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prime192v2

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

Parameters

NameValue
p0xfffffffffffffffffffffffffffffffeffffffffffffffff
a0xfffffffffffffffffffffffffffffffefffffffffffffffc
b0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953
G(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, 0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15)
n0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31
h0x1

Characteristics

  • OID:
    1.2.840.10045.3.1.2
  • Seed:
    31A92EE2029FD10D901B113E990710F0D21AC6B6
  • j-invariant:
    2188073006583539552141688552564683396860111048461359479401
  • Trace of Frobenius:
    128840479891808162805939905231
  • Discriminant:
    3136318742261921876063208570368096687049382158828912127687
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    1569275433846670190958947355769706484048025134396096264012
  • CM-discriminant:
    25108406941546723055343157692701825184443826638755359939885
  • Conductor:
    1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffc)
b = K(0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953)
E = EllipticCurve(K, (a, b))
G = E(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, 0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15)
E.set_order(0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffc, p)
b = Mod(0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31 * 0x1
G = [Mod(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, p), Mod(0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15, p)]

JSON

{
"name": "prime192v2",
"desc": "",
"oid": "1.2.840.10045.3.1.2",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
"bits": 192
},
"params": {
"a": {
"raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
},
"b": {
"raw": "0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953"
}
},
"generator": {
"x": {
"raw": "0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a"
},
"y": {
"raw": "0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15"
}
},
"order": "0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31",
"cofactor": "0x1",
"characteristics": {
"seed": "31A92EE2029FD10D901B113E990710F0D21AC6B6",
"j_invariant": "2188073006583539552141688552564683396860111048461359479401",
"anomalous": false,
"cm_disc": "25108406941546723055343157692701825184443826638755359939885",
"conductor": "1",
"discriminant": "3136318742261921876063208570368096687049382158828912127687",
"embedding_degree": "1569275433846670190958947355769706484048025134396096264012",
"torsion_degrees": [
{
"full": 3,
"least": 3,
"r": 2
},
{
"full": 8,
"least": 8,
"r": 3
},
{
"full": 20,
"least": 4,
"r": 5
},
{
"full": 6,
"least": 2,
"r": 7
}
],
"supersingular": false,
"trace_of_frobenius": "128840479891808162805939905231"
}
}

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