Parameters

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"
  }
}