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brainpoolP384r1

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

Parameters

NameValue
p0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53
a0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826
b0x4a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11
G(0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e, 0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315)
n0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565
h0x1

Characteristics

  • OID:
    1.3.36.3.3.2.8.1.1.11
  • j-invariant:
    3238708593163173875725998049354875763971987662971288152397580059844841553716806725943092933139820860272505955713980
  • Trace of Frobenius:
    5973228999478432667446284273866865475630836211106699249391
  • Discriminant:
    15706321267409195131547714311286280972817133485416071074801987083215365961472833785802507452304377823439072770708055
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    5414817692529829043267309210583151244949029096754412150018911318705402875339628884490673779342225813057400429680985

SAGE

p = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53
K = GF(p)
a = K(0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826)
b = K(0x4a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11)
E = EllipticCurve(K, (a, b))
G = E(0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e, 0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315)
E.set_order(0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565 * 0x1)

PARI/GP

p = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53
a = Mod(0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826, p)
b = Mod(0x4a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11, p)
E = ellinit([a, b])
E[16][1] = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565 * 0x1
G = [Mod(0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e, p), Mod(0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315, p)]

JSON

{
"name": "brainpoolP384r1",
"desc": "",
"oid": "1.3.36.3.3.2.8.1.1.11",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53",
"bits": 384
},
"params": {
"a": {
"raw": "0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826"
},
"b": {
"raw": "0x4a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11"
}
},
"generator": {
"x": {
"raw": "0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e"
},
"y": {
"raw": "0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315"
}
},
"order": "0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565",
"cofactor": "0x1",
"characteristics": {
"j_invariant": "3238708593163173875725998049354875763971987662971288152397580059844841553716806725943092933139820860272505955713980",
"anomalous": false,
"discriminant": "15706321267409195131547714311286280972817133485416071074801987083215365961472833785802507452304377823439072770708055",
"embedding_degree": "5414817692529829043267309210583151244949029096754412150018911318705402875339628884490673779342225813057400429680985",
"supersingular": false,
"trace_of_frobenius": "5973228999478432667446284273866865475630836211106699249391"
}
}

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