Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.12
• j-invariant:
  3238708593163173875725998049354875763971987662971288152397580059844841553716806725943092933139820860272505955713980
• Trace of Frobenius:
  5973228999478432667446284273866865475630836211106699249391
• Discriminant:
  3737679651751396944816679318673518402321361287567315288737952401285446129378198042881937137830060298805293841235164
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  5414817692529829043267309210583151244949029096754412150018911318705402875339628884490673779342225813057400429680985

SAGE

p = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53
K = GF(p)
a = K(0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec50)
b = K(0x7f519eada7bda81bd826dba647910f8c4b9346ed8ccdc64e4b1abd11756dce1d2074aa263b88805ced70355a33b471ee)
E = EllipticCurve(K, (a, b))
G = E(0x18de98b02db9a306f2afcd7235f72a819b80ab12ebd653172476fecd462aabffc4ff191b946a5f54d8d0aa2f418808cc, 0x25ab056962d30651a114afd2755ad336747f93475b7a1fca3b88f2b6a208ccfe469408584dc2b2912675bf5b9e582928)
E.set_order(0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565 * 0x1)

PARI/GP

p = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53
a = Mod(0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec50, p)
b = Mod(0x7f519eada7bda81bd826dba647910f8c4b9346ed8ccdc64e4b1abd11756dce1d2074aa263b88805ced70355a33b471ee, p)
E = ellinit([a, b])
E[16][1] = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565 * 0x1
G = [Mod(0x18de98b02db9a306f2afcd7235f72a819b80ab12ebd653172476fecd462aabffc4ff191b946a5f54d8d0aa2f418808cc, p), Mod(0x25ab056962d30651a114afd2755ad336747f93475b7a1fca3b88f2b6a208ccfe469408584dc2b2912675bf5b9e582928, p)]

JSON

{
  "name": "brainpoolP384t1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.12",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53",
    "bits": 384
  },
  "params": {
    "a": {
      "raw": "0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec50"
    },
    "b": {
      "raw": "0x7f519eada7bda81bd826dba647910f8c4b9346ed8ccdc64e4b1abd11756dce1d2074aa263b88805ced70355a33b471ee"
    }
  },
  "generator": {
    "x": {
      "raw": "0x18de98b02db9a306f2afcd7235f72a819b80ab12ebd653172476fecd462aabffc4ff191b946a5f54d8d0aa2f418808cc"
    },
    "y": {
      "raw": "0x25ab056962d30651a114afd2755ad336747f93475b7a1fca3b88f2b6a208ccfe469408584dc2b2912675bf5b9e582928"
    }
  },
  "order": "0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "3238708593163173875725998049354875763971987662971288152397580059844841553716806725943092933139820860272505955713980",
    "anomalous": false,
    "discriminant": "3737679651751396944816679318673518402321361287567315288737952401285446129378198042881937137830060298805293841235164",
    "embedding_degree": "5414817692529829043267309210583151244949029096754412150018911318705402875339628884490673779342225813057400429680985",
    "supersingular": false,
    "trace_of_frobenius": "5973228999478432667446284273866865475630836211106699249391"
  }
}