Curve from https://datatracker.ietf.org/doc/html/rfc7748

Parameters

Characteristics

SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
A = K(0x262a6)
B = K(0x01)
E = EllipticCurve(K, ((3 - A^2)/(3 * B^2), (2 * A^3 - 9 * A)/(27 * B^3)))
def to_weierstrass(A, B, x, y):
	return (x/B + A/(3*B), y/B)
def to_montgomery(A, B, u, v):
	return (B * (u - A/(3*B)), B*v)
G = E(*to_weierstrass(A, B, K(0x05), K(0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a)))
E.set_order(0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3 * 0x04)
# This curve is a Weierstrass curve (SAGE does not support Montgomery curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_montgomery functions to convert the points.

JSON

{
  "name": "Curve448",
  "desc": "Curve from https://datatracker.ietf.org/doc/html/rfc7748",
  "form": "Montgomery",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
    "bits": 448
  },
  "params": {
    "a": {
      "raw": "0x262a6"
    },
    "b": {
      "raw": "0x01"
    }
  },
  "generator": {
    "x": {
      "raw": "0x05"
    },
    "y": {
      "raw": "0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a"
    }
  },
  "order": "0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3",
  "cofactor": "0x04",
  "characteristics": {}
}