First cut of bulletproofs
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package bulletproofs
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import (
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"cwtch.im/tapir/primitives/core"
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"encoding/json"
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"git.openprivacy.ca/openprivacy/libricochet-go/log"
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"github.com/bwesterb/go-ristretto"
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"strconv"
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)
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// InnerProductProof encapsulates an inner product proof
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type InnerProductProof struct {
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L core.PointVector
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R core.PointVector
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A core.Scalar
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B core.Scalar
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}
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// ProveInnerProduct generates a proof for <a,b>, the inner product of a and b
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func ProveInnerProduct(a, b core.ScalarVector, u core.Point, P *ristretto.Point, G, H core.GeneratorVector, transcript *core.Transcript) InnerProductProof {
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n := len(a)
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transcript.AddToTranscript("n", []byte(strconv.Itoa(n)))
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Lvec := core.PointVector{}
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Rvec := core.PointVector{}
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Gbytes, _ := json.Marshal(G)
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transcript.AddToTranscript("G", Gbytes)
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Hbytes, _ := json.Marshal(H)
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transcript.AddToTranscript("H", Hbytes)
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transcript.AddToTranscript("P'", P.Bytes())
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for n != 1 {
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np := n / 2
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aL, aR := a[:np], a[np:]
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bL, bR := b[:np], b[np:]
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GL, GR := G[:np], G[np:]
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HL, HR := H[:np], H[np:]
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cL := core.InnerProduct(aL, bR)
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cR := core.InnerProduct(aR, bL)
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L := core.MultiExp(append(aL.Join(bR), cL), append(GR.Join(HL), u))
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R := core.MultiExp(append(aR.Join(bL), cR), append(GL.Join(HR), u))
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transcript.AddToTranscript("L", L.Bytes())
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Lvec = append(Lvec, L)
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transcript.AddToTranscript("R", R.Bytes())
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Rvec = append(Rvec, R)
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u := transcript.CommitToTranscriptScalar("u")
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uinv := new(ristretto.Scalar).Inverse(u)
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for i := 0; i < len(aL); i++ {
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aL_ := new(ristretto.Scalar).Mul(aL[i], u)
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aL[i] = aL_.Add(aL_, new(ristretto.Scalar).Mul(aR[i], uinv))
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bL_ := new(ristretto.Scalar).Mul(bL[i], uinv)
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bL[i] = bL_.Add(bL_, new(ristretto.Scalar).Mul(bR[i], u))
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GL[i] = core.MultiExp(core.ScalarVector{uinv, u}, core.GeneratorVector{GL[i], GR[i]})
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HL[i] = core.MultiExp(core.ScalarVector{u, uinv}, core.GeneratorVector{HL[i], HR[i]})
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}
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x2 := new(ristretto.Scalar).Square(u)
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P_ := new(ristretto.Point).ScalarMult(L, x2)
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P_.Add(P_, P)
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P_.Add(P_, new(ristretto.Point).ScalarMult(R, new(ristretto.Scalar).Inverse(x2)))
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P = P_
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transcript.AddToTranscript("P'", P.Bytes())
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a = aL
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b = bL
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G = GL
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H = HL
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Gbytes, _ := json.Marshal(G)
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transcript.AddToTranscript("G", Gbytes)
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Hbytes, _ := json.Marshal(H)
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transcript.AddToTranscript("H", Hbytes)
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n = np
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}
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return InnerProductProof{Lvec, Rvec, a[0], b[0]}
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}
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// Verify checks the given inner product proof
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func Verify(proof InnerProductProof, n int, u, P *ristretto.Point, G, H core.GeneratorVector, transcript *core.Transcript) bool {
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transcript.AddToTranscript("n", []byte(strconv.Itoa(n)))
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np := n / 2
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Gbytes, _ := json.Marshal(G)
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transcript.AddToTranscript("G", Gbytes)
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Hbytes, _ := json.Marshal(H)
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transcript.AddToTranscript("H", Hbytes)
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transcript.AddToTranscript("P'", P.Bytes())
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for i := range proof.L {
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GL, GR := G[:np], G[np:]
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HL, HR := H[:np], H[np:]
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transcript.AddToTranscript("L", proof.L[i].Bytes())
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transcript.AddToTranscript("R", proof.R[i].Bytes())
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x := transcript.CommitToTranscriptScalar("u")
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xinv := new(ristretto.Scalar).Inverse(x)
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for j := 0; j < np; j++ {
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GL[j] = core.MultiExp(core.ScalarVector{xinv, x}, core.GeneratorVector{GL[j], GR[j]})
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HL[j] = core.MultiExp(core.ScalarVector{x, xinv}, core.GeneratorVector{HL[j], HR[j]})
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}
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x2 := new(ristretto.Scalar).Square(x)
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P_ := new(ristretto.Point).ScalarMult(proof.L[i], x2)
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P_.Add(P_, P)
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P_.Add(P_, new(ristretto.Point).ScalarMult(proof.R[i], new(ristretto.Scalar).Inverse(x2)))
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P = P_
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transcript.AddToTranscript("P'", P.Bytes())
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G = GL
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H = HL
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Gbytes, _ := json.Marshal(G)
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transcript.AddToTranscript("G", Gbytes)
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Hbytes, _ := json.Marshal(H)
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transcript.AddToTranscript("H", Hbytes)
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np = np / 2
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}
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c := new(ristretto.Scalar).Mul(proof.A, proof.B)
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P_ := core.MultiExp(core.ScalarVector{proof.A, proof.B, c}, core.GeneratorVector{G[0], H[0], u})
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log.Debugf("P:%v\nP':%v\n", P, P_)
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return P.Equals(P_)
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}
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package bulletproofs
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import (
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"cwtch.im/tapir/primitives/core"
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"git.openprivacy.ca/openprivacy/libricochet-go/log"
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"github.com/bwesterb/go-ristretto"
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"testing"
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)
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func assert(t *testing.T, expected *ristretto.Scalar, actual *ristretto.Scalar) {
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if expected.Equals(actual) {
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t.Logf("inner_product matched: %v", actual)
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} else {
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t.Fatalf("c should be %v instead: %v", expected, actual)
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}
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}
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func Test_inner_product(t *testing.T) {
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one := new(ristretto.Scalar).SetOne()
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zero := new(ristretto.Scalar).SetZero()
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a := core.ScalarVector{one, zero, one, zero}
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b := core.ScalarVector{zero, one, zero, one}
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c := core.InnerProduct(a, b)
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assert(t, zero, c)
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a = core.ScalarVector{one, one, one, zero}
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b = core.ScalarVector{one, one, zero, one}
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c = core.InnerProduct(a, b)
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assert(t, new(ristretto.Scalar).Add(one, one), c)
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}
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func TestProveInnerProduct(t *testing.T) {
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log.SetLevel(log.LevelDebug)
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one := new(ristretto.Scalar).SetOne()
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zero := new(ristretto.Scalar).SetZero()
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a := core.ScalarVector{one, zero, one, one}
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b := core.ScalarVector{zero, one, one, one}
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c := core.InnerProduct(a, b)
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G := make(core.GeneratorVector, 4)
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H := make(core.GeneratorVector, 4)
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for i := 0; i < 4; i++ {
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G[i] = new(ristretto.Point).Rand()
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H[i] = new(ristretto.Point).Rand()
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}
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u := new(ristretto.Point).Rand()
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P_ := core.MultiExp(append(a.Join(b), c), append(G.Join(H), u))
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proverTranscript := core.NewTranscript("test_innerproductproof")
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verifierTranscript := core.NewTranscript("test_innerproductproof")
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proof := ProveInnerProduct(a, b, u, new(ristretto.Point).Set(P_), core.CopyVector(G), core.CopyVector(H), proverTranscript)
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if Verify(proof, 4, u, new(ristretto.Point).Set(P_), core.CopyVector(G), core.CopyVector(H), verifierTranscript) {
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t.Logf("Inner Product Proof Passed!")
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} else {
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t.Logf("%v\n\n%v\n", proverTranscript.OutputTranscriptToAudit(), verifierTranscript.OutputTranscriptToAudit())
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t.Fatalf("Inner Product Proof Failed!")
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}
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}
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package bulletproofs
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import (
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"cwtch.im/tapir/primitives/core"
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"git.openprivacy.ca/openprivacy/libricochet-go/log"
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"github.com/bwesterb/go-ristretto"
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"math/big"
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)
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// RangeProof encapsulates a proof that V = [0, max) where max is defined by the Setup function
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type RangeProof struct {
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A *ristretto.Point
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S *ristretto.Point
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T1 *ristretto.Point
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T2 *ristretto.Point
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TauX *ristretto.Scalar
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InnerProduct *ristretto.Scalar
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Mu *ristretto.Scalar
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IPP InnerProductProof
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V *ristretto.Point
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}
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// CommitmentsParams encapsulates the commitment parameters for a given range proof
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type CommitmentsParams struct {
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G core.GeneratorVector
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H core.GeneratorVector
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u *ristretto.Point
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g *ristretto.Point
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h *ristretto.Point
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max int
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}
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// Setup generates multiple independent commitment parameters from the underlying transcript
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func Setup(max int, transcript *core.Transcript) (c CommitmentsParams) {
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c.G = transcript.CommitToGenerators("G", int(max))
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c.H = transcript.CommitToGenerators("H", int(max))
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c.u = transcript.CommitToGenerator("u")
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c.g = transcript.CommitToGenerator("g")
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c.h = transcript.CommitToGenerator("h")
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c.max = max
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return
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}
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// GenerateRangeProof creates a valid rangeproof that value is within [0,max) under the given transcript
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// It returns the rangeproof and a random scalar "gamma" that can be used to open V, the commitement to v vGgH
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func GenerateRangeProof(value int32, c CommitmentsParams, transcript *core.Transcript) (RangeProof, *ristretto.Scalar) {
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one := new(ristretto.Scalar).SetOne()
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two := new(ristretto.Scalar).Add(one, one)
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two_n := core.PowerVector(two, c.max)
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gamma := new(ristretto.Scalar).Rand()
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aL := valueToVector(value, c.max)
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aR := core.VectorAddScalar(aL, new(ristretto.Scalar).Neg(one))
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alpha := new(ristretto.Scalar).Rand()
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vs := new(ristretto.Scalar).SetBigInt(big.NewInt(int64(value)))
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V := core.MultiExp(core.ScalarVector{gamma, vs}, core.GeneratorVector{c.h, c.g})
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A := core.MultiExp(append(aL.Join(aR), alpha), append(c.G.Join(c.H), c.h))
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Sl := make(core.ScalarVector, c.max)
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Sr := make(core.ScalarVector, c.max)
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for i := 0; i < c.max; i++ {
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Sl[i] = new(ristretto.Scalar).Rand()
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Sr[i] = new(ristretto.Scalar).Rand()
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}
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p := new(ristretto.Scalar).Rand()
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S := core.MultiExp(append(Sl.Join(Sr), p), append(c.G.Join(c.H), c.h))
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transcript.AddToTranscript("A", A.Bytes())
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transcript.AddToTranscript("S", S.Bytes())
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y := transcript.CommitToTranscriptScalar("y")
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z := transcript.CommitToTranscriptScalar("z")
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y_n := core.PowerVector(y, c.max)
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z2 := new(ristretto.Scalar).Square(z)
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l0 := core.VectorAddScalar(aL, new(ristretto.Scalar).Neg(z))
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//l1 == Sr
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r0 := core.EntrywiseSum(core.EntryWiseProduct(y_n, core.VectorAddScalar(aR, z)), core.VectorMulScalar(two_n, z2))
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r1 := core.EntryWiseProduct(Sr, y_n)
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t0 := new(ristretto.Scalar).Add(new(ristretto.Scalar).Mul(z2, vs), delta(y_n, z, c.max))
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t1 := new(ristretto.Scalar).Add(core.InnerProduct(Sl, r0), core.InnerProduct(l0, r1))
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t2 := core.InnerProduct(Sl, r1)
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tau1 := new(ristretto.Scalar).Rand()
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tau2 := new(ristretto.Scalar).Rand()
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T1 := core.MultiExp(core.ScalarVector{t1, tau1}, core.GeneratorVector{c.g, c.h})
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T2 := core.MultiExp(core.ScalarVector{t2, tau2}, core.GeneratorVector{c.g, c.h})
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transcript.AddToTranscript("T1", T1.Bytes())
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transcript.AddToTranscript("T2", T2.Bytes())
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x := transcript.CommitToTranscriptScalar("x")
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// T(X) = t0 + t1x + t2x
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TX := new(ristretto.Scalar).Set(t0)
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TX.Add(TX, new(ristretto.Scalar).Mul(t1, x))
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TX.Add(TX, new(ristretto.Scalar).Mul(t2, new(ristretto.Scalar).Square(x)))
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l := core.EntrywiseSum(core.VectorAddScalar(aL, new(ristretto.Scalar).Neg(z)), core.VectorMulScalar(Sl, x))
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_r := core.EntrywiseSum(core.VectorAddScalar(aR, z), core.VectorMulScalar(Sr, x))
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r := core.EntrywiseSum(core.EntryWiseProduct(y_n, _r), core.VectorMulScalar(two_n, z2))
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iplr := core.InnerProduct(l, r)
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log.Debugf("T(X) = %v", TX)
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log.Debugf("ipp = %v", iplr)
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log.Debugf("equal: %v", TX.Equals(iplr))
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// generate h'
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H_ := make(core.GeneratorVector, c.max)
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H_[0] = c.H[0]
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for i := 1; i < c.max; i++ {
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H_[i] = new(ristretto.Point).ScalarMult(c.H[i], new(ristretto.Scalar).Inverse(y_n[i]))
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}
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P := core.MultiExp(l.Join(r), c.G.Join(H_))
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log.Debugf("P: %v", P)
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uP := new(ristretto.Point).Add(P, new(ristretto.Point).ScalarMult(c.u, iplr))
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log.Debugf("uP: %v", uP)
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ipp := ProveInnerProduct(l, r, c.u, new(ristretto.Point).Set(uP), core.CopyVector(c.G), core.CopyVector(H_), transcript)
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taux := new(ristretto.Scalar).Mul(tau2, new(ristretto.Scalar).Square(x))
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taux = taux.Add(taux, new(ristretto.Scalar).Mul(tau1, x))
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taux = taux.Add(taux, new(ristretto.Scalar).Mul(z2, gamma))
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mu := new(ristretto.Scalar).Add(alpha, new(ristretto.Scalar).Mul(p, x))
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return RangeProof{A, S, T1, T2, taux, iplr, mu, ipp, V}, gamma
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}
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// VerifyRangeProof returns true if the given proof passes all the checks for a given set of commitment parameters
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// and the given transcript
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func VerifyRangeProof(proof RangeProof, c CommitmentsParams, transcript *core.Transcript) bool {
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one := new(ristretto.Scalar).SetOne()
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two := new(ristretto.Scalar).Add(one, one)
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two_n := core.PowerVector(two, c.max)
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transcript.AddToTranscript("A", proof.A.Bytes())
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transcript.AddToTranscript("S", proof.S.Bytes())
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y := transcript.CommitToTranscriptScalar("y")
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z := transcript.CommitToTranscriptScalar("z")
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transcript.AddToTranscript("T1", proof.T1.Bytes())
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transcript.AddToTranscript("T2", proof.T2.Bytes())
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x := transcript.CommitToTranscriptScalar("x")
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y_n := core.PowerVector(y, c.max)
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// generate h'
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H_ := make(core.GeneratorVector, c.max)
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H_[0] = c.H[0]
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for i := 1; i < c.max; i++ {
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H_[i] = new(ristretto.Point).ScalarMult(c.H[i], new(ristretto.Scalar).Inverse(y_n[i]))
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}
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// check t = t(x) = t0 + t1.x + t1.x^2
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lhs := core.MultiExp(core.ScalarVector{proof.InnerProduct, proof.TauX}, core.GeneratorVector{c.g, c.h})
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rhs := core.MultiExp(core.ScalarVector{new(ristretto.Scalar).Square(z), delta(y_n, z, c.max), x, new(ristretto.Scalar).Square(x)}, core.GeneratorVector{proof.V, c.g, proof.T1, proof.T2})
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log.Debugf("lhs: %v", lhs)
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log.Debugf("rhs: %v", rhs)
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log.Debugf("equal: %v", lhs.Equals(rhs))
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if lhs.Equals(rhs) {
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// compute P
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negz := new(ristretto.Scalar).Neg(z)
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negzG := new(ristretto.Point).SetZero()
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for _, gen := range c.G {
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negzG = negzG.Add(negzG, new(ristretto.Point).ScalarMult(gen, negz))
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}
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mul := core.EntrywiseSum(core.VectorMulScalar(y_n, z), core.VectorMulScalar(two_n, new(ristretto.Scalar).Square(z)))
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Pr := new(ristretto.Point).Set(proof.A)
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Pr = Pr.Add(Pr, new(ristretto.Point).ScalarMult(proof.S, x))
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Pr = Pr.Add(Pr, negzG)
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Pr = Pr.Add(Pr, core.MultiExp(mul, H_))
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Pl := new(ristretto.Point).Sub(Pr, new(ristretto.Point).ScalarMult(c.h, proof.Mu))
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// check inner product
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uP := new(ristretto.Point).Add(Pl, new(ristretto.Point).ScalarMult(c.u, proof.InnerProduct))
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return Verify(proof.IPP, c.max, c.u, new(ristretto.Point).Set(uP), core.CopyVector(c.G), core.CopyVector(H_), transcript)
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}
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return false
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}
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func delta(y_n core.ScalarVector, z core.Scalar, max int) core.Scalar {
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one := new(ristretto.Scalar).SetOne()
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// (z-z^2)
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z2 := new(ristretto.Scalar).Square(z)
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result := new(ristretto.Scalar).Sub(z, z2)
|
||||
// (z-z^2) * <1^n,y^n>
|
||||
result.Mul(result, core.InnerProduct(core.IdentityVector(max), y_n))
|
||||
two := new(ristretto.Scalar).Add(one, one)
|
||||
two_n := core.PowerVector(two, max)
|
||||
// (z-z^2) * <1^n,y^n> - z^3 *<1n,2n>
|
||||
z3 := new(ristretto.Scalar).Mul(z2, z)
|
||||
return result.Sub(result, new(ristretto.Scalar).Mul(z3, core.InnerProduct(core.IdentityVector(max), two_n)))
|
||||
}
|
||||
|
||||
func valueToVector(value int32, max int) core.ScalarVector {
|
||||
one := new(ristretto.Scalar).SetOne()
|
||||
zero := new(ristretto.Scalar).SetZero()
|
||||
result := core.ScalarVector{}
|
||||
for len(result) != max {
|
||||
v := value & 0x0001
|
||||
if v == 1 {
|
||||
result = append(result, one)
|
||||
} else {
|
||||
result = append(result, zero)
|
||||
}
|
||||
value = value >> 1
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
package bulletproofs
|
||||
|
||||
import (
|
||||
"cwtch.im/tapir/primitives/core"
|
||||
"encoding/json"
|
||||
"git.openprivacy.ca/openprivacy/libricochet-go/log"
|
||||
"testing"
|
||||
)
|
||||
|
||||
func TestProove(t *testing.T) {
|
||||
log.SetLevel(log.LevelDebug)
|
||||
|
||||
proverTranscript := core.NewTranscript("rangeproof")
|
||||
verifierTranscript := core.NewTranscript("rangeproof")
|
||||
|
||||
rangeproof, _ := GenerateRangeProof(10, Setup(32, proverTranscript), proverTranscript)
|
||||
if VerifyRangeProof(rangeproof, Setup(32, verifierTranscript), verifierTranscript) == true {
|
||||
t.Logf("Range Proof Passed!")
|
||||
t.Logf("%v\n\n%v\n", proverTranscript.OutputTranscriptToAudit(), verifierTranscript.OutputTranscriptToAudit())
|
||||
jsonProof, _ := json.Marshal(rangeproof)
|
||||
t.Logf("RangeProof: %s", jsonProof)
|
||||
} else {
|
||||
t.Logf("%v\n\n%v\n", proverTranscript.OutputTranscriptToAudit(), verifierTranscript.OutputTranscriptToAudit())
|
||||
t.Fatalf("Failed to Verify Range Proof")
|
||||
}
|
||||
|
||||
}
|
||||
|
|
@ -0,0 +1,137 @@
|
|||
package core
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"github.com/bwesterb/go-ristretto"
|
||||
)
|
||||
|
||||
// Scalar is short hand for a ristretto scalar
|
||||
type Scalar *ristretto.Scalar
|
||||
|
||||
// Point is short hand of a ristretto point
|
||||
type Point *ristretto.Point
|
||||
|
||||
// ScalarVector explicit type checking
|
||||
type ScalarVector []Scalar
|
||||
|
||||
// PointVector explicit type checking
|
||||
type PointVector []*ristretto.Point
|
||||
|
||||
// GeneratorVector explicit type checking
|
||||
type GeneratorVector []*ristretto.Point
|
||||
|
||||
// CopyVector safely copies a vector
|
||||
func CopyVector(G GeneratorVector) GeneratorVector {
|
||||
H := make(GeneratorVector, len(G))
|
||||
for i, g := range G {
|
||||
H[i] = new(ristretto.Point).Set(g)
|
||||
}
|
||||
return H
|
||||
}
|
||||
|
||||
// InnerProduct takes the inner product of a and b i.e. <a,b>
|
||||
func InnerProduct(a, b ScalarVector) *ristretto.Scalar {
|
||||
if len(a) != len(b) {
|
||||
panic(fmt.Sprintf("len(a) = %v ; len(b) = %v;", len(a), len(b)))
|
||||
}
|
||||
|
||||
result := new(ristretto.Scalar).SetZero()
|
||||
for i, ai := range a {
|
||||
result.Add(result, new(ristretto.Scalar).Mul(ai, b[i]))
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// MultiExp takes in a vector of scalars = {a,b,c...} and a vector of generator = {A,B,C...} and outputs
|
||||
// {aA,bB,cC}
|
||||
func MultiExp(a ScalarVector, G GeneratorVector) *ristretto.Point {
|
||||
if len(a) != len(G) {
|
||||
panic(fmt.Sprintf("len(a) = %v ; len(b) = %v;", len(a), len(G)))
|
||||
}
|
||||
result := new(ristretto.Point).SetZero()
|
||||
for i, ai := range a {
|
||||
aG := new(ristretto.Point).ScalarMult(G[i], ai)
|
||||
result = new(ristretto.Point).Add(result, aG)
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// Join is defined for a vector of Scalars
|
||||
func (a ScalarVector) Join(b ScalarVector) ScalarVector {
|
||||
list := make(ScalarVector, len(a)+len(b))
|
||||
for i := 0; i < len(a); i++ {
|
||||
list[i] = new(ristretto.Scalar).Set(a[i])
|
||||
}
|
||||
for i := len(a); i < len(b)+len(b); i++ {
|
||||
list[i] = new(ristretto.Scalar).Set(b[i-len(a)])
|
||||
}
|
||||
return list
|
||||
}
|
||||
|
||||
// Join as defined for a vector of Generators
|
||||
func (a GeneratorVector) Join(b GeneratorVector) GeneratorVector {
|
||||
list := make(GeneratorVector, len(a)+len(b))
|
||||
for i := 0; i < len(a); i++ {
|
||||
list[i] = new(ristretto.Point).Set(a[i])
|
||||
}
|
||||
for i := len(a); i < len(b)+len(b); i++ {
|
||||
list[i] = new(ristretto.Point).Set(b[i-len(a)])
|
||||
}
|
||||
return list
|
||||
}
|
||||
|
||||
// VectorAddScalar takes in a vector v = {a,b,c..} and a scalar s and outputs {a+s,b+s,c+s....}
|
||||
func VectorAddScalar(vector ScalarVector, scalar *ristretto.Scalar) ScalarVector {
|
||||
result := make(ScalarVector, len(vector))
|
||||
for i := range vector {
|
||||
result[i] = new(ristretto.Scalar).Add(vector[i], scalar)
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// VectorMulScalar takes in a vector v = {a,b,c..} and a scalar s and outputs {as,bs,cs....}
|
||||
func VectorMulScalar(vector ScalarVector, scalar *ristretto.Scalar) ScalarVector {
|
||||
result := make(ScalarVector, len(vector))
|
||||
for i := range vector {
|
||||
result[i] = new(ristretto.Scalar).Mul(vector[i], scalar)
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// EntrywiseSum takes the entry wise sum of two vectors
|
||||
func EntrywiseSum(vector ScalarVector, vector2 ScalarVector) ScalarVector {
|
||||
result := make(ScalarVector, len(vector))
|
||||
for i, v := range vector {
|
||||
result[i] = new(ristretto.Scalar).Add(v, vector2[i])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// EntryWiseProduct takes the entry wise product of two vectors
|
||||
func EntryWiseProduct(vector ScalarVector, vector2 ScalarVector) ScalarVector {
|
||||
result := make(ScalarVector, len(vector))
|
||||
for i, v := range vector {
|
||||
result[i] = new(ristretto.Scalar).Mul(v, vector2[i])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// IdentityVector is a convenience function to generate a vector v = {1,1,1...1}
|
||||
func IdentityVector(n int) ScalarVector {
|
||||
result := make(ScalarVector, n)
|
||||
for i := 0; i < n; i++ {
|
||||
result[i] = new(ristretto.Scalar).SetOne()
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// PowerVector creates a vector v = {1,x,x^2,x^3..x^n}
|
||||
func PowerVector(x *ristretto.Scalar, n int) ScalarVector {
|
||||
result := make(ScalarVector, n)
|
||||
result[0] = new(ristretto.Scalar).SetOne()
|
||||
result[1] = new(ristretto.Scalar).Set(x)
|
||||
for i := 1; i < n; i++ {
|
||||
result[i] = new(ristretto.Scalar).Mul(result[i-1], result[1])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
|
@ -82,6 +82,22 @@ func (t *Transcript) CommitToPRNG(label string) PRNG {
|
|||
return PRNG{prng: prng}
|
||||
}
|
||||
|
||||
// CommitToGenerator derives a verifiably random generator from the transcript
|
||||
func (t *Transcript) CommitToGenerator(label string) *ristretto.Point {
|
||||
c := t.CommitToTranscript(label)
|
||||
cs := [32]byte{}
|
||||
copy(cs[:], c[:])
|
||||
return new(ristretto.Point).SetElligator(&cs)
|
||||
}
|
||||
|
||||
// CommitToGenerators derives a set of verifiably random generators from the transcript
|
||||
func (t *Transcript) CommitToGenerators(label string, n int) (generators []*ristretto.Point) {
|
||||
for i := 0; i < n; i++ {
|
||||
generators = append(generators, t.CommitToGenerator(fmt.Sprintf("%v-%d", label, i)))
|
||||
}
|
||||
return generators
|
||||
}
|
||||
|
||||
// CommitToTranscriptScalar is a convenience method for CommitToTranscript which returns a ristretto Scalar
|
||||
func (t *Transcript) CommitToTranscriptScalar(label string) *ristretto.Scalar {
|
||||
c := t.CommitToTranscript(label)
|
||||
|
|
|
|||
Loading…
Reference in New Issue