mirror of
https://github.com/emmansun/gmsm.git
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378 lines
8.9 KiB
Go
378 lines
8.9 KiB
Go
package bn256
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import (
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"crypto/rand"
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"errors"
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"io"
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"math/big"
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"sync"
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)
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func randomK(r io.Reader) (k *big.Int, err error) {
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for {
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k, err = rand.Int(r, Order)
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if err != nil || k.Sign() > 0 {
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return
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}
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}
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}
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// G1 is an abstract cyclic group. The zero value is suitable for use as the
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// output of an operation, but cannot be used as an input.
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type G1 struct {
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p *curvePoint
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}
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// Gen1 is the generator of G1.
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var Gen1 = &G1{curveGen}
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var g1GeneratorTable *[32 * 2]curvePointTable
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var g1GeneratorTableOnce sync.Once
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func (g *G1) generatorTable() *[32 * 2]curvePointTable {
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g1GeneratorTableOnce.Do(func() {
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g1GeneratorTable = new([32 * 2]curvePointTable)
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base := NewCurveGenerator()
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for i := 0; i < 32*2; i++ {
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g1GeneratorTable[i][0] = &curvePoint{}
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g1GeneratorTable[i][0].Set(base)
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g1GeneratorTable[i][1] = &curvePoint{}
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g1GeneratorTable[i][1].Double(g1GeneratorTable[i][0])
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g1GeneratorTable[i][2] = &curvePoint{}
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g1GeneratorTable[i][2].Add(g1GeneratorTable[i][1], base)
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g1GeneratorTable[i][3] = &curvePoint{}
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g1GeneratorTable[i][3].Double(g1GeneratorTable[i][1])
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g1GeneratorTable[i][4] = &curvePoint{}
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g1GeneratorTable[i][4].Add(g1GeneratorTable[i][3], base)
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g1GeneratorTable[i][5] = &curvePoint{}
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g1GeneratorTable[i][5].Double(g1GeneratorTable[i][2])
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g1GeneratorTable[i][6] = &curvePoint{}
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g1GeneratorTable[i][6].Add(g1GeneratorTable[i][5], base)
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g1GeneratorTable[i][7] = &curvePoint{}
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g1GeneratorTable[i][7].Double(g1GeneratorTable[i][3])
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g1GeneratorTable[i][8] = &curvePoint{}
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g1GeneratorTable[i][8].Add(g1GeneratorTable[i][7], base)
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g1GeneratorTable[i][9] = &curvePoint{}
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g1GeneratorTable[i][9].Double(g1GeneratorTable[i][4])
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g1GeneratorTable[i][10] = &curvePoint{}
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g1GeneratorTable[i][10].Add(g1GeneratorTable[i][9], base)
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g1GeneratorTable[i][11] = &curvePoint{}
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g1GeneratorTable[i][11].Double(g1GeneratorTable[i][5])
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g1GeneratorTable[i][12] = &curvePoint{}
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g1GeneratorTable[i][12].Add(g1GeneratorTable[i][11], base)
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g1GeneratorTable[i][13] = &curvePoint{}
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g1GeneratorTable[i][13].Double(g1GeneratorTable[i][6])
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g1GeneratorTable[i][14] = &curvePoint{}
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g1GeneratorTable[i][14].Add(g1GeneratorTable[i][13], base)
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base.Double(base)
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base.Double(base)
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base.Double(base)
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base.Double(base)
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}
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})
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return g1GeneratorTable
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}
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// RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r.
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func RandomG1(r io.Reader) (*big.Int, *G1, error) {
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k, err := randomK(r)
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if err != nil {
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return nil, nil, err
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}
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g1, err := new(G1).ScalarBaseMult(NormalizeScalar(k.Bytes()))
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return k, g1, err
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}
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func (g *G1) String() string {
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return "sm9.G1" + g.p.String()
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}
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func NormalizeScalar(scalar []byte) []byte {
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if len(scalar) == 32 {
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return scalar
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}
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s := new(big.Int).SetBytes(scalar)
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if len(scalar) > 32 {
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s.Mod(s, Order)
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}
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out := make([]byte, 32)
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return s.FillBytes(out)
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}
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// ScalarBaseMult sets e to scaler*g where g is the generator of the group and then
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// returns e.
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func (e *G1) ScalarBaseMult(scalar []byte) (*G1, error) {
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if len(scalar) != 32 {
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return nil, errors.New("invalid scalar length")
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}
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if e.p == nil {
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e.p = &curvePoint{}
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}
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//e.p.Mul(curveGen, k)
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tables := e.generatorTable()
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// This is also a scalar multiplication with a four-bit window like in
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// ScalarMult, but in this case the doublings are precomputed. The value
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// [windowValue]G added at iteration k would normally get doubled
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// (totIterations-k)×4 times, but with a larger precomputation we can
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// instead add [2^((totIterations-k)×4)][windowValue]G and avoid the
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// doublings between iterations.
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t := NewCurvePoint()
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e.p.SetInfinity()
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tableIndex := len(tables) - 1
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for _, byte := range scalar {
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windowValue := byte >> 4
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tables[tableIndex].Select(t, windowValue)
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e.p.Add(e.p, t)
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tableIndex--
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windowValue = byte & 0b1111
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tables[tableIndex].Select(t, windowValue)
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e.p.Add(e.p, t)
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tableIndex--
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}
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return e, nil
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}
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// ScalarMult sets e to a*k and then returns e.
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func (e *G1) ScalarMult(a *G1, scalar []byte) (*G1, error) {
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if e.p == nil {
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e.p = &curvePoint{}
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}
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//e.p.Mul(a.p, k)
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// Compute a curvePointTable for the base point a.
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var table = curvePointTable{NewCurvePoint(), NewCurvePoint(), NewCurvePoint(),
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NewCurvePoint(), NewCurvePoint(), NewCurvePoint(), NewCurvePoint(),
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NewCurvePoint(), NewCurvePoint(), NewCurvePoint(), NewCurvePoint(),
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NewCurvePoint(), NewCurvePoint(), NewCurvePoint(), NewCurvePoint()}
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table[0].Set(a.p)
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for i := 1; i < 15; i += 2 {
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table[i].Double(table[i/2])
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table[i+1].Add(table[i], a.p)
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}
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// Instead of doing the classic double-and-add chain, we do it with a
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// four-bit window: we double four times, and then add [0-15]P.
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t := &G1{NewCurvePoint()}
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e.p.SetInfinity()
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for i, byte := range scalar {
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// No need to double on the first iteration, as p is the identity at
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// this point, and [N]∞ = ∞.
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if i != 0 {
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e.Double(e)
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e.Double(e)
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e.Double(e)
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e.Double(e)
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}
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windowValue := byte >> 4
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table.Select(t.p, windowValue)
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e.Add(e, t)
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e.Double(e)
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e.Double(e)
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e.Double(e)
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e.Double(e)
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windowValue = byte & 0b1111
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table.Select(t.p, windowValue)
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e.Add(e, t)
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}
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return e, nil
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}
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// Add sets e to a+b and then returns e.
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func (e *G1) Add(a, b *G1) *G1 {
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if e.p == nil {
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e.p = &curvePoint{}
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}
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e.p.Add(a.p, b.p)
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return e
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}
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// Double sets e to [2]a and then returns e.
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func (e *G1) Double(a *G1) *G1 {
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if e.p == nil {
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e.p = &curvePoint{}
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}
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e.p.Double(a.p)
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return e
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}
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// Neg sets e to -a and then returns e.
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func (e *G1) Neg(a *G1) *G1 {
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if e.p == nil {
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e.p = &curvePoint{}
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}
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e.p.Neg(a.p)
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return e
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}
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// Set sets e to a and then returns e.
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func (e *G1) Set(a *G1) *G1 {
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if e.p == nil {
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e.p = &curvePoint{}
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}
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e.p.Set(a.p)
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return e
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}
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// Marshal converts e to a byte slice.
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func (e *G1) Marshal() []byte {
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// Each value is a 256-bit number.
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const numBytes = 256 / 8
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ret := make([]byte, numBytes*2)
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e.fillBytes(ret)
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return ret
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}
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// MarshalUncompressed converts e to a byte slice with prefix
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func (e *G1) MarshalUncompressed() []byte {
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// Each value is a 256-bit number.
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const numBytes = 256 / 8
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ret := make([]byte, numBytes*2+1)
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ret[0] = 4
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e.fillBytes(ret[1:])
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return ret
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}
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// MarshalCompressed converts e to a byte slice with compress prefix.
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// If the point is not on the curve (or is the conventional point at infinity), the behavior is undefined.
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func (e *G1) MarshalCompressed() []byte {
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// Each value is a 256-bit number.
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const numBytes = 256 / 8
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ret := make([]byte, numBytes+1)
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if e.p == nil {
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e.p = &curvePoint{}
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}
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e.p.MakeAffine()
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temp := &gfP{}
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montDecode(temp, &e.p.y)
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temp.Marshal(ret[1:])
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ret[0] = (ret[numBytes] & 1) | 2
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montDecode(temp, &e.p.x)
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temp.Marshal(ret[1:])
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return ret
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}
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// UnmarshalCompressed sets e to the result of converting the output of Marshal back into
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// a group element and then returns e.
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func (e *G1) UnmarshalCompressed(data []byte) ([]byte, error) {
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// Each value is a 256-bit number.
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const numBytes = 256 / 8
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if len(data) < 1+numBytes {
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return nil, errors.New("sm9.G1: not enough data")
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}
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if data[0] != 2 && data[0] != 3 { // compressed form
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return nil, errors.New("sm9.G1: invalid point compress byte")
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}
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if e.p == nil {
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e.p = &curvePoint{}
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} else {
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e.p.x.Set(zero)
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e.p.y.Set(zero)
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}
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e.p.x.Unmarshal(data[1:])
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montEncode(&e.p.x, &e.p.x)
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x3 := e.p.polynomial(&e.p.x)
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e.p.y.Sqrt(x3)
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montDecode(x3, &e.p.y)
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if byte(x3[0]&1) != data[0]&1 {
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gfpNeg(&e.p.y, &e.p.y)
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}
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if e.p.x.Equal(zero) == 1 && e.p.y.Equal(zero) == 1 {
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// This is the point at infinity.
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e.p.SetInfinity()
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} else {
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e.p.z.Set(one)
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e.p.t.Set(one)
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if !e.p.IsOnCurve() {
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return nil, errors.New("sm9.G1: malformed point")
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}
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}
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return data[numBytes+1:], nil
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}
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func (e *G1) fillBytes(buffer []byte) {
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const numBytes = 256 / 8
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if e.p == nil {
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e.p = &curvePoint{}
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}
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e.p.MakeAffine()
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if e.p.IsInfinity() {
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return
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}
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temp := &gfP{}
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montDecode(temp, &e.p.x)
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temp.Marshal(buffer)
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montDecode(temp, &e.p.y)
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temp.Marshal(buffer[numBytes:])
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}
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// Unmarshal sets e to the result of converting the output of Marshal back into
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// a group element and then returns e.
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func (e *G1) Unmarshal(m []byte) ([]byte, error) {
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// Each value is a 256-bit number.
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const numBytes = 256 / 8
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if len(m) < 2*numBytes {
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return nil, errors.New("sm9.G1: not enough data")
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}
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if e.p == nil {
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e.p = &curvePoint{}
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} else {
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e.p.x.Set(zero)
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e.p.y.Set(zero)
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}
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e.p.x.Unmarshal(m)
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e.p.y.Unmarshal(m[numBytes:])
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montEncode(&e.p.x, &e.p.x)
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montEncode(&e.p.y, &e.p.y)
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if e.p.x.Equal(zero) == 1 && e.p.y.Equal(zero) == 1 {
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// This is the point at infinity.
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e.p.SetInfinity()
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} else {
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e.p.z.Set(one)
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e.p.t.Set(one)
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if !e.p.IsOnCurve() {
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return nil, errors.New("sm9.G1: malformed point")
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}
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}
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return m[2*numBytes:], nil
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}
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// Equal compare e and other
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func (e *G1) Equal(other *G1) bool {
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if e.p == nil && other.p == nil {
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return true
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}
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return e.p.Equal(other.p)
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}
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// IsOnCurve returns true if e is on the curve.
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func (e *G1) IsOnCurve() bool {
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return e.p.IsOnCurve()
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}
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