Curve from https://github.com/relic-toolkit/relic

Parameters

Sources

• RELIC: Efficient LIbrary for Cryptography

Characteristics

• j-invariant:
  13933415508088675400005384796018172765978821022446569396801076210943
• Trace of Frobenius:
  300921746732130612121844277365056
• Discriminant:
  88671474903936507947829812165347252667124612628390269359838445395559
• Embedding degree:
  5391989333430127958933403017403926119681341547901583890128508181590
• CM-discriminant:
  -88013998525868146970191166912191547453398359252925306734643974307
• Conductor:
  70

SAGE

p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffb
K = GF(p)
a = K(0x4648D10B419379D50F4BA01869D9AE363285E01FE66920878EE075B0)
b = K(0x4C4DCEDFAC09383A0311B98EE9637415B9134B4115FDB760C1A3D419)
E = EllipticCurve(K, (a, b))
G = E(0xFF9D7EDD97D523012FFAACA32B7C90F1A8E026F21972C789A8484A2B, 0x3E9036ADC1A41FCE2F2CA08E2D1BE4F6D97E30CA7761DB1F3E2F2CE96)
E.set_order(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC4A75594D4923FC93D42713CDAF * 0x04)

PARI/GP

p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffb
a = Mod(0x4648D10B419379D50F4BA01869D9AE363285E01FE66920878EE075B0, p)
b = Mod(0x4C4DCEDFAC09383A0311B98EE9637415B9134B4115FDB760C1A3D419, p)
E = ellinit([a, b])
E[16][1] = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC4A75594D4923FC93D42713CDAF * 0x04
G = [Mod(0xFF9D7EDD97D523012FFAACA32B7C90F1A8E026F21972C789A8484A2B, p), Mod(0x3E9036ADC1A41FCE2F2CA08E2D1BE4F6D97E30CA7761DB1F3E2F2CE96, p)]

JSON

{
  "name": "Curve4417",
  "desc": "Curve from https://github.com/relic-toolkit/relic",
  "sources": [
    {
      "name": "RELIC: Efficient LIbrary for Cryptography",
      "url": "https://github.com/relic-toolkit/relic"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffb",
    "bits": 226
  },
  "params": {
    "a": {
      "raw": "0x4648D10B419379D50F4BA01869D9AE363285E01FE66920878EE075B0"
    },
    "b": {
      "raw": "0x4C4DCEDFAC09383A0311B98EE9637415B9134B4115FDB760C1A3D419"
    }
  },
  "generator": {
    "x": {
      "raw": "0xFF9D7EDD97D523012FFAACA32B7C90F1A8E026F21972C789A8484A2B"
    },
    "y": {
      "raw": "0x3E9036ADC1A41FCE2F2CA08E2D1BE4F6D97E30CA7761DB1F3E2F2CE96"
    }
  },
  "order": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC4A75594D4923FC93D42713CDAF",
  "cofactor": "0x04",
  "characteristics": {
    "cm_disc": "-88013998525868146970191166912191547453398359252925306734643974307",
    "conductor": "70",
    "discriminant": "88671474903936507947829812165347252667124612628390269359838445395559",
    "j_invariant": "13933415508088675400005384796018172765978821022446569396801076210943",
    "embedding_degree": "5391989333430127958933403017403926119681341547901583890128508181590",
    "trace_of_frobenius": "300921746732130612121844277365056"
  }
}