Skip to main content

Standard curve database

Search

brainpoolP160t1

160-bit prime field Weierstrass curve.
y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0xe95e4a5f737059dc60dfc7ad95b3d8139515620f
a0xe95e4a5f737059dc60dfc7ad95b3d8139515620c
b0x7a556b6dae535b7b51ed2c4d7daa7a0b5c55f380
G(0xb199b13b9b34efc1397e64baeb05acc265ff2378, 0xadd6718b7c7c1961f0991b842443772152c9e0ad)
n0xe95e4a5f737059dc60df5991d45029409e60fc09
h0x1

Characteristics

  • OID:
    1.3.36.3.3.2.8.1.1.2
  • j-invariant:
    387367055434500543477184371239969891945180101787
  • Trace of Frobenius:
    519972310379544251229703
  • Discriminant:
    101000112507510591754853229447574388964119053944
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    444099199480014958275695012943393788070980856152
  • CM-discriminant:
    592132265973353277700926857248628510609391551437
  • Conductor:
    3

SAGE

p = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f
K = GF(p)
a = K(0xe95e4a5f737059dc60dfc7ad95b3d8139515620c)
b = K(0x7a556b6dae535b7b51ed2c4d7daa7a0b5c55f380)
E = EllipticCurve(K, (a, b))
G = E(0xb199b13b9b34efc1397e64baeb05acc265ff2378, 0xadd6718b7c7c1961f0991b842443772152c9e0ad)
E.set_order(0xe95e4a5f737059dc60df5991d45029409e60fc09 * 0x1)

PARI/GP

p = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f
a = Mod(0xe95e4a5f737059dc60dfc7ad95b3d8139515620c, p)
b = Mod(0x7a556b6dae535b7b51ed2c4d7daa7a0b5c55f380, p)
E = ellinit([a, b])
E[16][1] = 0xe95e4a5f737059dc60df5991d45029409e60fc09 * 0x1
G = [Mod(0xb199b13b9b34efc1397e64baeb05acc265ff2378, p), Mod(0xadd6718b7c7c1961f0991b842443772152c9e0ad, p)]

JSON

{
"name": "brainpoolP160t1",
"desc": "",
"oid": "1.3.36.3.3.2.8.1.1.2",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xe95e4a5f737059dc60dfc7ad95b3d8139515620f",
"bits": 160
},
"params": {
"a": {
"raw": "0xe95e4a5f737059dc60dfc7ad95b3d8139515620c"
},
"b": {
"raw": "0x7a556b6dae535b7b51ed2c4d7daa7a0b5c55f380"
}
},
"generator": {
"x": {
"raw": "0xb199b13b9b34efc1397e64baeb05acc265ff2378"
},
"y": {
"raw": "0xadd6718b7c7c1961f0991b842443772152c9e0ad"
}
},
"order": "0xe95e4a5f737059dc60df5991d45029409e60fc09",
"cofactor": "0x1",
"characteristics": {
"j_invariant": "387367055434500543477184371239969891945180101787",
"anomalous": false,
"cm_disc": "592132265973353277700926857248628510609391551437",
"conductor": "3",
"discriminant": "101000112507510591754853229447574388964119053944",
"embedding_degree": "444099199480014958275695012943393788070980856152",
"torsion_degrees": [
{
"full": 3,
"least": 3,
"r": 2
},
{
"full": 6,
"least": 2,
"r": 3
},
{
"full": 12,
"least": 12,
"r": 5
},
{
"full": 8,
"least": 8,
"r": 7
},
{
"full": 55,
"least": 5,
"r": 11
}
],
"supersingular": false,
"trace_of_frobenius": "519972310379544251229703"
}
}

© 2020 Jan Jancar | Built with Dox theme for Gatsby