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P-224

224-bit prime field Weierstrass curve.
Also known as: secp224r1wap-wsg-idm-ecid-wtls12ansip224r1
y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0xffffffffffffffffffffffffffffffff000000000000000000000001
a0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
b0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
G(0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34)
n0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
h0x1

Characteristics

  • OID:
    1.3.132.0.33
  • Seed:
    BD71344799D5C7FCDC45B59FA3B9AB8F6A948BC5
  • j-invariant:
    20781977079628996477063007379734849057519732242287194936686605794677
  • Trace of Frobenius:
    4733100108545601916421827343930821
  • Discriminant:
    8133954887115844930654026312464158747844254983800706208418026371607
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    8986648889050213264889005029006541980152602571474797240560907456020
  • CM-discriminant:
    107839786668602559178668060348078517961131556494503316152212921264703
  • Conductor:
    1

SAGE

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe)
b = K(0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4)
E = EllipticCurve(K, (a, b))
G = E(0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34)
E.set_order(0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d * 0x1)

PARI/GP

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe, p)
b = Mod(0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d * 0x1
G = [Mod(0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, p), Mod(0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34, p)]

JSON

{
"name": "P-224",
"desc": "",
"oid": "1.3.132.0.33",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xffffffffffffffffffffffffffffffff000000000000000000000001",
"bits": 224
},
"params": {
"a": {
"raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe"
},
"b": {
"raw": "0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4"
}
},
"generator": {
"x": {
"raw": "0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21"
},
"y": {
"raw": "0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"
}
},
"order": "0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d",
"cofactor": "0x1",
"aliases": [
"secg/secp224r1",
"wtls/wap-wsg-idm-ecid-wtls12",
"x963/ansip224r1"
],
"characteristics": {
"seed": "BD71344799D5C7FCDC45B59FA3B9AB8F6A948BC5",
"j_invariant": "20781977079628996477063007379734849057519732242287194936686605794677",
"anomalous": false,
"cm_disc": "107839786668602559178668060348078517961131556494503316152212921264703",
"conductor": "1",
"discriminant": "8133954887115844930654026312464158747844254983800706208418026371607",
"embedding_degree": "8986648889050213264889005029006541980152602571474797240560907456020",
"torsion_degrees": [
{
"full": 3,
"least": 3,
"r": 2
},
{
"full": 2,
"least": 2,
"r": 3
},
{
"full": 6,
"least": 6,
"r": 5
}
],
"supersingular": false,
"trace_of_frobenius": "4733100108545601916421827343930821"
}
}

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