_pkg.dev: drop crypto/elliptic

It's the same implementation that we have in pkg/crypto (based on
https://github.com/vsergeev/btckeygenie) but with tests preserved. I don't see
any reason to port tests from it because even the pkg/crypto copy should go
away to fix #245.
This commit is contained in:
Roman Khimov 2019-08-26 18:44:38 +03:00
parent 2275b9e4ad
commit b19190b32f
4 changed files with 0 additions and 632 deletions

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## Package - Elliptic
### Why
The curve and arithmetic functions have been modularised, so that curves can be swapped in and out, without effecting the functionality.
The modular arithmetic used is not specialised for a specific curve.
In order to use this package, you must declare an ellipticcurve struct and then set the curve.
Example:
`
curve = NewEllipticCurve(Secp256k1)
`
If no curve is set, the default curve is the r1 curve used for NEO. The tests are done using the k1 curve, so in the elliptic_test.go file, the curve is changed accordingly.

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package elliptic
/*
This file was originally made by vsergeev.
Modifications have been made under the MIT license.
License: MIT
*/
import (
"math/big"
)
var curve Curve
type curveType string
const (
// Secp256r1 curve type
Secp256r1 curveType = "Secp256r1"
// Secp256k1 curve type
Secp256k1 curveType = "Secp256k1"
)
// SetCurveSecp256r1 Will set the curve parameters to match Secp256r1
func (ChosenCurve *Curve) SetCurveSecp256r1() {
ChosenCurve.P, _ = new(big.Int).SetString("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", 16) //Q
ChosenCurve.A, _ = new(big.Int).SetString("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC", 16)
ChosenCurve.B, _ = new(big.Int).SetString("5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B", 16)
ChosenCurve.G.X, _ = new(big.Int).SetString("6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", 16)
ChosenCurve.G.Y, _ = new(big.Int).SetString("4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5", 16)
ChosenCurve.N, _ = new(big.Int).SetString("FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551", 16)
ChosenCurve.H, _ = new(big.Int).SetString("01", 16)
ChosenCurve.Name = "Secp256r1"
}
// SetCurveSecp256k1 Will set the curve parameters to match Secp256k1
func (ChosenCurve *Curve) SetCurveSecp256k1() {
ChosenCurve.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16)
ChosenCurve.A, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000000", 16)
ChosenCurve.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16)
ChosenCurve.G.X, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
ChosenCurve.G.Y, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
ChosenCurve.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
ChosenCurve.H, _ = new(big.Int).SetString("01", 16)
ChosenCurve.Name = "Secp256k1"
}
//NewEllipticCurve will instantiate a new EllipticCurve
//Defaults to secp256r1
func NewEllipticCurve(ct curveType) Curve {
var curve Curve
switch ct {
case Secp256k1:
curve.SetCurveSecp256k1()
case Secp256r1:
curve.SetCurveSecp256r1()
default:
curve.SetCurveSecp256r1()
}
return curve
}

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/*
This file has been modified under the MIT license.
Original: https://github.com/vsergeev/btckeygenie
*/
package elliptic
import (
nativeelliptic "crypto/elliptic"
"encoding/hex"
"errors"
"fmt"
"math/big"
)
// Point represents a point on an EllipticCurve.
type Point struct {
X *big.Int
Y *big.Int
}
// Curve represents the parameters of a short Weierstrass equation elliptic curve.
/* y**2 = x**3 + a*x + b % p */
type Curve struct {
A *big.Int
B *big.Int
P *big.Int
G Point
N *big.Int
H *big.Int
Name string
}
// dump dumps the bytes of a point for debugging.
func (p *Point) dump() {
fmt.Print(p.format())
}
// format formats the bytes of a point for debugging.
func (p *Point) format() string {
if p.X == nil && p.Y == nil {
return "(inf,inf)"
}
return fmt.Sprintf("(%s,%s)", hex.EncodeToString(p.X.Bytes()), hex.EncodeToString(p.Y.Bytes()))
}
// Params represent the paramters for the Elliptic Curve
func (ec Curve) Params() *nativeelliptic.CurveParams {
return &nativeelliptic.CurveParams{
P: ec.P,
N: ec.N,
B: ec.B,
Gx: ec.G.X,
Gy: ec.G.Y,
BitSize: 256,
Name: ec.Name,
}
}
/*** Modular Arithmetic ***/
/* NOTE: Returning a new z each time below is very space inefficient, but the
* alternate accumulator based design makes the point arithmetic functions look
* absolutely hideous. I may still change this in the future. */
// addMod computes z = (x + y) % p.
func addMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
z = new(big.Int).Add(x, y)
z.Mod(z, p)
return z
}
// subMod computes z = (x - y) % p.
func subMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
z = new(big.Int).Sub(x, y)
z.Mod(z, p)
return z
}
// mulMod computes z = (x * y) % p.
func mulMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
n := new(big.Int).Set(x)
z = big.NewInt(0)
for i := 0; i < y.BitLen(); i++ {
if y.Bit(i) == 1 {
z = addMod(z, n, p)
}
n = addMod(n, n, p)
}
return z
}
// invMod computes z = (1/x) % p.
func invMod(x *big.Int, p *big.Int) (z *big.Int) {
z = new(big.Int).ModInverse(x, p)
return z
}
// expMod computes z = (x^e) % p.
func expMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
z = new(big.Int).Exp(x, y, p)
return z
}
// sqrtMod computes z = sqrt(x) % p.
func sqrtMod(x *big.Int, p *big.Int) (z *big.Int) {
/* assert that p % 4 == 3 */
if new(big.Int).Mod(p, big.NewInt(4)).Cmp(big.NewInt(3)) != 0 {
panic("p is not equal to 3 mod 4!")
}
/* z = sqrt(x) % p = x^((p+1)/4) % p */
/* e = (p+1)/4 */
e := new(big.Int).Add(p, big.NewInt(1))
e = e.Rsh(e, 2)
z = expMod(x, e, p)
return z
}
/*** Point Arithmetic on Curve ***/
// IsInfinity checks if point P is infinity on EllipticCurve ec.
func (ec *Curve) IsInfinity(P Point) bool {
/* We use (nil,nil) to represent O, the point at infinity. */
if P.X == nil && P.Y == nil {
return true
}
return false
}
// IsOnCurve checks if point P is on EllipticCurve ec.
func (ec Curve) IsOnCurve(P1, P2 *big.Int) bool {
P := Point{P1, P2}
if ec.IsInfinity(P) {
return false
}
/* y**2 = x**3 + a*x + b % p */
lhs := mulMod(P.Y, P.Y, ec.P)
rhs := addMod(
addMod(
expMod(P.X, big.NewInt(3), ec.P),
mulMod(ec.A, P.X, ec.P), ec.P),
ec.B, ec.P)
if lhs.Cmp(rhs) == 0 {
return true
}
return false
}
// Add computes R = P + Q on EllipticCurve ec.
func (ec Curve) Add(P1, P2, Q1, Q2 *big.Int) (R1 *big.Int, R2 *big.Int) {
/* See rules 1-5 on SEC1 pg.7 http://www.secg.org/collateral/sec1_final.pdf */
P := Point{P1, P2}
Q := Point{Q1, Q2}
R := Point{}
if ec.IsInfinity(P) && ec.IsInfinity(Q) {
/* Rule #1 Identity */
/* R = O + O = O */
R.X = nil
R.Y = nil
} else if ec.IsInfinity(P) {
/* Rule #2 Identity */
/* R = O + Q = Q */
R.X = new(big.Int).Set(Q.X)
R.Y = new(big.Int).Set(Q.Y)
} else if ec.IsInfinity(Q) {
/* Rule #2 Identity */
/* R = P + O = P */
R.X = new(big.Int).Set(P.X)
R.Y = new(big.Int).Set(P.Y)
} else if P.X.Cmp(Q.X) == 0 && addMod(P.Y, Q.Y, ec.P).Sign() == 0 {
/* Rule #3 Identity */
/* R = (x,y) + (x,-y) = O */
R.X = nil
R.Y = nil
} else if P.X.Cmp(Q.X) == 0 && P.Y.Cmp(Q.Y) == 0 && P.Y.Sign() != 0 {
/* Rule #5 Point doubling */
/* R = P + P */
/* Lambda = (3*P.X*P.X + a) / (2*P.Y) */
num := addMod(
mulMod(big.NewInt(3),
mulMod(P.X, P.X, ec.P), ec.P),
ec.A, ec.P)
den := invMod(mulMod(big.NewInt(2), P.Y, ec.P), ec.P)
lambda := mulMod(num, den, ec.P)
/* R.X = lambda*lambda - 2*P.X */
R.X = subMod(
mulMod(lambda, lambda, ec.P),
mulMod(big.NewInt(2), P.X, ec.P),
ec.P)
/* R.Y = lambda*(P.X - R.X) - P.Y */
R.Y = subMod(
mulMod(lambda, subMod(P.X, R.X, ec.P), ec.P),
P.Y, ec.P)
} else if P.X.Cmp(Q.X) != 0 {
/* Rule #4 Point addition */
/* R = P + Q */
/* Lambda = (Q.Y - P.Y) / (Q.X - P.X) */
num := subMod(Q.Y, P.Y, ec.P)
den := invMod(subMod(Q.X, P.X, ec.P), ec.P)
lambda := mulMod(num, den, ec.P)
/* R.X = lambda*lambda - P.X - Q.X */
R.X = subMod(
subMod(
mulMod(lambda, lambda, ec.P),
P.X, ec.P),
Q.X, ec.P)
/* R.Y = lambda*(P.X - R.X) - P.Y */
R.Y = subMod(
mulMod(lambda,
subMod(P.X, R.X, ec.P), ec.P),
P.Y, ec.P)
} else {
panic(fmt.Sprintf("Unsupported point addition: %v + %v", P.format(), Q.format()))
}
return R.X, R.Y
}
// ScalarMult computes Q = k * P on EllipticCurve ec.
func (ec Curve) ScalarMult(P1, P2 *big.Int, l []byte) (Q1, Q2 *big.Int) {
/* Note: this function is not constant time, due to the branching nature of
* the underlying point Add() function. */
/* Montgomery Ladder Point Multiplication
*
* Implementation based on pseudocode here:
* See https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder */
P := Point{P1, P2}
k := big.Int{}
k.SetBytes(l)
var R0 Point
var R1 Point
R0.X = nil
R0.Y = nil
R1.X = new(big.Int).Set(P.X)
R1.Y = new(big.Int).Set(P.Y)
for i := ec.N.BitLen() - 1; i >= 0; i-- {
if k.Bit(i) == 0 {
R1.X, R1.Y = ec.Add(R0.X, R0.Y, R1.X, R1.Y)
R0.X, R0.Y = ec.Add(R0.X, R0.Y, R0.X, R0.Y)
} else {
R0.X, R0.Y = ec.Add(R0.X, R0.Y, R1.X, R1.Y)
R1.X, R1.Y = ec.Add(R1.X, R1.Y, R1.X, R1.Y)
}
}
return R0.X, R0.Y
}
// ScalarBaseMult computes Q = k * G on EllipticCurve ec.
func (ec Curve) ScalarBaseMult(k []byte) (Q1, Q2 *big.Int) {
return ec.ScalarMult(ec.G.X, ec.G.Y, k)
}
// Decompress decompresses coordinate x and ylsb (y's least significant bit) into a Point P on EllipticCurve ec.
func (ec *Curve) Decompress(x *big.Int, ylsb uint) (P Point, err error) {
/* y**2 = x**3 + a*x + b % p */
rhs := addMod(
addMod(
expMod(x, big.NewInt(3), ec.P),
mulMod(ec.A, x, ec.P),
ec.P),
ec.B, ec.P)
/* y = sqrt(rhs) % p */
y := sqrtMod(rhs, ec.P)
/* Use -y if opposite lsb is required */
if y.Bit(0) != (ylsb & 0x1) {
y = subMod(big.NewInt(0), y, ec.P)
}
P.X = x
P.Y = y
if !ec.IsOnCurve(P.X, P.Y) {
return P, errors.New("compressed (x, ylsb) not on curve")
}
return P, nil
}
// Double will return the (x1+x1,y1+y1)
func (ec Curve) Double(x1, y1 *big.Int) (x, y *big.Int) {
x = &big.Int{}
x.SetBytes([]byte{0x00})
y = &big.Int{}
y.SetBytes([]byte{0x00})
return x, y
}

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/* btckeygenie v1.0.0
* https://github.com/vsergeev/btckeygenie
* License: MIT
*/
package elliptic
import (
"encoding/hex"
"math/big"
"testing"
)
func init() {
curve = NewEllipticCurve(Secp256k1)
}
func hex2int(hexstring string) (v *big.Int) {
v, _ = new(big.Int).SetString(hexstring, 16)
return v
}
func TestOnCurve(t *testing.T) {
if !curve.IsOnCurve(curve.G.X, curve.G.Y) {
t.Fatal("failure G on curve")
}
t.Log("G on curve")
}
func TestInfinity(t *testing.T) {
O := Point{nil, nil}
/* O not on curve */
if curve.IsOnCurve(O.X, O.Y) {
t.Fatal("failure O on curve")
}
/* O is infinity */
if !curve.IsInfinity(O) {
t.Fatal("failure O not infinity on curve")
}
t.Log("O is not on curve and is infinity")
}
func TestPointAdd(t *testing.T) {
X := "50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352"
Y := "2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6"
P := Point{hex2int(X), hex2int(Y)}
O := Point{nil, nil}
/* R = O + O = O */
{
R1, R2 := curve.Add(O.X, O.Y, O.X, O.Y)
R := Point{R1, R2}
if !curve.IsInfinity(R) {
t.Fatal("failure O + O = O")
}
t.Log("success O + O = O")
}
/* R = P + O = P */
{
R1, R2 := curve.Add(P.X, P.Y, O.X, O.Y)
R := Point{R1, R2}
if R.X.Cmp(P.X) != 0 || R.Y.Cmp(P.Y) != 0 {
t.Fatal("failure P + O = P")
}
t.Log("success P + O = P")
}
/* R = O + Q = Q */
{
R1, R2 := curve.Add(O.X, O.Y, P.X, P.Y)
R := Point{R1, R2}
if R.X.Cmp(P.X) != 0 || R.Y.Cmp(P.Y) != 0 {
t.Fatal("failure O + Q = Q")
}
t.Log("success O + Q = Q")
}
/* R = (x,y) + (x,-y) = O */
{
Q := Point{P.X, subMod(big.NewInt(0), P.Y, curve.P)}
R1, R2 := curve.Add(P.X, P.Y, Q.X, Q.Y)
R := Point{R1, R2}
if !curve.IsInfinity(R) {
t.Fatal("failure (x,y) + (x,-y) = O")
}
t.Log("success (x,y) + (x,-y) = O")
}
/* R = P + P */
{
PP := Point{hex2int("5dbcd5dfea550eb4fd3b5333f533f086bb5267c776e2a1a9d8e84c16a6743d82"), hex2int("8dde3986b6cbe395da64b6e95fb81f8af73f6e0cf1100555005bb4ba2a6a4a07")}
R1, R2 := curve.Add(P.X, P.Y, P.X, P.Y)
R := Point{R1, R2}
if R.X.Cmp(PP.X) != 0 || R.Y.Cmp(PP.Y) != 0 {
t.Fatal("failure P + P")
}
t.Log("success P + P")
}
Q := Point{hex2int("a83b8de893467d3a88d959c0eb4032d9ce3bf80f175d4d9e75892a3ebb8ab7e5"), hex2int("370f723328c24b7a97fe34063ba68f253fb08f8645d7c8b9a4ff98e3c29e7f0d")}
PQ := Point{hex2int("fe7d540002e4355eb0ec36c217b4735495de7bd8634055ded3683b0e9da70ef1"), hex2int("fc033c1d74cb34e087a3495e505c0fc0e9e3e8297994878d89d882254ce8a9ef")}
/* R = P + Q */
{
R1, R2 := curve.Add(P.X, P.Y, Q.X, Q.Y)
R := Point{R1, R2}
if R.X.Cmp(PQ.X) != 0 || R.Y.Cmp(PQ.Y) != 0 {
t.Fatal("failure P + Q")
}
t.Log("success P + Q")
}
/* R = Q + P */
{
R1, R2 := curve.Add(Q.X, Q.Y, P.X, P.Y)
R := Point{R1, R2}
if R.X.Cmp(PQ.X) != 0 || R.Y.Cmp(PQ.Y) != 0 {
t.Fatal("failure Q + P")
}
t.Log("success Q + P")
}
}
func TestPointScalarMult(t *testing.T) {
X := "50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352"
Y := "2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6"
P := Point{hex2int(X), hex2int(Y)}
/* Q = k*P */
{
T := Point{hex2int("87d592bfdd24adb52147fea343db93e10d0585bc66d91e365c359973c0dc7067"), hex2int("a374e206cb7c8cd1074bdf9bf6ddea135f983aaa6475c9ab3bb4c38a0046541b")}
input, _ := hex.DecodeString("14eb373700c3836404acd0820d9fa8dfa098d26177ca6e18b1c7f70c6af8fc18")
Q1, Q2 := curve.ScalarMult(P.X, P.Y, input)
Q := Point{Q1, Q2}
if Q.X.Cmp(T.X) != 0 || Q.Y.Cmp(T.Y) != 0 {
t.Fatal("failure k*P")
}
t.Log("success k*P")
}
/* Q = n*G = O */
{
Q1, Q2 := curve.ScalarMult(curve.G.X, curve.G.Y, curve.N.Bytes())
Q := Point{Q1, Q2}
if !curve.IsInfinity(Q) {
t.Fatal("failure n*G = O")
}
t.Log("success n*G = O")
}
}
func TestPointScalarBaseMult(t *testing.T) {
/* Sample Private Key */
D := "18e14a7b6a307f426a94f8114701e7c8e774e7f9a47e2c2035db29a206321725"
/* Sample Corresponding Public Key */
X := "50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352"
Y := "2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6"
P := Point{hex2int(X), hex2int(Y)}
/* Q = d*G = P */
Q1, Q2 := curve.ScalarBaseMult(hex2int(D).Bytes())
Q := Point{Q1, Q2}
if P.X.Cmp(Q.X) != 0 || P.Y.Cmp(Q.Y) != 0 {
t.Fatal("failure Q = d*G")
}
t.Log("success Q = d*G")
/* Q on curve */
if !curve.IsOnCurve(Q.X, Q.Y) {
t.Fatal("failure Q on curve")
}
t.Log("success Q on curve")
/* R = 0*G = O */
R1, R2 := curve.ScalarBaseMult(big.NewInt(0).Bytes())
R := Point{R1, R2}
if !curve.IsInfinity(R) {
t.Fatal("failure 0*G = O")
}
t.Log("success 0*G = O")
}
func TestPointDecompress(t *testing.T) {
/* Valid points */
var validDecompressVectors = []Point{
{hex2int("50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352"), hex2int("2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6")},
{hex2int("a83b8de893467d3a88d959c0eb4032d9ce3bf80f175d4d9e75892a3ebb8ab7e5"), hex2int("370f723328c24b7a97fe34063ba68f253fb08f8645d7c8b9a4ff98e3c29e7f0d")},
{hex2int("f680556678e25084a82fa39e1b1dfd0944f7e69fddaa4e03ce934bd6b291dca0"), hex2int("52c10b721d34447e173721fb0151c68de1106badb089fb661523b8302a9097f5")},
{hex2int("241febb8e23cbd77d664a18f66ad6240aaec6ecdc813b088d5b901b2e285131f"), hex2int("513378d9ff94f8d3d6c420bd13981df8cd50fd0fbd0cb5afabb3e66f2750026d")},
}
for i := 0; i < len(validDecompressVectors); i++ {
P, err := curve.Decompress(validDecompressVectors[i].X, validDecompressVectors[i].Y.Bit(0))
if err != nil {
t.Fatalf("failure decompress P, got error %v on index %d", err, i)
}
if P.X.Cmp(validDecompressVectors[i].X) != 0 || P.Y.Cmp(validDecompressVectors[i].Y) != 0 {
t.Fatalf("failure decompress P, got mismatch on index %d", i)
}
}
t.Log("success Decompress() on valid vectors")
/* Invalid points */
var invalidDecompressVectors = []struct {
X *big.Int
YLsb uint
}{
{hex2int("c8e337cee51ae9af3c0ef923705a0cb1b76f7e8463b3d3060a1c8d795f9630fd"), 0},
{hex2int("c8e337cee51ae9af3c0ef923705a0cb1b76f7e8463b3d3060a1c8d795f9630fd"), 1},
}
for i := 0; i < len(invalidDecompressVectors); i++ {
_, err := curve.Decompress(invalidDecompressVectors[i].X, invalidDecompressVectors[i].YLsb)
if err == nil {
t.Fatalf("failure decompress invalid P, got decompressed point on index %d", i)
}
}
t.Log("success Decompress() on invalid vectors")
}