DiSSECT

Name	B-233 (nist/B-233, secg/sect233r1, x962/ansit233r1)
Category	nist
Field	Binary
Field polynomial	$x^{233} + x^{74} + 1$
Field bits	233
Form	Weierstrass $y^{2} = x^{3} + a x + b$
Param $a$	0x000000000000000000000000000000000000000000000000000000000001
Param $b$	0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
Generator $x$	0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
Generator $y$	0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
Simulation seed	0x74d59ff07f6b413d0ea14b344b20a2db049b50c3

Order	0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
Cofactor	0x2
Trace $t$	-0x27d2e9ce5f14d244063a4c079fc1ad

$cofactor ()$
order	0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
cofactor	0x2

$discriminant ()$
cm_disc	-0x1ce0efeb2ea5a553eed56a0c8a4bca205c5305973c2190c7cfe6293b117
factorization	['0x7', '0x25f', '0x33ab00b639', '0xa488689bf7', '0xd69cf03f370ed4df158db869b94af7fca6d1']
max_conductor	0x1

$twist_order (d e g = 1)$
twist_cardinality	0x1ffffffffffffffffffffffffffffd82d1631a0eb2dbbf9c5b3f8603e54
factorization	None

$twist_order (d e g = 2)$
twist_cardinality	0x4000000000000000000000000000000000000000000000000000000000231f1014d15a5aac112a95f375b435dfa3acfa68c3de6f383019d6c4eea
factorization	None

$kn_factorization (k = 1)$
(+)factorization	['0x29', '0x47', '0x2d06c584b475239ddb3d78bea8ac616cb0652a923b78ec3ba6a73bb1']
(+)largest_factor_bitlen	0xde
(-)factorization	['0x3', '0x5', '0x5', '0x4f', '0x89', '0x15d', '0x841', '0x3ac7353f7f894a34875f936ab343ba06a56fb5b999ab54b95']
(-)largest_factor_bitlen	0xc2

$kn_factorization (k = 2)$
(+)factorization	['0x3', '0x3', '0xb', '0x9ad', '0x128e01a4d', '0xebfc2a56a87fbafd3ec380f075d94c0fb56b001b0d1c07']
(+)largest_factor_bitlen	0xb8
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 3)$
(+)factorization	['0x7', '0x13', '0x17', '0x1d', '0x6d', '0x17c66c595a89a4a71', '0x70183c297838b71668240b5b573f4846b1941']
(+)largest_factor_bitlen	0x93
(-)factorization	['0x1faf', '0x8992188383f', '0x5a369e83852a1fff282c8032462010241feab4be03979']
(-)largest_factor_bitlen	0xb3

$kn_factorization (k = 4)$
(+)factorization	['0x5', '0x2bcd8e198dc9', '0x141c9dc5409cc7', '0x7706f29e5cf3d5cd44a638bcec4116f99b']
(+)largest_factor_bitlen	0x87
(-)factorization	['0x3', '0x7', '0x7', '0x1b1', '0x268703', '0x36bb30baec1388c6bcffb2362d18741189a72e23af3fbd749f']
(-)largest_factor_bitlen	0xc6

$kn_factorization (k = 5)$
(+)factorization	['0x3', '0x43', '0x21ccf4218d2015155', '0x47413e4085f1f45565', '0x15a90b15fb846b44f3ce9777']
(+)largest_factor_bitlen	0x5d
(-)factorization	['0x1f', '0x125ea3ae9', '0x1295212501b71', '0x3dee760aa8678137142c6f74217c1940afc0f3']
(-)largest_factor_bitlen	0x96

$kn_factorization (k = 6)$
(+)factorization	['0xc0000000000000000000000000000eef17ad63a7ced98255dc82dbe8a15']
(+)largest_factor_bitlen	0xec
(-)factorization	['0x5', '0xd', '0x1522061eff', '0x23c846c975b8444d1f425c3c9c628f51fc87aad1f9d94bdad']
(-)largest_factor_bitlen	0xc2

$kn_factorization (k = 7)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	['0x3', '0x3', '0x3', '0x11', '0x295', '0xf596a7', '0x326fc4c1330e3a90c2c6b7ab223b260e6639013570596ee51']
(-)largest_factor_bitlen	0xc2

$kn_factorization (k = 8)$
(+)factorization	['0x3', '0x1954681b7', '0x35e70639f41e4b9acb1048a1411b6bb4934f83f9e5795b6435d']
(+)largest_factor_bitlen	0xca
(-)factorization	['0x23c1bf', '0x2d97d201', '0x7b68f1365b', '0x33eae5bdc3132f9637', '0x19b2f82e308a550e66d5']
(-)largest_factor_bitlen	0x4d

$torsion_extension (l = 2)$
least	None
full	None
relative	None

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

$torsion_extension (l = 5)$
least	0x2
full	0x4
relative	0x2

$torsion_extension (l = 7)$
least	0x6
full	0x7
relative	0x1

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

$torsion_extension (l = 13)$
least	0xa8
full	0xa8
relative	0x1

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

$conductor (d e g = 2)$
ratio_sqrt	0x27d2e9ce5f14d244063a4c079fc1ad
factorization	['0x13a41', '0x21523', '0x2fd9f9f1', '0x5356d07c67dd1f']

$conductor (d e g = 3)$
ratio_sqrt	0x431f1014d15a5aac112a95f375b435dfa3acfa68c3de6f383019d6c4ee9
factorization	['0x1f', '0x67', '0x6493f', '0x1a2f969', '0x4e4770526bb9ef', '0x1b5ee72faa6035be44929fcfca4510f9']

$conductor (d e g = 4)$
ratio_sqrt	0x576ab01f2a5c578169c19adbbbfab4ab8d19924e46a189fe04786b0c0c72d6284a58318d1520b35f6b65fc75
factorization	['0x3', '0x5', '0xb', '0x11', '0x17', '0x13a41', '0x21523', '0x2fd9f9f1', '0x113a47f519', '0x5356d07c67dd1f', '0xa91b8c273890688473f', '0x32290e7ca88a80f30da5815a225']

$embedding ()$
embedding_degree_complement	0x2
complement_bit_length	0x2

$class_number ()$
upper	0x45057c97fa2b6c87d7f2484225adab9
lower	0x40e919

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

$small_prime_order (l = 3)$
order	0x800000000000000000000000000009f4ba7397c53491018e9301e7f06b
complement_bit_length	0x2

$small_prime_order (l = 5)$
order	0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d6
complement_bit_length	0x1

$small_prime_order (l = 7)$
order	0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d6
complement_bit_length	0x1

$small_prime_order (l = 11)$
order	0x800000000000000000000000000009f4ba7397c53491018e9301e7f06b
complement_bit_length	0x2

$small_prime_order (l = 13)$
order	0x800000000000000000000000000009f4ba7397c53491018e9301e7f06b
complement_bit_length	0x2

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

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

$division_polynomials (l = 5)$
factorization	[['0x1', '0x2'], ['0x2', '0x1'], ['0x4', '0x2']]
len	0x3

$volcano (l = 2)$
crater_degree	0x2
depth	0x0

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

$volcano (l = 5)$
crater_degree	0x2
depth	0x0

$volcano (l = 7)$
crater_degree	0x1
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	0x2
depth	0x0

$isogeny_extension (l = 2)$
least	None
full	None
relative	None

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

$isogeny_extension (l = 5)$
least	0x1
full	0x4
relative	0x4

$isogeny_extension (l = 7)$
least	0x1
full	0x7
relative	0x7

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

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

$isogeny_extension (l = 17)$
least	0x1
full	0x4
relative	0x4

$isogeny_extension (l = 19)$
least	0x1
full	0x12
relative	0x12

$trace_factorization (d e g = 1)$
trace	-0x27d2e9ce5f14d244063a4c079fc1ad
trace_factorization	['0x13a41', '0x21523', '0x2fd9f9f1', '0x5356d07c67dd1f']
number_of_factors	0x4

$trace_factorization (d e g = 2)$
trace	-0x27d2e9ce5f14d244063a4c079fc1ad
trace_factorization	['0x3', '0x5', '0xb', '0x11', '0x17', '0x113a47f519', '0xa91b8c273890688473f', '0x32290e7ca88a80f30da5815a225']
number_of_factors	0x8

$isogeny_neighbors (l = 2)$
len	0x3

$isogeny_neighbors (l = 3)$
len	0x0

$isogeny_neighbors (l = 5)$
len	0x2

$q_torsion ()$
Q_torsion	0x1

$hamming_x (w e i g h t = 1)$
x_coord_count	0xe9
expected	0x75
ratio	0.50215

$hamming_x (w e i g h t = 2)$
x_coord_count	0x6994
expected	0x353e
ratio	0.50429

$hamming_x (w e i g h t = 3)$
x_coord_count	0x1fc184
expected	0x10158c
ratio	0.50649

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

$pow_distance ()$
distance	0x27d2e9ce5f14d244063a4c079fc1ae
ratio	6.675532331333225e+34
distance 32	0xe
distance 64	0x12

$multiples_x (k = 1)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 2)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 3)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 4)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 5)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 6)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 7)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 8)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 9)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 10)$
Hx	None
bits	None
difference	None
ratio	None

$x962_invariant ()$
r	0x0

$brainpool_overlap ()$
o	None

$weierstrass ()$
a	None
b	None

Curve detail

Definition

Characteristics

Traits