DiSSECT

Name	secp128r2
Category	secg
Description	A randomly generated curve. [SEC2v1](https://www.secg.org/SEC2-Ver-1.0.pdf) states 'E was chosen verifiably at random as specified in ANSI X9.62 [1] from the seed'.
Field	Prime (0xfffffffdffffffffffffffffffffffff)
Field bits	128
Form	Weierstrass $y^{2} = x^{3} + a x + b$
Param $a$	0xd6031998d1b3bbfebf59cc9bbff9aee1
Param $b$	0x5eeefca380d02919dc2c6558bb6d8a5d
Generator $x$	0x7b6aa5d85e572983e6fb32a7cdebc140
Generator $y$	0x27b6916a894d3aee7106fe805fc34b44
Simulation seed	0x4d696e67687561517512d8f03431fce63b88f4

Order	0x3fffffff7fffffffbe0024720613b5a3
Cofactor	0x4
$j$ -invariant	0x92a06b59be064918b6fdd808c5363c53
Trace $t$	0x107ff6e37e7b12974
Embedding degree $k$	0x2e8ba2e85d1745d1445d31c74a3ce13
CM discriminant	-0xbbf04b2917c794a45cddd32f93b868db

$cofactor ()$
order	0x3fffffff7fffffffbe0024720613b5a3
cofactor	0x4

$discriminant ()$
cm_disc	-0xbbf04b2917c794a45cddd32f93b868db
factorization	['0x2', '0x2', '0x17', '0x2f', '0x2c81d87d4c70a03da895275b131db3']
max_conductor	0x2

$twist_order (d e g = 1)$
twist_cardinality	0xfffffffe0000000107ff6e37e7b12974
factorization	None

$twist_order (d e g = 2)$
twist_cardinality	0xfffffffc00000003fffffffffffffffd103ed35ba0e1ad6e8c88b341b11e5c94
factorization	None

$kn_factorization (k = 1)$
(+)factorization	['0x3', '0x65', '0x97', '0x26b', '0x425', '0x96b', '0x3e29e92cd491936c88319']
(+)largest_factor_bitlen	0x52
(-)factorization	['0x5', '0x7', '0x7', '0x119', '0x1c91e07', '0x3123826f3', '0x2c702b182c2c4b']
(-)largest_factor_bitlen	0x36

$kn_factorization (k = 2)$
(+)factorization	['0xd', '0x1541f6b', '0x6dda4f1f', '0x4514c98d4eae3f4529']
(+)largest_factor_bitlen	0x47
(-)factorization	['0x3', '0x3', '0x3', '0x3', '0x11', '0x35', '0xce3', '0x1ce65b', '0x13c0a5138a91e7b1b40eb']
(-)largest_factor_bitlen	0x51

$kn_factorization (k = 3)$
(+)factorization	['0x25', '0x59', '0x19c42f', '0x7e72716a5', '0x4b0f554dae63e09b']
(+)largest_factor_bitlen	0x3f
(-)factorization	['0xb', '0x17', '0x1d', '0x3b23', '0x740081dbeeb5777416a0eba919']
(-)largest_factor_bitlen	0x67

$kn_factorization (k = 4)$
(+)factorization	['0x3', '0x5', '0x1f', '0x71f8388d1bafd23', '0x4f24dbc71659fcab']
(+)largest_factor_bitlen	0x3f
(-)factorization	['0x13', '0x977', '0x1b717b', '0x351e0de82d8112311be3d9e9']
(-)largest_factor_bitlen	0x5e

$kn_factorization (k = 5)$
(+)factorization	['0x147e57249003', '0x3e757257aac3a2012e403f']
(+)largest_factor_bitlen	0x56
(-)factorization	['0x3', '0x862b1', '0x507f27b072995', '0xa1d0d8ff0eb6e95']
(-)largest_factor_bitlen	0x3c

$kn_factorization (k = 6)$
(+)factorization	['0x7', '0x151', '0x5cf7908c75b6793', '0x1cb0065f9b83dfe5']
(+)largest_factor_bitlen	0x3d
(-)factorization	['0x5', '0x133333330cccccccb9000aef01d2b67db']
(-)largest_factor_bitlen	0x81

$kn_factorization (k = 7)$
(+)factorization	['0x3', '0x3', '0xfb', '0x107', '0x1618f87cd0b67b', '0x8f208bedc58d523']
(+)largest_factor_bitlen	0x3c
(-)factorization	['0x3b', '0x2b13', '0x9a61', '0x6de13', '0x2b966f4fa725f3860d81']
(-)largest_factor_bitlen	0x4e

$kn_factorization (k = 8)$
(+)factorization	['0xb', '0xd3', '0xe1e38b13f6bc2acab2e77709e67651']
(+)largest_factor_bitlen	0x78
(-)factorization	['0x3', '0x7', '0x2e3', '0xb29', '0x6cc5ae3e3', '0x71fe31d476a450f493']
(-)largest_factor_bitlen	0x47

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

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

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

$torsion_extension (l = 7)$
least	0x6
full	0x6
relative	0x1

$torsion_extension (l = 11)$
least	0x78
full	0x78
relative	0x1

$torsion_extension (l = 13)$
least	0x3
full	0xc
relative	0x4

$torsion_extension (l = 17)$
least	0x30
full	0x30
relative	0x1

$conductor (d e g = 2)$
ratio_sqrt	0x107ff6e37e7b12974
factorization	['0x2', '0x2', '0x3', '0x15fff3d9fdf96e1f']

$conductor (d e g = 3)$
ratio_sqrt	0x103ed355a0e1ad6e8c88b341b11e5c91
factorization	['0x7', '0x11', '0x8354953', '0x50be5c23', '0xd7fd0473a47da0f']

$conductor (d e g = 4)$
ratio_sqrt	0xf73ead85d21d11c1856d248950edd591e960c5fa2278abd8
factorization	['0x2', '0x2', '0x2', '0x3', '0x13', '0x9d31', '0x15fff3d9fdf96e1f', '0xa467a09a4bad6308e0b6b9aa1dd']

$embedding ()$
embedding_degree_complement	0x16
complement_bit_length	0x5

$class_number ()$
upper	0x181d06a4c4cd3e6de9
lower	0x40

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

$small_prime_order (l = 3)$
order	0x3fffffff7fffffffbe0024720613b5a2
complement_bit_length	0x2

$small_prime_order (l = 5)$
order	0x1fffffffbfffffffdf0012390309dad1
complement_bit_length	0x3

$small_prime_order (l = 7)$
order	0x3fffffff7fffffffbe0024720613b5a2
complement_bit_length	0x2

$small_prime_order (l = 11)$
order	0x3fffffff7fffffffbe0024720613b5a2
complement_bit_length	0x2

$small_prime_order (l = 13)$
order	0x3fffffff7fffffffbe0024720613b5a2
complement_bit_length	0x2

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

$division_polynomials (l = 3)$
factorization	[['0x2', '0x2']]
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	0x2
depth	0x0

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

$volcano (l = 13)$
crater_degree	0x2
depth	0x0

$volcano (l = 17)$
crater_degree	0x0
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	0x2
full	0x2
relative	0x1

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

$isogeny_extension (l = 7)$
least	0x1
full	0x3
relative	0x3

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

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

$isogeny_extension (l = 17)$
least	0x3
full	0x3
relative	0x1

$isogeny_extension (l = 19)$
least	0x4
full	0x4
relative	0x1

$trace_factorization (d e g = 1)$
trace	0x107ff6e37e7b12974
trace_factorization	['0x2', '0x2', '0x3', '0x15fff3d9fdf96e1f']
number_of_factors	0x3

$trace_factorization (d e g = 2)$
trace	0x107ff6e37e7b12974
trace_factorization	['0x2', '0x13', '0x9d31', '0xa467a09a4bad6308e0b6b9aa1dd']
number_of_factors	0x4

$isogeny_neighbors (l = 2)$
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	0x41
expected	0x40
ratio	0.98462

$hamming_x (w e i g h t = 2)$
x_coord_count	0xf74
expected	0xfe0
ratio	1.0273

$hamming_x (w e i g h t = 3)$
x_coord_count	0x2992c
expected	0x29ac0
ratio	1.00237

$square_4p1 ()$
p	0x1
order	0x7

$pow_distance ()$
distance	0x20000000107ff6e37e7b12974
ratio	2147483646.74219
distance 32	0xc
distance 64	0xc

$multiples_x (k = 1)$
Hx	0x7b6aa5d85e572983e6fb32a7cdebc140
bits	0x7f
difference	0x1
ratio	1.00794

$multiples_x (k = 2)$
Hx	0xf69ff511dbd13171f8d75488000fbca2
bits	0x80
difference	0x0
ratio	1.01587

$multiples_x (k = 3)$
Hx	0x54321ece622a59689ae8a38844655ebd
bits	0x7f
difference	0x1
ratio	1.00794

$multiples_x (k = 4)$
Hx	0x161ff7528b899b2d0c28607ca52c5b86
bits	0x7d
difference	0x3
ratio	0.99206

$multiples_x (k = 5)$
Hx	0x7f8a99721379f16d21efa0004302e7a
bits	0x7b
difference	0x5
ratio	0.97619

$multiples_x (k = 6)$
Hx	0x95a708d73ce03fd53ea8161b53e211af
bits	0x80
difference	0x0
ratio	1.01587

$multiples_x (k = 7)$
Hx	0x15a8efa245d73c333474af00f24ececb
bits	0x7d
difference	0x3
ratio	0.99206

$multiples_x (k = 8)$
Hx	0x4a622baa13e39176f9cad031b249a725
bits	0x7f
difference	0x1
ratio	1.00794

$multiples_x (k = 9)$
Hx	0xd69d80396264fd174a92e872cc9e4ba0
bits	0x80
difference	0x0
ratio	1.01587

$multiples_x (k = 10)$
Hx	0xf08568a9d55bdc725287f5da65b138c0
bits	0x80
difference	0x0
ratio	1.01587

$x962_invariant ()$
r	0x1def19fd392155bb3f430f1ad91327d8

$brainpool_overlap ()$
o	None

$weierstrass ()$
a	0xd6031998d1b3bbfebf59cc9bbff9aee1
b	0x5eeefca380d02919dc2c6558bb6d8a5d

Curve detail

Definition

Characteristics

Traits