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curve.go
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curve.go
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package caigo
/*
Although the library adheres to the 'elliptic/curve' interface.
All testing has been done against library function explicity.
It is recommended to use in the same way(i.e. `curve.Sign` and not `ecdsa.Sign`).
*/
import (
"crypto/elliptic"
"encoding/json"
"fmt"
"io/ioutil"
"math/big"
"net/http"
"os"
)
var sc StarkCurve
/*
Returned stark curve includes several values above and beyond
what the 'elliptic' interface calls for to facilitate common starkware functions
*/
type StarkCurve struct {
*elliptic.CurveParams
EcGenX *big.Int
EcGenY *big.Int
MinusShiftPointX *big.Int
MinusShiftPointY *big.Int
Max *big.Int
Alpha *big.Int
ConstantPoints [][]*big.Int
}
// struct definition for parsing 'pedersen_params.json'
type StarkCurvePayload struct {
License []string `json:"_license"`
Comment string `json:"_comment"`
FieldPrime *big.Int `json:"FIELD_PRIME"`
FieldGen int `json:"FIELD_GEN"`
EcOrder *big.Int `json:"EC_ORDER"`
Alpha int64 `json:"ALPHA"`
Beta *big.Int `json:"BETA"`
ConstantPoints [][]*big.Int `json:"CONSTANT_POINTS"`
}
func SC(opts ...CurveOption) (StarkCurve, error) {
var gopts curveOptions
for _, opt := range opts {
opt.apply(&gopts)
}
if gopts.initConstants {
err := InitWithConstants(gopts.paramsPath)
return sc, err
}
InitCurve()
return sc, nil
}
/*
Not all operations require a stark curve initialization
including the provided constant points. Here you can
initialize the curve without the constant points
*/
func InitCurve() {
sc.CurveParams = &elliptic.CurveParams{Name: "stark-curve"}
sc.P, _ = new(big.Int).SetString("3618502788666131213697322783095070105623107215331596699973092056135872020481", 10) // Field Prime ./pedersen_json
sc.N, _ = new(big.Int).SetString("3618502788666131213697322783095070105526743751716087489154079457884512865583", 10) // Order of base point ./pedersen_json
sc.B, _ = new(big.Int).SetString("3141592653589793238462643383279502884197169399375105820974944592307816406665", 10) // Constant of curve equation ./pedersen_json
sc.Gx, _ = new(big.Int).SetString("2089986280348253421170679821480865132823066470938446095505822317253594081284", 10) // (x, _) of basepoint ./pedersen_json
sc.Gy, _ = new(big.Int).SetString("1713931329540660377023406109199410414810705867260802078187082345529207694986", 10) // (_, y) of basepoint ./pedersen_json
sc.EcGenX, _ = new(big.Int).SetString("874739451078007766457464989774322083649278607533249481151382481072868806602", 10)
sc.EcGenY, _ = new(big.Int).SetString("152666792071518830868575557812948353041420400780739481342941381225525861407", 10)
sc.MinusShiftPointX, _ = new(big.Int).SetString("2089986280348253421170679821480865132823066470938446095505822317253594081284", 10) // MINUS_SHIFT_POINT = (SHIFT_POINT[0], FIELD_PRIME - SHIFT_POINT[1])
sc.MinusShiftPointY, _ = new(big.Int).SetString("1904571459125470836673916673895659690812401348070794621786009710606664325495", 10) // MINUS_SHIFT_POINT = (SHIFT_POINT[0], FIELD_PRIME - SHIFT_POINT[1])
sc.Max, _ = new(big.Int).SetString("3618502788666131106986593281521497120414687020801267626233049500247285301248", 10) // 2 ** 251
sc.Alpha = big.NewInt(1)
sc.BitSize = 252
}
/*
Various starknet functions require constant points be initialized.
In this case use 'InitWithConstants'. Given an empty string this will
init the curve by pulling the 'pedersen_params.json' file from Starkware
official github repository. For production deployments it is recommended
to have the file stored locally.
*/
func InitWithConstants(path string) (err error) {
sc.CurveParams = &elliptic.CurveParams{Name: "stark-curve-with-constants"}
scPayload := &StarkCurvePayload{}
if path != "" {
scFile, err := os.Open(path)
if err != nil {
return err
}
defer scFile.Close()
scBytes, err := ioutil.ReadAll(scFile)
if err != nil {
return err
}
json.Unmarshal(scBytes, &scPayload)
} else {
url := "https://raw.githubusercontent.com/starkware-libs/cairo-lang/master/src/starkware/crypto/starkware/crypto/signature/pedersen_params.json"
method := "GET"
client := &http.Client{}
req, err := http.NewRequest(method, url, nil)
if err != nil {
return err
}
req.Header.Add("Content-Type", "application/json")
resp, err := client.Do(req)
if err != nil {
return err
}
defer resp.Body.Close()
err = json.NewDecoder(resp.Body).Decode(scPayload)
if err != nil {
return err
}
}
if len(scPayload.ConstantPoints) == 0 {
return fmt.Errorf("could not decode stark curve json")
}
sc.P = scPayload.FieldPrime
sc.N = scPayload.EcOrder
sc.B = scPayload.Beta
sc.Gx = scPayload.ConstantPoints[0][0]
sc.Gy = scPayload.ConstantPoints[0][1]
sc.EcGenX = scPayload.ConstantPoints[1][0]
sc.EcGenY = scPayload.ConstantPoints[1][1]
sc.MinusShiftPointX, _ = new(big.Int).SetString("2089986280348253421170679821480865132823066470938446095505822317253594081284", 10) // MINUS_SHIFT_POINT = (SHIFT_POINT[0], FIELD_PRIME - SHIFT_POINT[1])
sc.MinusShiftPointY, _ = new(big.Int).SetString("1904571459125470836673916673895659690812401348070794621786009710606664325495", 10)
sc.Max, _ = new(big.Int).SetString("3618502788666131106986593281521497120414687020801267626233049500247285301248", 10) // 2 ** 251
sc.Alpha = big.NewInt(scPayload.Alpha)
sc.BitSize = 252
sc.ConstantPoints = scPayload.ConstantPoints
return nil
}
// Get relevant elliptic curve parameters for the Stark Cruve
func (sc StarkCurve) Params() *elliptic.CurveParams {
return sc.CurveParams
}
// Gets two points on an elliptic curve mod p and returns their sum.
// Assumes affine form (x, y) is spread (x1 *big.Int, y1 *big.Int)
//
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/math_utils.py)
func (sc StarkCurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
yDelta := new(big.Int).Sub(y1, y2)
xDelta := new(big.Int).Sub(x1, x2)
m := DivMod(yDelta, xDelta, sc.P)
xm := new(big.Int).Mul(m, m)
x = new(big.Int).Sub(xm, x1)
x = x.Sub(x, x2)
x = x.Mod(x, sc.P)
y = new(big.Int).Sub(x1, x)
y = y.Mul(m, y)
y = y.Sub(y, y1)
y = y.Mod(y, sc.P)
return x, y
}
// Doubles a point on an elliptic curve with the equation y^2 = x^3 + alpha*x + beta mod p.
// Assumes affine form (x, y) is spread (x1 *big.Int, y1 *big.Int)
//
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/math_utils.py)
func (sc StarkCurve) Double(x1, y1 *big.Int) (x, y *big.Int) {
xin := new(big.Int).Mul(big.NewInt(3), x1)
xin = xin.Mul(xin, x1)
xin = xin.Add(xin, sc.Alpha)
yin := new(big.Int).Mul(y1, big.NewInt(2))
m := DivMod(xin, yin, sc.P)
xout := new(big.Int).Mul(m, m)
xmed := new(big.Int).Mul(big.NewInt(2), x1)
xout = xout.Sub(xout, xmed)
xout = xout.Mod(xout, sc.P)
yout := new(big.Int).Sub(x1, xout)
yout = yout.Mul(m, yout)
yout = yout.Sub(yout, y1)
yout = yout.Mod(yout, sc.P)
return xout, yout
}
func (sc StarkCurve) ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int) {
m := new(big.Int).SetBytes(k)
x, y = sc.EcMult(m, x1, y1)
return x, y
}
func (sc StarkCurve) ScalarBaseMult(k []byte) (x, y *big.Int) {
return sc.ScalarMult(sc.Gx, sc.Gy, k)
}
func (sc StarkCurve) IsOnCurve(x, y *big.Int) bool {
left := new(big.Int).Mul(y, y)
left = left.Mod(left, sc.P)
right := new(big.Int).Mul(x, x)
right = right.Mul(right, x)
right = right.Mod(right, sc.P)
ri := new(big.Int).Mul(big.NewInt(1), x)
right = right.Add(right, ri)
right = right.Add(right, sc.B)
right = right.Mod(right, sc.P)
if left.Cmp(right) == 0 {
return true
} else {
return false
}
}
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/math_utils.py)
func (sc StarkCurve) InvModCurveSize(x *big.Int) *big.Int {
return DivMod(big.NewInt(1), x, sc.N)
}
// Given the x coordinate of a stark_key, returns a possible y coordinate such that together the
// point (x,y) is on the curve.
// Note: the real y coordinate is either y or -y.
//
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/signature.py)
func (sc StarkCurve) GetYCoordinate(starkX *big.Int) *big.Int {
y := new(big.Int).Mul(starkX, starkX)
y = y.Mul(y, starkX)
yin := new(big.Int).Mul(sc.Alpha, starkX)
y = y.Add(y, yin)
y = y.Add(y, sc.B)
y = y.Mod(y, sc.P)
y = y.ModSqrt(y, sc.P)
return y
}
// Computes m * point + shift_point using the same steps like the AIR and throws an exception if
// and only if the AIR errors.
//
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/signature.py)
func (sc StarkCurve) MimicEcMultAir(mout, x1, y1, x2, y2 *big.Int) (x *big.Int, y *big.Int, err error) {
m := new(big.Int).Set(mout)
if m.Cmp(big.NewInt(0)) != 1 || m.Cmp(sc.Max) != -1 {
return x, y, fmt.Errorf("too many bits %v", m.BitLen())
}
psx := x2
psy := y2
for i := 0; i < 251; i++ {
if psx == x1 {
return x, y, fmt.Errorf("xs are the same")
}
if m.Bit(0) == 1 {
psx, psy = sc.Add(psx, psy, x1, y1)
}
x1, y1 = sc.Double(x1, y1)
m = m.Rsh(m, 1)
}
if m.Cmp(big.NewInt(0)) != 0 {
return psx, psy, fmt.Errorf("m doesn't equal zero")
}
return psx, psy, nil
}
// Multiplies by m a point on the elliptic curve with equation y^2 = x^3 + alpha*x + beta mod p.
// Assumes affine form (x, y) is spread (x1 *big.Int, y1 *big.Int) and that 0 < m < order(point).
//
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/math_utils.py)
func (sc StarkCurve) EcMult(m, x1, y1 *big.Int) (x, y *big.Int) {
var _ecMult func(m, x1, y1 *big.Int) (x, y *big.Int)
_add := func(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
yDelta := new(big.Int).Sub(y1, y2)
xDelta := new(big.Int).Sub(x1, x2)
m := DivMod(yDelta, xDelta, sc.P)
xm := new(big.Int).Mul(m, m)
x = new(big.Int).Sub(xm, x1)
x = x.Sub(x, x2)
x = x.Mod(x, sc.P)
y = new(big.Int).Sub(x1, x)
y = y.Mul(m, y)
y = y.Sub(y, y1)
y = y.Mod(y, sc.P)
return x, y
}
// alpha is our Y
_ecMult = func(m, x1, y1 *big.Int) (x, y *big.Int) {
if m.BitLen() == 1 {
return x1, y1
}
mk := new(big.Int).Mod(m, big.NewInt(2))
if mk.Cmp(big.NewInt(0)) == 0 {
h := new(big.Int).Div(m, big.NewInt(2))
c, d := sc.Double(x1, y1)
return _ecMult(h, c, d)
}
n := new(big.Int).Sub(m, big.NewInt(1))
e, f := _ecMult(n, x1, y1)
return _add(e, f, x1, y1)
}
x, y = _ecMult(m, x1, y1)
return x, y
}
// Finds a nonnegative integer 0 <= x < p such that (m * x) % p == n
//
// (ref: https://github.com/starkware-libs/cairo-lang/blob/master/src/starkware/crypto/starkware/crypto/signature/math_utils.py)
func DivMod(n, m, p *big.Int) *big.Int {
q := new(big.Int)
gx := new(big.Int)
gy := new(big.Int)
q = q.GCD(gx, gy, m, p)
r := new(big.Int).Mul(n, gx)
r = r.Mod(r, p)
return r
}
// Adheres to 'starknet.js' hash non typedData
func (sc StarkCurve) HashTx(addr *big.Int, tx Transaction) (hash *big.Int, err error) {
calldataArray := []*big.Int{big.NewInt(int64(len(tx.Calldata)))}
for _, cd := range tx.Calldata {
calldataArray = append(calldataArray, SNValToBN(cd))
}
cdHash, err := sc.HashElements(calldataArray)
if err != nil {
return hash, err
}
txHashData := []*big.Int{
SNValToBN(tx.ContractAddress),
GetSelectorFromName(tx.EntryPointSelector),
cdHash,
}
txHashData = append(txHashData, big.NewInt(int64(len(txHashData))))
hash, err = sc.HashElements(txHashData)
return hash, err
}
// Adheres to 'starknet.js' hash non typedData
func (sc StarkCurve) HashMsg(addr *big.Int, tx Transaction) (hash *big.Int, err error) {
calldataArray := []*big.Int{big.NewInt(int64(len(tx.Calldata)))}
for _, cd := range tx.Calldata {
calldataArray = append(calldataArray, HexToBN(cd))
}
cdHash, err := sc.HashElements(calldataArray)
if err != nil {
return hash, err
}
txHashData := []*big.Int{
addr,
SNValToBN(tx.ContractAddress),
GetSelectorFromName(tx.EntryPointSelector),
cdHash,
SNValToBN(tx.Nonce),
}
txHashData = append(txHashData, big.NewInt(int64(len(txHashData))))
hash, err = sc.HashElements(txHashData)
return hash, err
}