Curve used in: https://eprint.iacr.org/2010/354.pdf

Parameters

Sources

• High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves

SAGE

F.<x> = GF(0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001)[]
K = GF(0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001^2, name="x", modulus=u^2 + 0x05)
a = K(0x00)
b = K(0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000000 * u^1)
E = EllipticCurve(K, (a, b))
E.set_order(0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001 * 0x2370fb049d410fbe4e761a9886e50241dc42cf101e0000017e80600000000001)
G = E(K(0xa1cf585585a61c6e9880b1f2a5c539f7d906fff238fa6341e1de1a2e45c3f72 * u^1 + 0x19b0bea4afe4c330da93cc3533da38a9f430b471c6f8a536e81962ed967909b5), K(0x0ee97d6de9902a27d00e952232a78700863bc9aa9be960C32f5bf9fd0a32d345 * u^1 + 0x17abd366ebbd65333e49c711a80a0cf6d24adf1b9b3990eedcc91731384d2627))

JSON

{
  "name": "Fp254n2BNa",
  "desc": "Curve used in: https://eprint.iacr.org/2010/354.pdf",
  "sources": [
    {
      "name": "High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves",
      "url": "https://eprint.iacr.org/2010/354"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Extension",
    "base": "0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001",
    "bits": 508,
    "degree": 2,
    "poly": [
      {
        "power": 2,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x05"
      }
    ]
  },
  "params": {
    "a": {
      "poly": [
        {
          "power": 0,
          "coeff": "0x00"
        }
      ]
    },
    "b": {
      "poly": [
        {
          "power": 1,
          "coeff": "0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000000"
        }
      ]
    }
  },
  "generator": {
    "x": {
      "poly": [
        {
          "power": 1,
          "coeff": "0xa1cf585585a61c6e9880b1f2a5c539f7d906fff238fa6341e1de1a2e45c3f72"
        },
        {
          "power": 0,
          "coeff": "0x19b0bea4afe4c330da93cc3533da38a9f430b471c6f8a536e81962ed967909b5"
        }
      ]
    },
    "y": {
      "poly": [
        {
          "power": 1,
          "coeff": "0x0ee97d6de9902a27d00e952232a78700863bc9aa9be960C32f5bf9fd0a32d345"
        },
        {
          "power": 0,
          "coeff": "0x17abd366ebbd65333e49c711a80a0cf6d24adf1b9b3990eedcc91731384d2627"
        }
      ]
    }
  },
  "order": "0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001",
  "cofactor": "0x2370fb049d410fbe4e761a9886e50241dc42cf101e0000017e80600000000001"
}