DiSSECT

Name	ed-512-mont
Category	nums
Description	Original nums curve from https://eprint.iacr.org/2014/130.pdf
Field	Prime (0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff)
Field bits	512
Form	Twisted Edwards $a x^{2} + y^{2} = 1 + d x^{2} y^{2}$
Param $a$	0xfe14fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
Param $d$	0x12a9c

Order	0x3f853fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcccfd59cdc33470d103060513f6def4d37d9af21b2b2701fa331487ecb8db605
Cofactor	0x4
$j$ -invariant	0xcda9233a5135668daa95aecf615d3de755bef0f5e9be3c3c630af4a986c701d0f7e96570e595d6d5f14f57c807143c6f196221dc3c9b7ebdce5f445445871263
Trace $t$	0xccc0a98c8f32e3cbbf3e7ebb024842cb2099437935363f81733ade04d1c927ec

$cofactor ()$
order	0x3f853fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcccfd59cdc33470d103060513f6def4d37d9af21b2b2701fa331487ecb8db605
cofactor	0x4

$discriminant ()$
cm_disc	None
factorization	None
max_conductor	None

$twist_order (d e g = 1)$
twist_cardinality	0xfe15000000000000000000000000000000000000000000000000000000000000ccc0a98c8f32e3cbbf3e7ebb024842cb2099437935363f81733ade04d1c927ec
factorization	None

$twist_order (d e g = 2)$
twist_cardinality	0xfc2dadb8fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcab6f9f36c75ac9a08af085ad39c599b5f232fa7bdee1c82596e59fcf57b03e0af5816923d94bc218107020b75a8068024a83219aad2688cc3a60a09f0ed1c194
factorization	None

$kn_factorization (k = 1)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 2)$
(+)factorization	['0x5', '0x35', '0x1eae7d95bc609a90e7d95bc609a90e7d95bc609a90e7d95bc609a90e7d95bc6081d758b03bfdb80e09c06c597a69444058cd9d0b725441c010ffa75d1fa9e21']
(+)largest_factor_bitlen	0x1f9
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 3)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 4)$
(+)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	['0x683', '0xcebfe11e9d', '0xf192073a78e7cb16bea73a884df8e08aeeba2598539caed042e327ecb017344172753c61df6e0b2bb88502afcf1db0206969fd7a01f1ecfc2fa3']
(+)largest_factor_bitlen	0x1d0
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 6)$
(+)factorization	['0x7', '0xd9c8db6db6db6db6db6db6db6db6db6db6db6db6db6db6db6db6db6db6db6db62bed25878542182cc9ca6ecd6bc20fe42d337d05d263c9910af21d2070c14b7f']
(+)largest_factor_bitlen	0x200
(-)factorization	NO DATA (timed out)
(-)largest_factor_bitlen	NO DATA (timed out)

$kn_factorization (k = 7)$
(+)factorization	['0x3', '0x5', '0x5', '0x5', '0xd0db4ae9022d', '0x5d03cf613c4ac819f44f76f19da965060596ba8b7b20388329e09ecdaf5f10c4660b48062b84b7ff5abf350e748ac43830f5a8835c963c4a367']
(+)largest_factor_bitlen	0x1cb
(-)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	0x4
full	0x4
relative	0x1

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

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

$torsion_extension (l = 11)$
least	0x5
full	0xa
relative	0x2

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

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

$conductor (d e g = 2)$
ratio_sqrt	0xccc0a98c8f32e3cbbf3e7ebb024842cb2099437935363f81733ade04d1c927ec
factorization	['0x2', '0x2', '0x3', '0xb', '0x126a7', '0x159014d509844af1bde66e11381bebca7a143d1dbddd73d43bb703ba2ed']

$conductor (d e g = 3)$
ratio_sqrt	0x5a5160c938a5365f750f7a52c63a664a0dcd0584211e37da691a6030a84fc1f50a7e96dc26b43de7ef8fdf48a57f97fdb57cde6552d97733c59f5f60f12e3e6f
factorization	NO DATA (timed out)

$conductor (d e g = 4)$
ratio_sqrt	0x11374c6019e958e311459dd7ed700c023e790b8328d53b196ea35b03920935995e1e4b50afb121f6d3df75fea0ebeec6535c9e705caaeadcab009b4b62a0e4497e6d9472c1075c9d563ad9a4073f6bd15f68fd61aac008e72ec402e1b34824f68
factorization	NO DATA (timed out)

$embedding ()$
embedding_degree_complement	0x4
complement_bit_length	0x3

$class_number ()$
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	[['0x2', '0x2']]
len	0x1

$division_polynomials (l = 5)$
factorization	[['0x6', '0x2']]
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	0x2
depth	0x0

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

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

$volcano (l = 19)$
crater_degree	0x2
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	0x3
full	0x3
relative	0x1

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

$isogeny_extension (l = 11)$
least	0x1
full	0x2
relative	0x2

$isogeny_extension (l = 13)$
least	0x1
full	0x3
relative	0x3

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

$isogeny_extension (l = 19)$
least	0x1
full	0x6
relative	0x6

$trace_factorization (d e g = 1)$
trace	0xccc0a98c8f32e3cbbf3e7ebb024842cb2099437935363f81733ade04d1c927ec
trace_factorization	['0x2', '0x2', '0x3', '0xb', '0x126a7', '0x159014d509844af1bde66e11381bebca7a143d1dbddd73d43bb703ba2ed']
number_of_factors	0x5

$trace_factorization (d e g = 2)$
trace	0xccc0a98c8f32e3cbbf3e7ebb024842cb2099437935363f81733ade04d1c927ec
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	0x115
expected	0x100
ratio	0.92419

$hamming_x (w e i g h t = 2)$
x_coord_count	0x1009a
expected	0xff80
ratio	0.99571

$hamming_x (w e i g h t = 3)$
x_coord_count	0xa9b5d8
expected	0xa9ab00
ratio	0.99975

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

$pow_distance ()$
distance	0x1eb000000000000000000000000000000000000000000000000000000000000ccc0a98c8f32e3cbbf3e7ebb024842cb2099437935363f81733ade04d1c927ec
ratio	132.47454
distance 32	0xc
distance 64	0x14

$multiples_x (k = 1)$
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	0xdae4a1b74d6d4a0d2a1eced9efd278598ea89efec8ec27a4a282badcaad87cd86bd2a8e80e1fe97acc34c8de463d17be35c60dbbbe2aa2255f94763d74eee28e

$brainpool_overlap ()$
o	-0x10c5f9556cfa235d979056eec06293a5f484c46db6d3a0d4566aab69d87bd1c20609044e8b38d8befa9c3408

$weierstrass ()$
a	0x633346b019e85111b1fcea3b7f96b114e027b70e8ebcd0e7bfd5937be4724240191c0292730a9e7858d4fafb45522d522c497949f919898ad1234a49e0a925c1
b	0x1f82ca3d2ccfb6d97c02992ed97e9638678f62e60fa89bcf9bbcd8bc04c54b0bff228dd95c5c2308db4559c98540873e39890c872985408148643f9348129a22

Curve detail

Definition

Characteristics

Traits