DiSSECT

Name	id-tc26-gost-3410-2012-512-paramSetC
Category	gost
Description	RFC5832
Field	Prime (0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7)
Field bits	512
Form	Twisted Edwards $a x^{2} + y^{2} = 1 + d x^{2} y^{2}$
Param $a$	0x01
Param $d$	0x9e4f5d8c017d8d9f13a5cf3cdf5bfe4dab402d54198e31ebde28a0621050439ca6b39e0a515c06b304e2ce43e79e369e91a0cfc2bc2a22b4ca302dbb33ee7550
Generator $x$	0x12
Generator $y$	0x469af79d1fb1f5e16b99592b77a01e2a0fdfb0d01794368d9a56117f7b38669522dd4b650cf789eebf068c5d139732f0905622c04b2baae7600303ee73001a3d

Order	0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc98cdba46506ab004c33a9ff5147502cc8eda9e7a769a12694623cef47f023ed
Cofactor	0x4
$j$ -invariant	0x7811b126b066ba9248a6a3262106ed4ed3e34e71f487de6ec0a4205ff0adefa3faeed89084d8d9da172f958af0f805851c88dcf431eaae6c07b13c4c4f0b5780
Trace $t$	0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14

$cofactor ()$
order	0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc98cdba46506ab004c33a9ff5147502cc8eda9e7a769a12694623cef47f023ed
cofactor	0x4

$discriminant ()$
cm_disc	None
factorization	None
max_conductor	None

$twist_order (d e g = 1)$
twist_cardinality	0x10000000000000000000000000000000000000000000000000000000000000000d9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6bdc
factorization	None

$twist_order (d e g = 2)$
twist_cardinality	0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb8cb94c72054d8503be8910352f3bea2192314e0a57f445b20e04f77045db49aa026b83ec89a4f901b3fd86d0501732b44bf3f5a3d30f551ee1de0db2aa5d3226b4
factorization	None

$kn_factorization (k = 1)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	['0x13', '0x1f', '0x65', '0x1b1', '0x49ba9', '0x242f24520011e580bcc442e8d8efc0c41ac4b9e3ab3eb938494ff70e61a8b019b5c17a703185c4b8cde8483a64559322effc54b3a71ea3a801714b']
(-)largest_factor_bitlen	0x1d6

$kn_factorization (k = 2)$
(+)factorization	['0x5', '0x17', '0x5f251', '0x144a1fd497b', '0x97253444dcb3a8d75a44024cce6b9b46c9f5afc9810afdd5707a6bbbc9c4a2165825edf9e1eb78947bb128c06bc0765591e956b516d63559']
(+)largest_factor_bitlen	0x1c0
(-)factorization	['0x3', '0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa19779f0bb811c800cb346ffe2e1380776d246fbf13c45866e105f7d36a805fcd']
(-)largest_factor_bitlen	0x200

$kn_factorization (k = 3)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	['0x5', '0x7', '0x11', '0x53', '0x3fe1ccd43', '0xe656a39e9f1', '0x11bb3769d3f269b507d6458f946520cb1f2e09c78cc81c511848c08cc00237c5f7a573cc5e06fbcf9cb593f935bd33094c0036ca71']
(-)largest_factor_bitlen	0x1a5

$kn_factorization (k = 4)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 5)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	['0x3', '0xb11', '0x268e1c9d793cdffb2e3c6c50d864009a387275e4f37fecb8f1b14361900268e1a90a4e6696ec4056eda843f3a92d856443ab566baf861651fa4465e4093d71']
(-)largest_factor_bitlen	0x1f6

$kn_factorization (k = 6)$
(+)factorization	['0x47', '0x24df', '0x27da58da03f', '0x64e3fb6f5db915d', '0x990407cd135d686d30a7b9741c701446385611b1f799f40307be9334e65a7fc0b7e1b9ea4dac1f84b8da06d0bc407288ceb']
(+)largest_factor_bitlen	0x18c
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 7)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 8)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$torsion_extension (l = 2)$
least	0x1
full	0x2
relative	0x2

$torsion_extension (l = 3)$
least	0x8
full	0x8
relative	0x1

$torsion_extension (l = 5)$
least	0x18
full	0x18
relative	0x1

$torsion_extension (l = 7)$
least	0x18
full	0x18
relative	0x1

$torsion_extension (l = 11)$
least	0x28
full	0x28
relative	0x1

$torsion_extension (l = 13)$
least	0x1c
full	0x1c
relative	0x1

$torsion_extension (l = 17)$
least	0x8
full	0x10
relative	0x2

$conductor (d e g = 2)$
ratio_sqrt	0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14
factorization	['0x2', '0x2', '0x5c317', '0x256a87dbfb785d', '0x40a78bd3c312927729ade6e7bd3d1664b8303e831ade9f']

$conductor (d e g = 3)$
ratio_sqrt	0x46b38dfab27afc4176efcad0c415de6dceb1f5a80bba4df1fb088fba24b655fd947c13765b06fe4c02792fafe8cd4bb40c0a5c2cf0aae11e21f24d55a2d2cc37
factorization	NO DATA (timed out)

$conductor (d e g = 4)$
ratio_sqrt	0x115f34407435430cc0b29e10a92940926d533f2463e2494f55fb1fa5875b0a6013e8f5abbd143fa720e1b41e47010f5663dc310b7ae5e231a12da9eaac31b2a7262ea4532ee4f970d4090134fae2dd6501855fb603b498b6f1f9654c140c4ebd8
factorization	NO DATA (timed out)

$embedding ()$
embedding_degree_complement	None
complement_bit_length	None

$class_number ()$
upper	NO DATA (timed out)
lower	NO DATA (timed out)

$small_prime_order (l = 2)$
order	None
complement_bit_length	None

$small_prime_order (l = 3)$
order	None
complement_bit_length	None

$small_prime_order (l = 5)$
order	None
complement_bit_length	None

$small_prime_order (l = 7)$
order	None
complement_bit_length	None

$small_prime_order (l = 11)$
order	None
complement_bit_length	None

$small_prime_order (l = 13)$
order	None
complement_bit_length	None

$division_polynomials (l = 2)$
factorization	[['0x1', '0x1'], ['0x2', '0x1']]
len	0x2

$division_polynomials (l = 3)$
factorization	[['0x4', '0x1']]
len	0x1

$division_polynomials (l = 5)$
factorization	[['0xc', '0x1']]
len	0x1

$volcano (l = 2)$
crater_degree	0x0
depth	0x1

$volcano (l = 3)$
crater_degree	0x0
depth	0x0

$volcano (l = 5)$
crater_degree	0x0
depth	0x0

$volcano (l = 7)$
crater_degree	0x0
depth	0x0

$volcano (l = 11)$
crater_degree	0x0
depth	0x0

$volcano (l = 13)$
crater_degree	0x0
depth	0x0

$volcano (l = 17)$
crater_degree	0x2
depth	0x0

$volcano (l = 19)$
crater_degree	0x0
depth	0x0

$isogeny_extension (l = 2)$
least	0x1
full	0x2
relative	0x2

$isogeny_extension (l = 3)$
least	0x4
full	0x4
relative	0x1

$isogeny_extension (l = 5)$
least	0x6
full	0x6
relative	0x1

$isogeny_extension (l = 7)$
least	0x4
full	0x4
relative	0x1

$isogeny_extension (l = 11)$
least	0x4
full	0x4
relative	0x1

$isogeny_extension (l = 13)$
least	0x7
full	0x7
relative	0x1

$isogeny_extension (l = 17)$
least	0x1
full	0x10
relative	0x10

$isogeny_extension (l = 19)$
least	0x14
full	0x14
relative	0x1

$trace_factorization (d e g = 1)$
trace	0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14
trace_factorization	['0x2', '0x2', '0x5c317', '0x256a87dbfb785d', '0x40a78bd3c312927729ade6e7bd3d1664b8303e831ade9f']
number_of_factors	0x4

$trace_factorization (d e g = 2)$
trace	0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f6e14
trace_factorization	NO DATA (timed out)
number_of_factors	NO DATA (timed out)

$isogeny_neighbors (l = 2)$
len	0x1

$isogeny_neighbors (l = 3)$
len	0x0

$isogeny_neighbors (l = 5)$
len	0x0

$q_torsion ()$
Q_torsion	0x1

$hamming_x (w e i g h t = 1)$
x_coord_count	0x10b
expected	0x100
ratio	0.9588

$hamming_x (w e i g h t = 2)$
x_coord_count	0xff53
expected	0xff80
ratio	1.00069

$hamming_x (w e i g h t = 3)$
x_coord_count	0xa9a22e
expected	0xa9ab00
ratio	1.0002

$square_4p1 ()$
p	NO DATA (timed out)
order	0x1

$pow_distance ()$
distance	0xd9cc916e6be553fecf315802bae2bf4cdc49586162597b65ae770c42e03f704c
ratio	1.3610146068982212e+77
distance 32	0xc
distance 64	0xc

$multiples_x (k = 1)$
Hx	0xe2e31edfc23de7bdebe241ce593ef5de2295b7a9cbaef021d385f7074cea043aa27272a7ae602bf2a7b9033db9ed3610c6fb85487eae97aac5bc7928c1950148
bits	0x200
difference	0x0
ratio	1.00392

$multiples_x (k = 2)$
Hx	0x871aa434151a025d1ebc40692f847948deeeab7bef019df752f8218902314a910597d3d66e62415ae74ec5684df2354a92e19ae13833c5a7caddbe5d24741b7a
bits	0x200
difference	0x0
ratio	1.00392

$multiples_x (k = 3)$
Hx	0xb86f988f704e95f06480be926feb61ccac0953a24de8971cdb01f46d44a2a83ebfe0fe6e33585c31529f0b50e4102629905e5e9e792dfb14d28cafba809d5aa9
bits	0x200
difference	0x0
ratio	1.00392

$multiples_x (k = 4)$
Hx	0xbbd6805a6ea97e6e7172db913d414b47ee0ade7735db2eb683044a4ad81c129b23cee9b2c8b8c928d7e5330e2a56eb008d94efb859d11c074dc8c643f31a4866
bits	0x200
difference	0x0
ratio	1.00392

$multiples_x (k = 5)$
Hx	0x7215cd9ec101d99725813fd333f2e1121d73ca91ced61aa2fae8b727514dea7d6944a4a189d5a8fae5287a7728a157ed68b8691058241a0470acc2667b2e708a
bits	0x1ff
difference	0x1
ratio	1.00196

$multiples_x (k = 6)$
Hx	0x7f7ccda82fee97e7164efb676fafa418b54796fb864f8e5f17f20680b0ace788b01404d8a6149f5cc2216ec43586de2c07abc2b9bd900127f3ff3e197612942d
bits	0x1ff
difference	0x1
ratio	1.00196

$multiples_x (k = 7)$
Hx	0x36d1e509cfb515bc091444fc91ef3043e97e017c6ab40f89225cbc77596580462e5997aed6edb413cc9f1223c96c3a60ca1711dfec2eb95d8d3d1f87469493db
bits	0x1fe
difference	0x2
ratio	1.0

$multiples_x (k = 8)$
Hx	0x6175e4b3be5576d889f189d68460a34f7845f9a1937d7f62d8e921707c22ce49ca9c2a45cb462a6d20d4905623464d7a41d0dd72f95922c308978e7b0f5fb5d6
bits	0x1ff
difference	0x1
ratio	1.00196

$multiples_x (k = 9)$
Hx	0xd53def9a3910d3e07ac3ab7ce153d4d46762b3b9dfa89fecc79cdf25894f3e6a40a264a2b4b9f8b301610958e38cceb3689b67e414d5887d466b5723e5eb1d51
bits	0x200
difference	0x0
ratio	1.00392

$multiples_x (k = 10)$
Hx	0x976915361c4d03c3ad4ed63cd4e081b61276488b11bd6860de54c8ce523736f94b02239f169b5106a494ff4d9df8883e0d24c50764f2da7c8e917928cdf35faf
bits	0x200
difference	0x0
ratio	1.00392

$x962_invariant ()$
r	0x1a1f8d8c5ae0bbee1065c55bae8bcf43704214962d76af2447ca2fe9425c4674c48d3a75111a53ab8d831cb8d9bc8c2d87e9b6a53c83207443214838615665d2

$brainpool_overlap ()$
o	-0xa60c87c480d84fc3a97e230d884f8fa9e525c8d0cbc0d963900add4fe30c2e4b18f123d5c8637e5254778c78

$weierstrass ()$
a	0xdc9203e514a721875485a529d2c722fb187bc8980eb866644de41c68e143064546e861c0e2c9edd92ade71f46fcf50ff2ad97f951fda9f2a2eb6546f39689bd3
b	0xb4c4ee28cebc6c2c8ac12952cf37f16ac7efb6a9f69f4b57ffda2e4f0de5ade038cbc2fff719d2c18de0284b8bfef3b52b8cc7a5f5bf0a3c8d2319a5312557e1

Curve detail

Definition

Characteristics

Traits