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prime192v1

192-bit prime field Weierstrass curve.
Also known as: secp192r1P-192
y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0xfffffffffffffffffffffffffffffffeffffffffffffffff
a0xfffffffffffffffffffffffffffffffefffffffffffffffc
b0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
G(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811)
n0xffffffffffffffffffffffff99def836146bc9b1b4d22831
h0x1

Characteristics

  • OID:
    1.2.840.10045.3.1.1
  • Seed:
    3045AE6FC8422F64ED579528D38120EAE12196D5
  • j-invariant:
    6234286251230310114240839169629130138801351179850969208331
  • Trace of Frobenius:
    31607402316713927207482677199
  • Discriminant:
    5525402385154848923235289274741921730185152131202286251655
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    627710173538668076383578942317605901376719477318284228408
  • CM-discriminant:
    25108406941546723055343157692799058262018920874353817167917
  • Conductor:
    1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffc)
b = K(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1)
E = EllipticCurve(K, (a, b))
G = E(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811)
E.set_order(0xffffffffffffffffffffffff99def836146bc9b1b4d22831 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffc, p)
b = Mod(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 * 0x1
G = [Mod(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, p), Mod(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p)]

JSON

{
"name": "prime192v1",
"desc": "",
"oid": "1.2.840.10045.3.1.1",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
"bits": 192
},
"params": {
"a": {
"raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
},
"b": {
"raw": "0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1"
}
},
"generator": {
"x": {
"raw": "0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012"
},
"y": {
"raw": "0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"
}
},
"order": "0xffffffffffffffffffffffff99def836146bc9b1b4d22831",
"cofactor": "0x1",
"aliases": [
"secg/secp192r1",
"nist/P-192"
],
"characteristics": {
"seed": "3045AE6FC8422F64ED579528D38120EAE12196D5",
"j_invariant": "6234286251230310114240839169629130138801351179850969208331",
"anomalous": false,
"cm_disc": "25108406941546723055343157692799058262018920874353817167917",
"conductor": "1",
"discriminant": "5525402385154848923235289274741921730185152131202286251655",
"embedding_degree": "627710173538668076383578942317605901376719477318284228408",
"torsion_degrees": [
{
"full": 3,
"least": 3,
"r": 2
},
{
"full": 8,
"least": 8,
"r": 3
},
{
"full": 20,
"least": 4,
"r": 5
},
{
"full": 48,
"least": 48,
"r": 7
},
{
"full": 55,
"least": 5,
"r": 11
},
{
"full": 12,
"least": 4,
"r": 13
}
],
"supersingular": false,
"trace_of_frobenius": "31607402316713927207482677199"
}
}

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