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package ed25519group
import (
"math/big"
)
func q() *big.Int {
q := new(big.Int)
v := new(big.Int)
// Calculate 2^255
v.Exp(big.NewInt(2), big.NewInt(255), nil)
// calculate 2^255 - 19
q.Sub(v, big.NewInt(19))
return q
}
func l() *big.Int {
l := new(big.Int)
v := new(big.Int)
s := new(big.Int)
// Calculate 2^252
v.Exp(big.NewInt(2), big.NewInt(252), nil)
// Value to add to v to get o
s.SetString("27742317777372353535851937790883648493", 0)
l.Add(v, s)
return l
}
func d() *big.Int {
d := new(big.Int)
inv12166 := new(big.Int)
inv12166.ModInverse(big.NewInt(121666), Q)
// d = -121665 * inv(121666)
d.Mul(big.NewInt(-121665), inv12166)
return d
}
func by() *big.Int {
fiveInv := new(big.Int)
fiveInv.ModInverse(big.NewInt(5), Q)
// By = 4 * inv(5)
by := new(big.Int)
by.Mul(big.NewInt(4), fiveInv)
return by
}
func bx() *big.Int {
return xrecover(By)
}
func i() *big.Int {
q := new(big.Int)
q.Sub(Q, big.NewInt(1))
q.Div(q, big.NewInt(4))
i := new(big.Int)
i.Exp(big.NewInt(2), q, Q)
return i
}
func b() AffinePoint {
x := new(big.Int)
y := new(big.Int)
x.Mod(Bx, Q)
y.Mod(By, Q)
return AffinePoint{x, y}
}
func base() ExtendedPoint {
return B.ToExtended()
}
func extendedZero() ExtendedPoint {
z := AffinePoint{big.NewInt(0), big.NewInt(1)}
return z.ToExtended()
}
func twoD() *big.Int {
twoD := new(big.Int)
twoD.Mul(big.NewInt(2), D)
return twoD
}
var (
// Q is the order of group which is 2^255 - 19
Q = q()
// L is the order of subgroup which is 2^252 + 27742317777372353535851937790883648493
L = l()
// D is a constant TODO: fix the documentation
D = d()
// 2*D calculated to speed things up a bit
d2 = twoD()
// By is y co-ordinate of base point
By = by()
// Bx is X co-ordinate of the base point
Bx = bx()
// I is constant TODO fix the documentation
I = i()
// B is curve base point (generator point) in Affine form
B = b()
// Base is curve base point (generator point) in extended form
Base = base()
// Zero is identity element in extended co-ordinate system
Zero = extendedZero()
)
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