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point.go
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point.go
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package native
import (
"crypto/sha256"
"crypto/sha512"
"fmt"
"hash"
"io"
"math/big"
"github.com/pkg/errors"
"golang.org/x/crypto/blake2b"
"golang.org/x/crypto/sha3"
)
// EllipticPointHashType is to indicate which expand operation is used
// for hash to curve operations
type EllipticPointHashType uint
// EllipticPointHashName is to indicate the hash function is used
// for hash to curve operations
type EllipticPointHashName uint
const (
// XMD - use ExpandMsgXmd
XMD EllipticPointHashType = iota
// XOF - use ExpandMsgXof
XOF
)
const (
SHA256 EllipticPointHashName = iota
SHA512
SHA3_256
SHA3_384
SHA3_512
BLAKE2B
SHAKE128
SHAKE256
)
// EllipticPoint represents a Weierstrauss elliptic curve point
type EllipticPoint struct {
X *Field
Y *Field
Z *Field
Params *EllipticPointParams
Arithmetic EllipticPointArithmetic
}
// EllipticPointParams are the Weierstrauss curve parameters
// such as the name, the coefficients the generator point,
// and the prime bit size
type EllipticPointParams struct {
Name string
A *Field
B *Field
Gx *Field
Gy *Field
BitSize int
}
// EllipticPointHasher is the type of hashing methods for
// hashing byte sequences to curve point.
type EllipticPointHasher struct {
name EllipticPointHashName
hashType EllipticPointHashType
xmd hash.Hash
xof sha3.ShakeHash
}
// Name returns the hash name for this hasher
func (e *EllipticPointHasher) Name() string {
return e.name.String()
}
// Type returns the hash type for this hasher
func (e *EllipticPointHasher) Type() EllipticPointHashType {
return e.hashType
}
// Xmd returns the hash method for ExpandMsgXmd
func (e *EllipticPointHasher) Xmd() hash.Hash {
return e.xmd
}
// Xof returns the hash method for ExpandMsgXof
func (e *EllipticPointHasher) Xof() sha3.ShakeHash {
return e.xof
}
// EllipticPointHasherSha256 creates a point hasher that uses Sha256
func EllipticPointHasherSha256() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHA256,
hashType: XMD,
xmd: sha256.New(),
}
}
// EllipticPointHasherSha512 creates a point hasher that uses Sha512
func EllipticPointHasherSha512() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHA512,
hashType: XMD,
xmd: sha512.New(),
}
}
// EllipticPointHasherSha3256 creates a point hasher that uses Sha3256
func EllipticPointHasherSha3256() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHA3_256,
hashType: XMD,
xmd: sha3.New256(),
}
}
// EllipticPointHasherSha3384 creates a point hasher that uses Sha3384
func EllipticPointHasherSha3384() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHA3_384,
hashType: XMD,
xmd: sha3.New384(),
}
}
// EllipticPointHasherSha3512 creates a point hasher that uses Sha3512
func EllipticPointHasherSha3512() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHA3_512,
hashType: XMD,
xmd: sha3.New512(),
}
}
// EllipticPointHasherBlake2b creates a point hasher that uses Blake2b
func EllipticPointHasherBlake2b() *EllipticPointHasher {
h, _ := blake2b.New(64, []byte{})
return &EllipticPointHasher{
name: BLAKE2B,
hashType: XMD,
xmd: h,
}
}
// EllipticPointHasherShake128 creates a point hasher that uses Shake128
func EllipticPointHasherShake128() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHAKE128,
hashType: XOF,
xof: sha3.NewShake128(),
}
}
// EllipticPointHasherShake256 creates a point hasher that uses Shake256
func EllipticPointHasherShake256() *EllipticPointHasher {
return &EllipticPointHasher{
name: SHAKE128,
hashType: XOF,
xof: sha3.NewShake256(),
}
}
// EllipticPointArithmetic are the methods that specific curves
// need to implement for higher abstractions to wrap the point
type EllipticPointArithmetic interface {
// Hash a byte sequence to the curve using the specified hasher
// and dst and store the result in out
Hash(out *EllipticPoint, hasher *EllipticPointHasher, bytes, dst []byte) error
// Double arg and store the result in out
Double(out, arg *EllipticPoint)
// Add arg1 with arg2 and store the result in out
Add(out, arg1, arg2 *EllipticPoint)
// IsOnCurve tests arg if it represents a valid point on the curve
IsOnCurve(arg *EllipticPoint) bool
// ToAffine converts arg to affine coordinates storing the result in out
ToAffine(out, arg *EllipticPoint)
// RhsEq computes the right-hand side of the ecc equation
RhsEq(out, x *Field)
}
func (t EllipticPointHashType) String() string {
switch t {
case XMD:
return "XMD"
case XOF:
return "XOF"
}
return "unknown"
}
func (n EllipticPointHashName) String() string {
switch n {
case SHA256:
return "SHA-256"
case SHA512:
return "SHA-512"
case SHA3_256:
return "SHA3-256"
case SHA3_384:
return "SHA3-384"
case SHA3_512:
return "SHA3-512"
case BLAKE2B:
return "BLAKE2b"
case SHAKE128:
return "SHAKE-128"
case SHAKE256:
return "SHAKE-256"
}
return "unknown"
}
// Random creates a random point on the curve
// from the specified reader
func (p *EllipticPoint) Random(reader io.Reader) (*EllipticPoint, error) {
var seed [WideFieldBytes]byte
n, err := reader.Read(seed[:])
if err != nil {
return nil, errors.Wrap(err, "random could not read from stream")
}
if n != WideFieldBytes {
return nil, fmt.Errorf("insufficient bytes read %d when %d are needed", n, WideFieldBytes)
}
dst := []byte(fmt.Sprintf("%s_XMD:SHA-256_SSWU_RO_", p.Params.Name))
err = p.Arithmetic.Hash(p, EllipticPointHasherSha256(), seed[:], dst)
if err != nil {
return nil, errors.Wrap(err, "ecc hash failed")
}
return p, nil
}
// Hash uses the hasher to map bytes to a valid point
func (p *EllipticPoint) Hash(bytes []byte, hasher *EllipticPointHasher) (*EllipticPoint, error) {
dst := []byte(fmt.Sprintf("%s_%s:%s_SSWU_RO_", p.Params.Name, hasher.hashType, hasher.name))
err := p.Arithmetic.Hash(p, hasher, bytes, dst)
if err != nil {
return nil, errors.Wrap(err, "hash failed")
}
return p, nil
}
// Identity returns the identity point
func (p *EllipticPoint) Identity() *EllipticPoint {
p.X.SetZero()
p.Y.SetZero()
p.Z.SetZero()
return p
}
// Generator returns the base point for the curve
func (p *EllipticPoint) Generator() *EllipticPoint {
p.X.Set(p.Params.Gx)
p.Y.Set(p.Params.Gy)
p.Z.SetOne()
return p
}
// IsIdentity returns true if this point is at infinity
func (p *EllipticPoint) IsIdentity() bool {
return p.Z.IsZero() == 1
}
// Double this point
func (p *EllipticPoint) Double(point *EllipticPoint) *EllipticPoint {
p.Set(point)
p.Arithmetic.Double(p, point)
return p
}
// Neg negates this point
func (p *EllipticPoint) Neg(point *EllipticPoint) *EllipticPoint {
p.Set(point)
p.Y.Neg(p.Y)
return p
}
// Add adds the two points
func (p *EllipticPoint) Add(lhs, rhs *EllipticPoint) *EllipticPoint {
p.Set(lhs)
p.Arithmetic.Add(p, lhs, rhs)
return p
}
// Sub subtracts the two points
func (p *EllipticPoint) Sub(lhs, rhs *EllipticPoint) *EllipticPoint {
p.Set(lhs)
p.Arithmetic.Add(p, lhs, new(EllipticPoint).Neg(rhs))
return p
}
// Mul multiplies this point by the input scalar
func (p *EllipticPoint) Mul(point *EllipticPoint, scalar *Field) *EllipticPoint {
bytes := scalar.Bytes()
precomputed := [16]*EllipticPoint{}
precomputed[0] = new(EllipticPoint).Set(point).Identity()
precomputed[1] = new(EllipticPoint).Set(point)
for i := 2; i < 16; i += 2 {
precomputed[i] = new(EllipticPoint).Set(point).Double(precomputed[i>>1])
precomputed[i+1] = new(EllipticPoint).Set(point).Add(precomputed[i], point)
}
p.Identity()
for i := 0; i < 256; i += 4 {
// Brouwer / windowing method. window size of 4.
for j := 0; j < 4; j++ {
p.Double(p)
}
window := bytes[32-1-i>>3] >> (4 - i&0x04) & 0x0F
p.Add(p, precomputed[window])
}
return p
}
// Equal returns 1 if the two points are equal 0 otherwise.
func (p *EllipticPoint) Equal(rhs *EllipticPoint) int {
var x1, x2, y1, y2 Field
x1.Arithmetic = p.X.Arithmetic
x2.Arithmetic = p.X.Arithmetic
y1.Arithmetic = p.Y.Arithmetic
y2.Arithmetic = p.Y.Arithmetic
x1.Mul(p.X, rhs.Z)
x2.Mul(rhs.X, p.Z)
y1.Mul(p.Y, rhs.Z)
y2.Mul(rhs.Y, p.Z)
e1 := p.Z.IsZero()
e2 := rhs.Z.IsZero()
// Both at infinity or coordinates are the same
return (e1 & e2) | (^e1 & ^e2)&x1.Equal(&x2)&y1.Equal(&y2)
}
// Set copies clone into p
func (p *EllipticPoint) Set(clone *EllipticPoint) *EllipticPoint {
p.X = new(Field).Set(clone.X)
p.Y = new(Field).Set(clone.Y)
p.Z = new(Field).Set(clone.Z)
p.Params = clone.Params
p.Arithmetic = clone.Arithmetic
return p
}
// BigInt returns the x and y as big.Ints in affine
func (p *EllipticPoint) BigInt() (x, y *big.Int) {
t := new(EllipticPoint).Set(p)
p.Arithmetic.ToAffine(t, p)
x = t.X.BigInt()
y = t.Y.BigInt()
return
}
// SetBigInt creates a point from affine x, y
// and returns the point if it is on the curve
func (p *EllipticPoint) SetBigInt(x, y *big.Int) (*EllipticPoint, error) {
xx := &Field{
Params: p.Params.Gx.Params,
Arithmetic: p.Params.Gx.Arithmetic,
}
xx.SetBigInt(x)
yy := &Field{
Params: p.Params.Gx.Params,
Arithmetic: p.Params.Gx.Arithmetic,
}
yy.SetBigInt(y)
pp := new(EllipticPoint).Set(p)
zero := new(Field).Set(xx).SetZero()
one := new(Field).Set(xx).SetOne()
isIdentity := xx.IsZero() & yy.IsZero()
pp.X = xx.CMove(xx, zero, isIdentity)
pp.Y = yy.CMove(yy, zero, isIdentity)
pp.Z = one.CMove(one, zero, isIdentity)
if !p.Arithmetic.IsOnCurve(pp) && isIdentity == 0 {
return nil, fmt.Errorf("invalid coordinates")
}
return p.Set(pp), nil
}
// GetX returns the affine X coordinate
func (p *EllipticPoint) GetX() *Field {
t := new(EllipticPoint).Set(p)
p.Arithmetic.ToAffine(t, p)
return t.X
}
// GetY returns the affine Y coordinate
func (p *EllipticPoint) GetY() *Field {
t := new(EllipticPoint).Set(p)
p.Arithmetic.ToAffine(t, p)
return t.Y
}
// IsOnCurve determines if this point represents a valid curve point
func (p *EllipticPoint) IsOnCurve() bool {
return p.Arithmetic.IsOnCurve(p)
}
// ToAffine converts the point into affine coordinates
func (p *EllipticPoint) ToAffine(clone *EllipticPoint) *EllipticPoint {
p.Arithmetic.ToAffine(p, clone)
return p
}
// SumOfProducts computes the multi-exponentiation for the specified
// points and scalars and stores the result in `p`.
// Returns an error if the lengths of the arguments is not equal.
func (p *EllipticPoint) SumOfProducts(points []*EllipticPoint, scalars []*Field) (*EllipticPoint, error) {
const Upper = 256
const W = 4
const Windows = Upper / W // careful--use ceiling division in case this doesn't divide evenly
if len(points) != len(scalars) {
return nil, fmt.Errorf("length mismatch")
}
bucketSize := 1 << W
windows := make([]*EllipticPoint, Windows)
bytes := make([][32]byte, len(scalars))
buckets := make([]*EllipticPoint, bucketSize)
for i, scalar := range scalars {
bytes[i] = scalar.Bytes()
}
for i := range windows {
windows[i] = new(EllipticPoint).Set(p).Identity()
}
for i := 0; i < bucketSize; i++ {
buckets[i] = new(EllipticPoint).Set(p).Identity()
}
sum := new(EllipticPoint).Set(p)
for j := 0; j < len(windows); j++ {
for i := 0; i < bucketSize; i++ {
buckets[i].Identity()
}
for i := 0; i < len(scalars); i++ {
// j*W to get the nibble
// >> 3 to convert to byte, / 8
// (W * j & W) gets the nibble, mod W
// 1 << W - 1 to get the offset
index := bytes[i][j*W>>3] >> (W * j & W) & (1<<W - 1) // little-endian
buckets[index].Add(buckets[index], points[i])
}
sum.Identity()
for i := bucketSize - 1; i > 0; i-- {
sum.Add(sum, buckets[i])
windows[j].Add(windows[j], sum)
}
}
p.Identity()
for i := len(windows) - 1; i >= 0; i-- {
for j := 0; j < W; j++ {
p.Double(p)
}
p.Add(p, windows[i])
}
return p, nil
}