a87ed815aef5d9c5b7a726bcf839b36676a9abb982efdd'] |
| (+)largest_factor_bitlen | 0xf7 |
| (-)factorization | ['0x1f', '0x474c3d', '0x618e09', '0xe96dc9690ec786e4ead3d71e6b793aacdf92b08922421ab7fabeeea3301cb3ef16bd7320852da7b1d7f5'] |
| (-)largest_factor_bitlen | 0x150 |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x3', '0x3', '0x3', '0x3', '0x3', '0x3', '0x13aa50c4a727ae878cd14b802cf301c17e118eecaf953edbcb46f267725d5ac9c25b1d72289f77a65ecfd128cd38675'] |
| (+)largest_factor_bitlen | 0x179 |
| (-)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 | ['0x3', '0x13', '0x17', '0x89', '0x14482d', '0x126c252ee76b60dcf54f5ee3531013a15f652c1eab1810201fbcbe07703236094fd88e4ee7b6204e49f8fabd'] |
| (-)largest_factor_bitlen | 0x15d |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x30 |
| full | 0x30 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x5 |
| full | 0x5 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x3bbda3ec630981110caa5e0d854d777e40050c4f9160dde8 |
| factorization | ['0x2', '0x2', '0x2', '0x3', '0xd', '0x11', '0x25', '0xed6c4f4f11f80daf7451', '0x1582d7733e02aa32b888b87f'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x720f09f596588214b6cabd5912a3fd3b7cfc3c5e8a66eafdc66e856dba147f47c5ba5ddb0464348733ca6ac801a59c1b |
| factorization | ['0x95', '0xf17', '0x145e0077', '0xa33b7ce3dab4487153e5369488d181c1195fb38ffe684933d0a6c0c5064aa7445a0e76e51fada002339f'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x387cc7650acfbfdec99b81ab84f5767c1b7b29a0299b96672e8d58458fcababd4ad0368fd8b55b3ba5567d71d0651eae2c2a3566b2524274cf45eda8dfc80759cb350bae36abd8f0 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x1 |
| complement_bit_length | 0x1 |
| $\text{class_number}()$ | |
| upper | NO DATA (timed out) |
| lower | NO DATA (timed out) |
| $\text{small_prime_order}(l=2)$ | |
| 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 | [['0x1', '0x1'], ['0x2', '0x1']] |
| len | 0x2 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x2', '0x2']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0xc', '0x1']] |
| len | 0x1 |
| $\text{volcano}(l=2)$ | |
| crater_degree | 0x0 |
| depth | 0x1 |
| $\text{volcano}(l=3)$ | |
| 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 | 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 | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{isogeny_extension}(l=3)$ | |
| least | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x1 |
| full | 0x5 |
| relative | 0x5 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x2 |
| full | 0x2 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | 0x3bbda3ec630981110caa5e0d854d777e40050c4f9160dde8 |
| trace_factorization | ['0x2', '0x2', '0x2', '0x3', '0xd', '0x11', '0x25', '0xed6c4f4f11f80daf7451', '0x1582d7733e02aa32b888b87f'] |
| number_of_factors | 0x7 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0x3bbda3ec630981110caa5e0d854d777e40050c4f9160dde8 |
| trace_factorization | NO DATA (timed out) |
| number_of_factors | NO DATA (timed out) |
| $\text{isogeny_neighbors}(l=2)$ | |
| len | 0x1 |
| $\text{isogeny_neighbors}(l=3)$ | |
| len | 0x0 |
| $\text{isogeny_neighbors}(l=5)$ | |
| len | 0x0 |
| $\text{q_torsion}()$ | |
| Q_torsion | 0x1 |
| $\text{hamming_x}(weight=1)$ | |
| x_coord_count | 0xb5 |
| expected | 0xbf |
| ratio | 1.05525 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x8f18 |
| expected | 0x8ee0 |
| ratio | 0.99847 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x46dfc4 |
| expected | 0x46e15f |
| ratio | 1.00009 |
| $\text{square_4p1}()$ | |
| p | 0x3 |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0x3bbda3ec630981110caa5e0d854d777e40050c4f9160df8c |
| ratio | 1.3449255068404993e+58 |
| distance 32 | 0xc |
| distance 64 | 0xc |
| $\text{multiples_x}(k=1)$ | |
| 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 | 0x4d14c61edfdcecc01d3431064d406d80d2687017cf29e1108ab66e87a977968c7c9071ab030eac162f62a7e40bbe8028 |
| $\text{brainpool_overlap}()$ | |
| o | -0x3069e34e9d026d6d0ba4783b303128f2d204a9b06b4127ba37a62441 |
| $\text{weierstrass}()$ | |
| a | 0x16aeb6729c4555b87e08b82bfe58d789b9ea5f9ee6dd7f012c7eadb00e9ba8d451d09b082c80fd3bb86cded90b6f192d |
| b | 0x5747624fc9811b1d1a40210f8201c3fafe85a6ec23ae069343153d6e110b5842c0278560589181d5d79decc1a15b362d |