Curve detail
Definition
| Name | id-tc26-gost-3410-2012-256-paramSetA |
|---|---|
| Category | gost |
| Description | RFC5832 |
| Field | Prime (0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd97) |
| Field bits | 256 |
| Form | Twisted Edwards $ax^2 + y^2 = 1 + dx^2y^2$ |
| Param $a$ | 0x01 |
| Param $d$ | 0x605f6b7c183fa81578bc39cfad518132b9df62897009af7e522c32d6dc7bffb |
| Generator $x$ | 0x0d |
| Generator $y$ | 0x60ca1e32aa475b348488c38fab07649ce7ef8dbe87f22e81f92b2592dba300e7 |
Characteristics
| Order | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c67 |
| Cofactor | 0x4 |
| $j$-invariant | 0xd0d6242c5d7ec20b1345a8030dfd932fa2f3f36116504ba88f6f28d37bb278fb |
| Trace $t$ | -0x3f63377f21ed98d70456bd55b0d83404 |
| Embedding degree $k$ | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c66 |
| CM discriminant | -0xfc13810edd3c3c52cbe9b32681b1ecc05f4bb8c41c22aaa5b1b163ceabab9593 |
Traits
| $\text{cofactor}()$ | |
|---|---|
| order | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c67 |
| cofactor | 0x4 |
| $\text{discriminant}()$ | |
| cm_disc | -0xfc13810edd3c3c52cbe9b32681b1ecc05f4bb8c41c22aaa5b1b163ceabab9593 |
| factorization | ['0x2', '0x2', '0xd', '0x1cf', '0x373', '0x83425', '0x88afbf', '0x12e3527', '0x592fc9307', '0x1b9b8233121a6acf88713706af8a145d01'] |
| max_conductor | 0x2 |
| $\text{twist_order}(deg=1)$ | |
| twist_cardinality | 0xffffffffffffffffffffffffffffffffc09cc880de126728fba942aa4f27c994 |
| factorization | None |
| $\text{twist_order}(deg=2)$ | |
| twist_cardinality | 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb2c0fb1fbc48b0f0eb4d0593365f9384cfe82d11cef8f755569393a70c5515773f4 |
| factorization | None |
| $\text{kn_factorization}(k=1)$ | |
| (+)factorization | ['0x3', '0xd', '0x2cff', '0x14befc65', '0x1ccd5b7202698155b911cb3d59b60ed97fb9a0c2111fd581fd601'] |
| (+)largest_factor_bitlen | 0xd1 |
| (-)factorization | NO DATA (timed out) |
| (-)largest_factor_bitlen | NO DATA (timed out) |
| $\text{kn_factorization}(k=2)$ | |
| (+)factorization | ['0x7', '0x6b', '0xaefef98189bdb16375eacf1fc9505207b0494a81f86e76d549b75cda889bfd'] |
| (+)largest_factor_bitlen | 0xf8 |
| (-)factorization | ['0x3', '0x5', '0x1549', '0xbe113d', '0x228ef6e6cc9317f6bf2d3af7994d1859867d469111f5a4156abdde5'] |
| (-)largest_factor_bitlen | 0xda |
| $\text{kn_factorization}(k=3)$ | |
| (+)factorization | ['0x5', '0x16e1bb', '0x6b6781fd032e62fcb0e379b4058e29d18e88f8c45192bc41618fabc4a23'] |
| (+)largest_factor_bitlen | 0xeb |
| (-)factorization | ['0x89', '0x59b184abe9939ed5059b184abe9939ed668f2442f7551d41fdc86f2ed72fb7b'] |
| (-)largest_factor_bitlen | 0xfb |
| $\text{kn_factorization}(k=4)$ | |
| (+)factorization | ['0x3', '0x3', '0x3', '0x53e09a9ed3b051', '0x73c0b5cffaf1ac3bac2ce3c4f2f830ebc3bc0deb09b4a1c073'] |
| (+)largest_factor_bitlen | 0xc7 |
| (-)factorization | ['0x29', '0x409', '0x2acc67', '0x3c20a11f', '0x9da0e73756f7ab3509b52a97b35983e32a0b7a12be9c7e17'] |
| (-)largest_factor_bitlen | 0xc0 |
| $\text{kn_factorization}(k=5)$ | |
| (+)factorization | ['0x52f', '0x8cb', '0x1c153f69e1d1f8db39f14952eaf398b6644e70142c52ef741eca7f096529'] |
| (+)largest_factor_bitlen | 0xed |
| (-)factorization | ['0x3', '0x3', '0x7', '0x7', '0x3b9', '0xc799598a8b57c6a3bfd95dde51a2545c7ed3e9afac4131011fa7d443307b'] |
| (-)largest_factor_bitlen | 0xf0 |
| $\text{kn_factorization}(k=6)$ | |
| (+)factorization | ['0x1f', '0x67', '0x1677221', '0x2b7b273', '0x277a0a73', '0x47f32565', '0x13d6eff25bcb56f3', '0x2588edd95703cc7b3377'] |
| (+)largest_factor_bitlen | 0x4e |
| (-)factorization | ['0xe9', '0x2ccc81f', '0x54e898f4c77b9eb5f', '0x7194222561654b7de5eeaa81f14ec87fb722ac8f'] |
| (-)largest_factor_bitlen | 0x9f |
| $\text{kn_factorization}(k=7)$ | |
| (+)factorization | ['0x3', '0x11e3173d22299', '0xc124b21b41964104949ebf4895', '0x2c433edaeb4978b9f4dedd6abb3'] |
| (+)largest_factor_bitlen | 0x6a |
| (-)factorization | ['0x5', '0x11', '0x62275', '0x12e941', '0x6bc6ad', '0xa6bb5a9d0e3', '0xa9aa6b08f513993b9dee7edbf76e486922e8d'] |
| (-)largest_factor_bitlen | 0x94 |
| $\text{kn_factorization}(k=8)$ | |
| (+)factorization | ['0x5', '0x193b35d665d61', '0x24819f55b5b489', '0xcf7834ac421adb', '0x8c77d6f68245b85e6a7af587f'] |
| (+)largest_factor_bitlen | 0x64 |
| (-)factorization | ['0x3', '0x1d', '0x54279fb', '0x323c72364125ff47', '0x1a274556e32ad598ef', '0xdf3f7c94f6a50576b7c88a03'] |
| (-)largest_factor_bitlen | 0x60 |
| $\text{torsion_extension}(l=2)$ | |
| least | 0x1 |
| full | 0x2 |
| relative | 0x2 |
| $\text{torsion_extension}(l=3)$ | |
| least | 0x8 |
| full | 0x8 |
| relative | 0x1 |
| $\text{torsion_extension}(l=5)$ | |
| least | 0xc |
| full | 0xc |
| relative | 0x1 |
| $\text{torsion_extension}(l=7)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{torsion_extension}(l=11)$ | |
| least | 0x78 |
| full | 0x78 |
| relative | 0x1 |
| $\text{torsion_extension}(l=13)$ | |
| least | 0xc |
| full | 0xd |
| relative | 0x1 |
| $\text{torsion_extension}(l=17)$ | |
| least | 0x18 |
| full | 0x18 |
| relative | 0x1 |
| $\text{conductor}(deg=2)$ | |
| ratio_sqrt | 0x3f63377f21ed98d70456bd55b0d83404 |
| factorization | ['0x2', '0x2', '0xfd8cddfc87b6635c115af556c360d01'] |
| $\text{conductor}(deg=3)$ | |
| ratio_sqrt | 0xf04e043b74f0f14b2fa6cc9a06c7b3017d2ee310708aaa96c6c58f3aaeae5d87 |
| factorization | ['0x5', '0x7', '0x11', '0x2cad', '0x25073b61fda987a43ce41581a1de805df07fdeec95b6165ce19b1ddca11'] |
| $\text{conductor}(deg=4)$ | |
| ratio_sqrt | 0x7ae38ccd8029134259bce442edfc67bf2ebc14395ddff37aff4bd9b48bb3dc69e951f7dbdac773883b06d11da68b8478 |
| factorization | NO DATA (timed out) |
| $\text{embedding}()$ | |
| embedding_degree_complement | 0x1 |
| complement_bit_length | 0x1 |
| $\text{class_number}()$ | |
| upper | 0x380b1583486b76955febff864c6dd030ab |
| lower | 0x269bee464783 |
| $\text{small_prime_order}(l=2)$ | |
| order | None |
| complement_bit_length | None |
| $\text{small_prime_order}(l=3)$ | |
| order | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c66 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=5)$ | |
| order | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c66 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=7)$ | |
| order | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c66 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=11)$ | |
| order | 0x400000000000000000000000000000000fd8cddfc87b6635c115af556c360c66 |
| complement_bit_length | 0x2 |
| $\text{small_prime_order}(l=13)$ | |
| order | 0x2000000000000000000000000000000007ec66efe43db31ae08ad7aab61b0633 |
| complement_bit_length | 0x3 |
| $\text{division_polynomials}(l=2)$ | |
| factorization | [['0x1', '0x1'], ['0x2', '0x1']] |
| len | 0x2 |
| $\text{division_polynomials}(l=3)$ | |
| factorization | [['0x4', '0x1']] |
| len | 0x1 |
| $\text{division_polynomials}(l=5)$ | |
| factorization | [['0x6', '0x2']] |
| 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 | 0x2 |
| depth | 0x0 |
| $\text{volcano}(l=11)$ | |
| crater_degree | 0x0 |
| depth | 0x0 |
| $\text{volcano}(l=13)$ | |
| crater_degree | 0x1 |
| depth | 0x0 |
| $\text{volcano}(l=17)$ | |
| crater_degree | 0x0 |
| 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 | 0x3 |
| full | 0x3 |
| 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 | 0x1 |
| full | 0xd |
| relative | 0xd |
| $\text{isogeny_extension}(l=17)$ | |
| least | 0x3 |
| full | 0x3 |
| relative | 0x1 |
| $\text{isogeny_extension}(l=19)$ | |
| least | 0xa |
| full | 0xa |
| relative | 0x1 |
| $\text{trace_factorization}(deg=1)$ | |
| trace | -0x3f63377f21ed98d70456bd55b0d83404 |
| trace_factorization | ['0x2', '0x2', '0xfd8cddfc87b6635c115af556c360d01'] |
| number_of_factors | 0x2 |
| $\text{trace_factorization}(deg=2)$ | |
| trace | -0x3f63377f21ed98d70456bd55b0d83404 |
| trace_factorization | ['0x2', '0x3', '0x29', '0x65', '0x7f', '0x1b1', '0x61e4cab', '0x93d721e3', '0x16501314ebc1aa3', '0x13c9eba8337ac49f610afed686c7d'] |
| number_of_factors | 0xa |
| $\text{isogeny_neighbors}(l=2)$ | |
| 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 | 0x85 |
| expected | 0x80 |
| ratio | 0.96241 |
| $\text{hamming_x}(weight=2)$ | |
| x_coord_count | 0x4057 |
| expected | 0x4040 |
| ratio | 0.9986 |
| $\text{hamming_x}(weight=3)$ | |
| x_coord_count | 0x15590f |
| expected | 0x155540 |
| ratio | 0.9993 |
| $\text{square_4p1}()$ | |
| p | 0x5 |
| order | NO DATA (timed out) |
| $\text{pow_distance}()$ | |
| distance | 0x3f63377f21ed98d70456bd55b0d8319c |
| ratio | 1.3742803523162354e+39 |
| distance 32 | 0x4 |
| distance 64 | 0x1c |
| $\text{multiples_x}(k=1)$ | |
| Hx | 0x91e38443a5e82c0d880923425712b2bb658b9196932e02c78b2582fe742daa28 |
| bits | 0x100 |
| difference | 0x1 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=2)$ | |
| Hx | 0xeb8b85ae2b303ba4a990f78e81838dc91f0c17ddcafaf662de507dda8e51e3d0 |
| bits | 0x100 |
| difference | 0x1 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=3)$ | |
| Hx | 0x97689df8e46e80c91eee963fc354c842454198eca2c620ce170a757d061110c7 |
| bits | 0x100 |
| difference | 0x1 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=4)$ | |
| Hx | 0x34085b25e2d182d7ce02fb8434f85cbe6aeaf2c96537505edfcbbe5bb5467458 |
| bits | 0xfe |
| difference | 0x3 |
| ratio | 0.99608 |
| $\text{multiples_x}(k=5)$ | |
| Hx | 0x77cdedd31926a5c268950f8e3874de0dbac5ca3285b753a8e83bb19f8ec5cdda |
| bits | 0xff |
| difference | 0x2 |
| ratio | 1.0 |
| $\text{multiples_x}(k=6)$ | |
| Hx | 0xb70281437808c4f0e4809813cd83e69bd2048aaf43e274f77252a017c5525a42 |
| bits | 0x100 |
| difference | 0x1 |
| ratio | 1.00392 |
| $\text{multiples_x}(k=7)$ | |
| Hx | 0x2a425cd365954aea8f1fcae3b4d991feab35f2a893c938068190420bb445c816 |
| bits | 0xfe |
| difference | 0x3 |
| ratio | 0.99608 |
| $\text{multiples_x}(k=8)$ | |
| Hx | 0x4a4d920ebca4147740599112bd00062e333521294646ed545cc77fd2f3869fbd |
| bits | 0xff |
| difference | 0x2 |
| ratio | 1.0 |
| $\text{multiples_x}(k=9)$ | |
| Hx | 0x6eae70c0825fe4898afc7b907e41aaaaafa14081de013a26afcbbe3d11782978 |
| bits | 0xff |
| difference | 0x2 |
| ratio | 1.0 |
| $\text{multiples_x}(k=10)$ | |
| Hx | 0x7968db09b1cbb32de98252c39cc06421f3115fb88d566efe00ed75cf96c0c2ff |
| bits | 0xff |
| difference | 0x2 |
| ratio | 1.0 |
| $\text{x962_invariant}()$ | |
| r | 0x69310e5651ded2c76e08ac623def3a36004218a1729c2c80ba9eb60b4ad0db6f |
| $\text{brainpool_overlap}()$ | |
| o | 0x16360e853e0377d25b5d8b72 |
| $\text{weierstrass}()$ | |
| a | 0xc2173f1513981673af4892c23035a27ce25e2013bf95aa33b22c656f277e7335 |
| b | 0x295f9bae7428ed9ccc20e7c359a9d41a22fccd9108e17bf7ba9337a6f8ae9513 |