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package ed25519group
import (
"fmt"
"math/big"
)
// AffinePoint is original representation of points on twisted edwards curve
type AffinePoint struct {
X, Y *big.Int
}
// NotOnCurve is error emmited when the point got is not on the curve
type NotOnCurve struct{}
func (n *NotOnCurve) Error() string {
return "decoded point is not on curve"
}
// NewAffinePoint creates new affine point with big integer's given in string
// format and of provided base.
func NewAffinePoint(x, y string, base int) AffinePoint {
X := new(big.Int)
Y := new(big.Int)
X.SetString(x, base)
Y.SetString(y, base)
return AffinePoint{X, Y}
}
func (a AffinePoint) String() string {
return fmt.Sprintf("X: %s\nY: %s\n", a.X, a.Y)
}
// ToExtended converts AffinePoint to ExtendedPoint representation
func (a *AffinePoint) ToExtended() ExtendedPoint {
X := new(big.Int)
Y := new(big.Int)
T := new(big.Int)
xy := new(big.Int)
X.Mod(a.X, Q)
Y.Mod(a.Y, Q)
Z := big.NewInt(1)
// T = x*y % Q
xy.Mul(a.X, a.Y)
T.Mod(xy, Q)
return ExtendedPoint{X, Y, Z, T}
}
// IsOnCurve returns true if the given point is on curve
func (a *AffinePoint) IsOnCurve() bool {
x, y := a.X, a.Y
var mxx, xx, yy, mxxpyy, dxxyy, xxyy, minusX big.Int
// -x
minusX.Neg(x)
// -x *x
mxx.Mul(&minusX, x)
// x*x
xx.Mul(x, x)
// y*y
yy.Mul(y, y)
// -x*x + y*y
mxxpyy.Add(&mxx, &yy)
// x^2*y^2
xxyy.Mul(&xx, &yy)
// dx^2y^2
dxxyy.Mul(D, &xxyy)
var equation big.Int
// -x^2 + y^2 - 1 - dx^2y^2
equation.Sub(mxxpyy.Sub(&mxxpyy, big.NewInt(1)), &dxxyy)
var result big.Int
result.Mod(&equation, Q)
// Point is on curve if -x^2 + y^2 - 1 - dx^2y^2 % Q == 0
if result.Cmp(big.NewInt(0)) == 0 {
return true
}
return false
}
// Compress encodes the Affine Point into 32 byte little-endian b255 is the sign
func (a *AffinePoint) Compress() []byte {
x, y := a.X, a.Y
result := new(big.Int)
if !IsEven(x) {
// We need y += 1 << 255
var lsh big.Int
lsh.Lsh(big.NewInt(1), 255)
result.Add(y, &lsh)
} else {
result = y
}
resultBytes := result.Bytes()
reverse(resultBytes)
return resultBytes
}
// Decompress reconstructs the AffinePoint from given 32 byte which is
// considered as Y co-ordinate compressed using Compress function above
func (a *AffinePoint) Decompress(s []byte) error {
var clamp, oneShift big.Int
// (1 << 255) - 1
oneShift.Lsh(big.NewInt(1), 255)
clamp.Sub(&oneShift, big.NewInt(1))
// TODO check if bytes is more than 32 then we should throw error
b := make([]byte, len(s))
copy(b, s)
// Reversing is not required?. If I reverse the test fails may be
// because big.Int represents alredy in big endian?.
reverse(b)
unclamped := new(big.Int)
x := new(big.Int)
y := new(big.Int)
unclamped.SetBytes(b)
y.And(unclamped, &clamp)
x = xrecover(y)
var isXEven big.Int
isXEven.And(x, big.NewInt(1))
unclamped.And(unclamped, &oneShift)
if isXEven.Cmp(unclamped) != 0 {
x.Sub(Q, x)
}
a.X = x
a.Y = y
if !a.IsOnCurve() {
return &NotOnCurve{}
}
return nil
}
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