521-bit Random ECP Group

521-bit prime field Weierstrass curve.

Defined in IETF in RFC5114

y^2 \equiv x^3 + ax + b

Parameters

Name	Value
p0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF	`0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF`
a0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC	`0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC`
b0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00	`0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00`
G(0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66, 0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650)	`(0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66, 0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650)`
n0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409	`0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409`
h0x01	`0x01`

SAGE

p = 0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
K = GF(p)
a = K(0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC)
b = K(0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00)
E = EllipticCurve(K, (a, b))
G = E(0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66, 0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650)
E.set_order(0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409 * 0x01)

p = 0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
K = GF(p)
a = K(0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC)
b = K(0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00)
E = EllipticCurve(K, (a, b))
G = E(0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66, 0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650)
E.set_order(0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409 * 0x01)

SAGE

PARI/GP

p = 0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
a = Mod(0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC, p)
b = Mod(0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00, p)
E = ellinit([a, b])
E[16][1] = 0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409 * 0x01
G = [Mod(0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66, p), Mod(0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650, p)]

p = 0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
a = Mod(0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC, p)
b = Mod(0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00, p)
E = ellinit([a, b])
E[16][1] = 0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409 * 0x01
G = [Mod(0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66, p), Mod(0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650, p)]

PARI/GP

JSON

{
  "name": "521-bit Random ECP Group",
  "desc": "Defined in IETF in RFC5114",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "bits": 521
  },
  "params": {
    "a": {
      "raw": "0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC"
    },
    "b": {
      "raw": "0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00"
    }
  },
  "generator": {
    "x": {
      "raw": "0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
    },
    "y": {
      "raw": "0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650"
    }
  },
  "order": "0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
  "cofactor": "0x01"
}

{
  "name": "521-bit Random ECP Group",
  "desc": "Defined in IETF in RFC5114",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "bits": 521
  },
  "params": {
    "a": {
      "raw": "0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC"
    },
    "b": {
      "raw": "0x00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00"
    }
  },
  "generator": {
    "x": {
      "raw": "0x000000C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
    },
    "y": {
      "raw": "0x0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650"
    }
  },
  "order": "0x000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
  "cofactor": "0x01"
}

JSON