Curve detail
Definition
| Name | id-tc26-gost-3410-2012-512-paramSetC |
|---|---|
| Category | gost |
| Description | RFC5832 |
| Field | Prime (0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7) |
| Field bits | 512 |
| Form | Twisted Edwards $ax^2 + y^2 = 1 + dx^2y^2$ |
| Param $a$ | 0x01 |
| Param $d$ | 0x9e4f5d8c017d8d9f13a5cf3cdf5bfe4dab402d54198e31ebde28a0621050439ca6b39e0a515c06b304e2ce43e79e369e91a0cfc2bc2a22b4ca302dbb33ee7550 |
| Generator $x$ | 0x12 |
| Generator $y$ | 0x469af79d1fb1f5e16b99592b77a01e2a0fdfb0d01794368d9a56117f7b38669522dd4b650cf789eebf068c5d139732f0905622c04b2baae7600303ee73001a3d |
Characteristics
| Order | 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc98cdba46506ab004c33a9ff5147502cc8eda9e7a769a12694623cef47f023ed |
| Cofactor | 0x4 |
| $j$-invariant | 0x7811b126b066ba9248a6a3262106ed4ed3e34e71f487de6ec0a4205ff0adefa3faeed89084d8d9da172f958af0f805851c88dcf431eaae6c07b13c4c4f0b5780 |
| Trace $t$ | 0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc98cdba46506ab004c33a9ff5147502cc8eda9e7a769a12694623cef47f023ed |
| cofactor | 0x4 |
| $\text{discriminant}()$ | |
| cm_disc | None |
| factorization | None |
| max_conductor | None |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0x10000000000000000000000000000000000000000000000000000000000000000d9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6bdc |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb8cb94c72054d8503be8910352f3bea2192314e0a57f445b20e04f77045db49aa026b83ec89a4f901b3fd86d0501732b44bf3f5a3d30f551ee1de0db2aa5d3226b4 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x13', '0x1f', '0x65', '0x1b1', '0x49ba9', '0x242f24520011e580bcc442e8d8efc0c41ac4b9e3ab3eb938494ff70e61a8b019b5c17a703185c4b8cde8483a64559322effc54b3a71ea3a801714b'] |
| (-)largest_factor_bitlen | 0x1d6 |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x5', '0x17', '0x5f251', '0x144a1fd497b', '0x97253444dcb3a8d75a44024cce6b9b46c9f5afc9810afdd5707a6bbbc9c4a2165825edf9e1eb78947bb128c06bc0765591e956b516d63559'] |
| (+)largest_factor_bitlen | 0x1c0 |
| (-)factorization | ['0x3', '0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa19779f0bb811c800cb346ffe2e1380776d246fbf13c45866e105f7d36a805fcd'] |
| (-)largest_factor_bitlen | 0x200 |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x5', '0x7', '0x11', '0x53', '0x3fe1ccd43', '0xe656a39e9f1', '0x11bb3769d3f269b507d6458f946520cb1f2e09c78cc81c511848c08cc00237c5f7a573cc5e06fbcf9cb593f935bd33094c0036ca71'] |
| (-)largest_factor_bitlen | 0x1a5 |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | NO DATA (timed out) |
| (+)largest_factor_bitlen | NO DATA (timed out) |
| (-)factorization | ['0x3', '0xb11', '0x268e1c9d793cdffb2e3c6c50d864009a387275e4f37fecb8f1b14361900268e1a90a4e6696ec4056eda843f3a92d856443ab566baf861651fa4465e4093d71'] |
| (-)largest_factor_bitlen | 0x1f6 |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x47', '0x24df', '0x27da58da03f', '0x64e3fb6f5db915d', '0x990407cd135d686d30a7b9741c701446385611b1f799f40307be9334e65a7fc0b7e1b9ea4dac1f84b8da06d0bc407288ceb'] |
| (+)largest_factor_bitlen | 0x18c |
| (-)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 | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x28 |
| full | 0x28 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0x1c |
| full | 0x1c |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x8 |
| full | 0x10 |
| relative | 0x2 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14 |
| factorization | ['0x2', '0x2', '0x5c317', '0x256a87dbfb785d', '0x40a78bd3c312927729ade6e7bd3d1664b8303e831ade9f'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0x46b38dfab27afc4176efcad0c415de6dceb1f5a80bba4df1fb088fba24b655fd947c13765b06fe4c02792fafe8cd4bb40c0a5c2cf0aae11e21f24d55a2d2cc37 |
| factorization | NO DATA (timed out) |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x115f34407435430cc0b29e10a92940926d533f2463e2494f55fb1fa5875b0a6013e8f5abbd143fa720e1b41e47010f5663dc310b7ae5e231a12da9eaac31b2a7262ea4532ee4f970d4090134fae2dd6501855fb603b498b6f1f9654c140c4ebd8 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | None |
| complement_bit_length | None |
| $\text{class_number}()$ | |
| 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 | [['0x4', '0x1']] |
| 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 | 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 | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{isogeny_extension}(l=3)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=5)$ | |
| least | 0x6 |
| full | 0x6 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=7)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=11)$ | |
| least | 0x4 |
| full | 0x4 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=13)$ | |
| least | 0x7 |
| full | 0x7 |
| 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 | 0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14 |
| trace_factorization | ['0x2', '0x2', '0x5c317', '0x256a87dbfb785d', '0x40a78bd3c312927729ade6e7bd3d1664b8303e831ade9f'] |
| number_of_factors | 0x4 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | 0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14 |
| 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 | 0x10b |
| expected | 0x100 |
| ratio | 0.9588 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0xff53 |
| expected | 0xff80 |
| ratio | 1.00069 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0xa9a22e |
| expected | 0xa9ab00 |
| ratio | 1.0002 |
| $\text{square_4p1}()$ | |
| p | NO DATA (timed out) |
| order | 0x1 |
| $\text{pow_distance}()$ | |
| distance | 0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f704c |
| ratio | 1.3610146068982212e+77 |
| distance 32 | 0xc |
| distance 64 | 0xc |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0xe2e31edfc23de7bdebe241ce593ef5de2295b7a9cbaef021d385f7074cea043aa27272a7ae602bf2a7b9033db9ed3610c6fb85487eae97aac5bc7928c1950148 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0x871aa434151a025d1ebc40692f847948deeeab7bef019df752f8218902314a910597d3d66e62415ae74ec5684df2354a92e19ae13833c5a7caddbe5d24741b7a |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0xb86f988f704e95f06480be926feb61ccac0953a24de8971cdb01f46d44a2a83ebfe0fe6e33585c31529f0b50e4102629905e5e9e792dfb14d28cafba809d5aa9 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0xbbd6805a6ea97e6e7172db913d414b47ee0ade7735db2eb683044a4ad81c129b23cee9b2c8b8c928d7e5330e2a56eb008d94efb859d11c074dc8c643f31a4866 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0x7215cd9ec101d99725813fd333f2e1121d73ca91ced61aa2fae8b727514dea7d6944a4a189d5a8fae5287a7728a157ed68b8691058241a0470acc2667b2e708a |
| bits | 0x1ff |
| difference | 0x1 |
| ratio | 1.00196 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0x7f7ccda82fee97e7164efb676fafa418b54796fb864f8e5f17f20680b0ace788b01404d8a6149f5cc2216ec43586de2c07abc2b9bd900127f3ff3e197612942d |
| bits | 0x1ff |
| difference | 0x1 |
| ratio | 1.00196 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x36d1e509cfb515bc091444fc91ef3043e97e017c6ab40f89225cbc77596580462e5997aed6edb413cc9f1223c96c3a60ca1711dfec2eb95d8d3d1f87469493db |
| bits | 0x1fe |
| difference | 0x2 |
| ratio | 1.0 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x6175e4b3be5576d889f189d68460a34f7845f9a1937d7f62d8e921707c22ce49ca9c2a45cb462a6d20d4905623464d7a41d0dd72f95922c308978e7b0f5fb5d6 |
| bits | 0x1ff |
| difference | 0x1 |
| ratio | 1.00196 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0xd53def9a3910d3e07ac3ab7ce153d4d46762b3b9dfa89fecc79cdf25894f3e6a40a264a2b4b9f8b301610958e38cceb3689b67e414d5887d466b5723e5eb1d51 |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0x976915361c4d03c3ad4ed63cd4e081b61276488b11bd6860de54c8ce523736f94b02239f169b5106a494ff4d9df8883e0d24c50764f2da7c8e917928cdf35faf |
| bits | 0x200 |
| difference | 0x0 |
| ratio | 1.00392 |
| $\text{x962_invariant}()$ | |
| r | 0x1a1f8d8c5ae0bbee1065c55bae8bcf43704214962d76af2447ca2fe9425c4674c48d3a75111a53ab8d831cb8d9bc8c2d87e9b6a53c83207443214838615665d2 |
| $\text{brainpool_overlap}()$ | |
| o | -0xa60c87c480d84fc3a97e230d884f8fa9e525c8d0cbc0d963900add4fe30c2e4b18f123d5c8637e5254778c78 |
| $\text{weierstrass}()$ | |
| a | 0xdc9203e514a721875485a529d2c722fb187bc8980eb866644de41c68e143064546e861c0e2c9edd92ade71f46fcf50ff2ad97f951fda9f2a2eb6546f39689bd3 |
| b | 0xb4c4ee28cebc6c2c8ac12952cf37f16ac7efb6a9f69f4b57ffda2e4f0de5ade038cbc2fff719d2c18de0284b8bfef3b52b8cc7a5f5bf0a3c8d2319a5312557e1 |