)
type Curve struct {
- P *big.Int
- Q *big.Int
+ Name string // Just simple identifier
+
+ P *big.Int // Characteristic of the underlying prime field
+ Q *big.Int // Elliptic curve subgroup order
+
+ // Equation coefficients of the elliptic curve in canonical form
A *big.Int
B *big.Int
+ // Equation coefficients of the elliptic curve in twisted Edwards form
+ E *big.Int
+ D *big.Int
+
// Basic point X and Y coordinates
- Bx *big.Int
- By *big.Int
+ X *big.Int
+ Y *big.Int
// Temporary variable for the add method
t *big.Int
tx *big.Int
ty *big.Int
+
+ // Cached s/t parameters for Edwards curve points conversion
+ edS *big.Int
+ edT *big.Int
}
-func NewCurve(p, q, a, b, bx, by []byte) (*Curve, error) {
+func NewCurve(p, q, a, b, x, y, e, d *big.Int) (*Curve, error) {
c := Curve{
- P: bytes2big(p[:]),
- Q: bytes2big(q[:]),
- A: bytes2big(a[:]),
- B: bytes2big(b[:]),
- Bx: bytes2big(bx[:]),
- By: bytes2big(by[:]),
- t: big.NewInt(0),
- tx: big.NewInt(0),
- ty: big.NewInt(0),
+ Name: "unknown",
+ P: p,
+ Q: q,
+ A: a,
+ B: b,
+ X: x,
+ Y: y,
+ t: big.NewInt(0),
+ tx: big.NewInt(0),
+ ty: big.NewInt(0),
}
r1 := big.NewInt(0)
r2 := big.NewInt(0)
- r1.Mul(c.By, c.By)
+ r1.Mul(c.Y, c.Y)
r1.Mod(r1, c.P)
- r2.Mul(c.Bx, c.Bx)
+ r2.Mul(c.X, c.X)
r2.Add(r2, c.A)
- r2.Mul(r2, c.Bx)
+ r2.Mul(r2, c.X)
r2.Add(r2, c.B)
r2.Mod(r2, c.P)
- if r2.Cmp(big.NewInt(0)) == -1 {
- r2.Add(r2, c.P)
- }
+ c.pos(r2)
if r1.Cmp(r2) != 0 {
return nil, errors.New("Invalid curve parameters")
}
+ if e != nil && d != nil {
+ c.E = e
+ c.D = d
+ }
return &c, nil
}