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crypto/bulletproof/range_verifier.go

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+package bulletproof
+
+import (
+	"github.com/gtank/merlin"
+	"github.com/pkg/errors"
+
+	"github.com/onsonr/hway/crypto/core/curves"
+)
+
+// RangeVerifier is the struct used to verify RangeProofs
+// It specifies which curve to use and holds precomputed generators
+// See NewRangeVerifier() for verifier initialization.
+type RangeVerifier struct {
+	curve       curves.Curve
+	generators  *ippGenerators
+	ippVerifier *InnerProductVerifier
+}
+
+// NewRangeVerifier initializes a new verifier
+// It uses the specified domain to generate generators for vectors of at most maxVectorLength
+// A verifier can be used to verify range proofs for vectors of length less than or equal to maxVectorLength
+// A verifier is defined by an explicit curve.
+func NewRangeVerifier(maxVectorLength int, rangeDomain, ippDomain []byte, curve curves.Curve) (*RangeVerifier, error) {
+	generators, err := getGeneratorPoints(maxVectorLength, rangeDomain, curve)
+	if err != nil {
+		return nil, errors.Wrap(err, "range NewRangeProver")
+	}
+	ippVerifier, err := NewInnerProductVerifier(maxVectorLength, ippDomain, curve)
+	if err != nil {
+		return nil, errors.Wrap(err, "range NewRangeProver")
+	}
+	return &RangeVerifier{curve: curve, generators: generators, ippVerifier: ippVerifier}, nil
+}
+
+// Verify verifies the given range proof inputs
+// It implements the checking of L65 on pg 20
+// It also verifies the dot product of <l,r> using the inner product proof\
+// capV is a commitment to v using blinding factor gamma
+// n is the power that specifies the upper bound of the range, ie. 2^n
+// g, h, u are unique points used as generators for the blinding factor
+// transcript is a merlin transcript to be used for the fiat shamir heuristic.
+func (verifier *RangeVerifier) Verify(proof *RangeProof, capV curves.Point, proofGenerators RangeProofGenerators, n int, transcript *merlin.Transcript) (bool, error) {
+	// Length of vectors must be less than the number of generators generated
+	if n > len(verifier.generators.G) {
+		return false, errors.New("ipp vector length must be less than maxVectorLength")
+	}
+	// In case where len(a) is less than number of generators precomputed by prover, trim to length
+	proofG := verifier.generators.G[0:n]
+	proofH := verifier.generators.H[0:n]
+
+	// Calc y,z,x from Fiat Shamir heuristic
+	y, z, err := calcyz(capV, proof.capA, proof.capS, transcript, verifier.curve)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof verify")
+	}
+
+	x, err := calcx(proof.capT1, proof.capT2, transcript, verifier.curve)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof verify")
+	}
+
+	wBytes := transcript.ExtractBytes([]byte("getw"), 64)
+	w, err := verifier.curve.NewScalar().SetBytesWide(wBytes)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof prove")
+	}
+
+	// Calc delta(y,z)
+	deltayz, err := deltayz(y, z, n, verifier.curve)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof verify")
+	}
+
+	// Check tHat: L65, pg20
+	tHatIsValid := verifier.checktHat(proof, capV, proofGenerators.g, proofGenerators.h, deltayz, x, z)
+	if !tHatIsValid {
+		return false, errors.New("rangeproof verify tHat is invalid")
+	}
+
+	// Verify IPP
+	hPrime, err := gethPrime(proofH, y, verifier.curve)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof verify")
+	}
+
+	capPhmu, err := getPhmu(proofG, hPrime, proofGenerators.h, proof.capA, proof.capS, x, y, z, proof.mu, n, verifier.curve)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof verify")
+	}
+
+	ippVerified, err := verifier.ippVerifier.VerifyFromRangeProof(proofG, hPrime, capPhmu, proofGenerators.u.Mul(w), proof.tHat, proof.ipp, transcript)
+	if err != nil {
+		return false, errors.Wrap(err, "rangeproof verify")
+	}
+
+	return ippVerified, nil
+}
+
+// L65, pg20.
+func (*RangeVerifier) checktHat(proof *RangeProof, capV, g, h curves.Point, deltayz, x, z curves.Scalar) bool {
+	// g^tHat * h^tau_x
+	gtHat := g.Mul(proof.tHat)
+	htaux := h.Mul(proof.taux)
+	lhs := gtHat.Add(htaux)
+
+	// V^z^2 * g^delta(y,z) * Tau_1^x * Tau_2^x^2
+	capVzsquare := capV.Mul(z.Square())
+	gdeltayz := g.Mul(deltayz)
+	capTau1x := proof.capT1.Mul(x)
+	capTau2xsquare := proof.capT2.Mul(x.Square())
+	rhs := capVzsquare.Add(gdeltayz).Add(capTau1x).Add(capTau2xsquare)
+
+	// Compare lhs =? rhs
+	return lhs.Equal(rhs)
+}
+
+// gethPrime calculates new h prime generators as defined in L64 on pg20.
+func gethPrime(h []curves.Point, y curves.Scalar, curve curves.Curve) ([]curves.Point, error) {
+	hPrime := make([]curves.Point, len(h))
+	yInv, err := y.Invert()
+	yInvn := getknVector(yInv, len(h), curve)
+	if err != nil {
+		return nil, errors.Wrap(err, "gethPrime")
+	}
+	for i, hElem := range h {
+		hPrime[i] = hElem.Mul(yInvn[i])
+	}
+	return hPrime, nil
+}
+
+// Obtain P used for IPP verification
+// See L67 on pg20
+// Note P on L66 includes blinding factor hmu, this method removes that factor.
+func getPhmu(proofG, proofHPrime []curves.Point, h, capA, capS curves.Point, x, y, z, mu curves.Scalar, n int, curve curves.Curve) (curves.Point, error) {
+	// h'^(z*y^n + z^2*2^n)
+	zyn := multiplyScalarToScalarVector(z, getknVector(y, n, curve))
+	zsquaretwon := multiplyScalarToScalarVector(z.Square(), get2nVector(n, curve))
+	elemLastExponent, err := addPairwiseScalarVectors(zyn, zsquaretwon)
+	if err != nil {
+		return nil, errors.Wrap(err, "getPhmu")
+	}
+	lastElem := curve.Point.SumOfProducts(proofHPrime, elemLastExponent)
+
+	// S^x
+	capSx := capS.Mul(x)
+
+	// g^-z --> -z*<1,g>
+	onen := get1nVector(n, curve)
+	zNeg := z.Neg()
+	zinvonen := multiplyScalarToScalarVector(zNeg, onen)
+	zgdotonen := curve.Point.SumOfProducts(proofG, zinvonen)
+
+	// L66 on pg20
+	P := capA.Add(capSx).Add(zgdotonen).Add(lastElem)
+	hmu := h.Mul(mu)
+	Phmu := P.Sub(hmu)
+
+	return Phmu, nil
+}
+
+// Delta function for delta(y,z), See (39) on pg18.
+func deltayz(y, z curves.Scalar, n int, curve curves.Curve) (curves.Scalar, error) {
+	// z - z^2
+	zMinuszsquare := z.Sub(z.Square())
+	// 1^n
+	onen := get1nVector(n, curve)
+	// <1^n, y^n>
+	onendotyn, err := innerProduct(onen, getknVector(y, n, curve))
+	if err != nil {
+		return nil, errors.Wrap(err, "deltayz")
+	}
+	// (z - z^2)*<1^n, y^n>
+	termFirst := zMinuszsquare.Mul(onendotyn)
+
+	// <1^n, 2^n>
+	onendottwon, err := innerProduct(onen, get2nVector(n, curve))
+	if err != nil {
+		return nil, errors.Wrap(err, "deltayz")
+	}
+	// z^3*<1^n, 2^n>
+	termSecond := z.Cube().Mul(onendottwon)
+
+	// (z - z^2)*<1^n, y^n> - z^3*<1^n, 2^n>
+	out := termFirst.Sub(termSecond)
+
+	return out, nil
+}