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brainpoolP320r1

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

Parameters

NameValue
p0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
a0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4
b0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6
G(0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611, 0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1)
n0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311
h0x1

Characteristics

  • OID:
    1.3.36.3.3.2.8.1.1.9
  • j-invariant:
    358066247632993218655312856437643774447933684237000889712532007541779113891565375554334303101086
  • Trace of Frobenius:
    1829129012274291271856083956306349739816241699607
  • Discriminant:
    1358401829173490165066196853884775272351426867124642504866990308858277224964072636606742251556422
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    1763593322239166354161909842446019520889512772717686063760686124016784784845843468355685258203920
  • CM-discriminant:
    7054373288956665416647639369784078083558051090876231642079567369882707391252292922642189757914501
  • Conductor:
    1

SAGE

p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
K = GF(p)
a = K(0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4)
b = K(0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6)
E = EllipticCurve(K, (a, b))
G = E(0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611, 0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1)
E.set_order(0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311 * 0x1)

PARI/GP

p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
a = Mod(0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4, p)
b = Mod(0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6, p)
E = ellinit([a, b])
E[16][1] = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311 * 0x1
G = [Mod(0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611, p), Mod(0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1, p)]

JSON

{
"name": "brainpoolP320r1",
"desc": "",
"oid": "1.3.36.3.3.2.8.1.1.9",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27",
"bits": 320
},
"params": {
"a": {
"raw": "0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4"
},
"b": {
"raw": "0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6"
}
},
"generator": {
"x": {
"raw": "0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611"
},
"y": {
"raw": "0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1"
}
},
"order": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311",
"cofactor": "0x1",
"characteristics": {
"j_invariant": "358066247632993218655312856437643774447933684237000889712532007541779113891565375554334303101086",
"anomalous": false,
"cm_disc": "7054373288956665416647639369784078083558051090876231642079567369882707391252292922642189757914501",
"conductor": "1",
"discriminant": "1358401829173490165066196853884775272351426867124642504866990308858277224964072636606742251556422",
"embedding_degree": "1763593322239166354161909842446019520889512772717686063760686124016784784845843468355685258203920",
"torsion_degrees": [
{
"full": 3,
"least": 3,
"r": 2
},
{
"full": 8,
"least": 8,
"r": 3
},
{
"full": 4,
"least": 2,
"r": 5
}
],
"supersingular": false,
"trace_of_frobenius": "1829129012274291271856083956306349739816241699607"
}
}
JSON

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