refactor in sub packages

README.md

@@ -1,4 +1,4 @@
-# go-circom-prover-verifier [![GoDoc](https://godoc.org/github.com/iden3/go-circom-prover-verifier?status.svg)](https://godoc.org/github.com/iden3/go-circom-prover-verifier) [![Go Report Card](https://goreportcard.com/badge/github.com/iden3/go-circom-prover-verifier)](https://goreportcard.com/report/github.com/iden3/go-circom-prover-verifier)
+# go-circom-prover-verifier [![GoDoc](https://godoc.org/github.com/iden3/go-circom-prover-verifier?status.svg)](https://godoc.org/github.com/iden3/go-circom-prover-verifier) [![Go Report Card](https://goreportcard.com/badge/github.com/iden3/go-circom-prover-verifier)](https://goreportcard.com/report/github.com/iden3/go-circom-prover-verifier) [![Test](https://github.com/iden3/go-circom-prover-verifier/workflows/Test/badge.svg)](https://github.com/iden3/go-circom-prover-verifier/actions?query=workflow%3ATest)
 
 Experimental Go implementation of the [Groth16 protocol](https://eprint.iacr.org/2016/260.pdf) zkSNARK prover & verifier compatible with [circom](https://github.com/iden3/circom).
 

go.mod

@@ -1,8 +1,12 @@
-module gocircomprover
+module go-circom-prover-verifier
 
-go 1.13
+go 1.14
+
+replace github.com/iden3/go-circom-prover-verifier => ./
 
 require (
 	github.com/ethereum/go-ethereum v1.9.12
+	github.com/iden3/go-circom-prover-verifier v0.0.0-00010101000000-000000000000
 	github.com/stretchr/testify v1.5.1
+	golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4
 )

go.sum

@@ -61,6 +61,7 @@ github.com/graph-gophers/graphql-go v0.0.0-20191115155744-f33e81362277/go.mod h1
 github.com/hashicorp/golang-lru v0.0.0-20160813221303-0a025b7e63ad/go.mod h1:/m3WP610KZHVQ1SGc6re/UDhFvYD7pJ4Ao+sR/qLZy8=
 github.com/hpcloud/tail v1.0.0/go.mod h1:ab1qPbhIpdTxEkNHXyeSf5vhxWSCs/tWer42PpOxQnU=
 github.com/huin/goupnp v0.0.0-20161224104101-679507af18f3/go.mod h1:MZ2ZmwcBpvOoJ22IJsc7va19ZwoheaBk43rKg12SKag=
+github.com/iden3/go-circom-prover-verifier v0.0.0-20200409092022-a439651fafb0 h1:iyMhjvq7JKtKT6kEKuKghXiwanoa4/u7JSCKqUBqvds=
 github.com/influxdata/influxdb v1.2.3-0.20180221223340-01288bdb0883/go.mod h1:qZna6X/4elxqT3yI9iZYdZrWWdeFOOprn86kgg4+IzY=
 github.com/jackpal/go-nat-pmp v1.0.2-0.20160603034137-1fa385a6f458/go.mod h1:QPH045xvCAeXUZOxsnwmrtiCoxIr9eob+4orBN1SBKc=
 github.com/jmespath/go-jmespath v0.0.0-20180206201540-c2b33e8439af/go.mod h1:Nht3zPeWKUH0NzdCt2Blrr5ys8VGpn0CEB0cQHVjt7k=
@@ -119,6 +120,7 @@ github.com/tyler-smith/go-bip39 v1.0.1-0.20181017060643-dbb3b84ba2ef/go.mod h1:s
 github.com/urfave/cli v1.22.1/go.mod h1:Gos4lmkARVdJ6EkW0WaNv/tZAAMe9V7XWyB60NtXRu0=
 github.com/wsddn/go-ecdh v0.0.0-20161211032359-48726bab9208/go.mod h1:IotVbo4F+mw0EzQ08zFqg7pK3FebNXpaMsRy2RT+Ees=
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
+golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4 h1:QmwruyY+bKbDDL0BaglrbZABEali68eoMFhTZpCjYVA=
 golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
 golang.org/x/net v0.0.0-20180906233101-161cd47e91fd/go.mod h1:mL1N/T3taQHkDXs73rZJwtUhF3w3ftmwwsq0BUmARs4=
 golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=

parsers/parsers.go

@@ -1,4 +1,4 @@
-package gocircomprover
+package parsers
 
 import (
 	"bytes"
@@ -10,6 +10,7 @@ import (
 	"strings"
 
 	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+	"github.com/iden3/go-circom-prover-verifier/types"
 )
 
 // PkString is the equivalent to the Pk struct in string representation, containing the ProvingKey
@@ -53,14 +54,14 @@ type VkString struct {
 }
 
 // ParseWitness parses the json []byte data into the Witness struct
-func ParseWitness(wJson []byte) (Witness, error) {
+func ParseWitness(wJson []byte) (types.Witness, error) {
 	var ws WitnessString
 	err := json.Unmarshal(wJson, &ws)
 	if err != nil {
 		return nil, err
 	}
 
-	var w Witness
+	var w types.Witness
 	for i := 0; i < len(ws); i++ {
 		bi, err := stringToBigInt(ws[i])
 		if err != nil {
@@ -72,7 +73,7 @@ func ParseWitness(wJson []byte) (Witness, error) {
 }
 
 // ParsePk parses the json []byte data into the Pk struct
-func ParsePk(pkJson []byte) (*Pk, error) {
+func ParsePk(pkJson []byte) (*types.Pk, error) {
 	var pkStr PkString
 	err := json.Unmarshal(pkJson, &pkStr)
 	if err != nil {
@@ -82,8 +83,8 @@ func ParsePk(pkJson []byte) (*Pk, error) {
 	return pk, err
 }
 
-func pkStringToPk(ps PkString) (*Pk, error) {
+func pkStringToPk(ps PkString) (*types.Pk, error) {
-	var p Pk
+	var p types.Pk
 	var err error
 
 	p.A, err = arrayStringToG1(ps.A)
@@ -152,8 +153,8 @@ func pkStringToPk(ps PkString) (*Pk, error) {
 	return &p, nil
 }
 
-func proofStringToProof(pr ProofString) (*Proof, error) {
+func proofStringToProof(pr ProofString) (*types.Proof, error) {
-	var p Proof
+	var p types.Proof
 	var err error
 	p.A, err = stringToG1(pr.A)
 	if err != nil {
@@ -174,7 +175,7 @@ func proofStringToProof(pr ProofString) (*Proof, error) {
 }
 
 // ParseProof takes a json []byte and outputs the *Proof struct
-func ParseProof(pj []byte) (*Proof, error) {
+func ParseProof(pj []byte) (*types.Proof, error) {
 	var pr ProofString
 	err := json.Unmarshal(pj, &pr)
 	if err != nil {
@@ -203,7 +204,7 @@ func ParsePublicSignals(pj []byte) ([]*big.Int, error) {
 }
 
 // ParseVk takes a json []byte and outputs the *Vk struct
-func ParseVk(vj []byte) (*Vk, error) {
+func ParseVk(vj []byte) (*types.Vk, error) {
 	var vr VkString
 	err := json.Unmarshal(vj, &vr)
 	if err != nil {
@@ -213,8 +214,8 @@ func ParseVk(vj []byte) (*Vk, error) {
 	return v, err
 }
 
-func vkStringToVk(vr VkString) (*Vk, error) {
+func vkStringToVk(vr VkString) (*types.Vk, error) {
-	var v Vk
+	var v types.Vk
 	var err error
 	v.Alpha, err = stringToG1(vr.Alpha)
 	if err != nil {
@@ -464,7 +465,7 @@ func stringToG2(h [][]string) (*bn256.G2, error) {
 }
 
 // ProofToJson outputs the Proof i Json format
-func ProofToJson(p *Proof) ([]byte, error) {
+func ProofToJson(p *types.Proof) ([]byte, error) {
 	var ps ProofString
 	ps.A = make([]string, 3)
 	ps.B = make([][]string, 3)

parsers/parsers_test.go

@@ -1,4 +1,4 @@
-package gocircomprover
+package parsers
 
 import (
 	"testing"

prover/arithmetic.go

@@ -1,4 +1,4 @@
-package gocircomprover
+package prover
 
 import (
 	"bytes"

prover/ifft.go

@@ -1,4 +1,4 @@
-package gocircomprover
+package prover
 
 import (
 	"math"

prover/prover.go

@@ -1,10 +1,11 @@
-package gocircomprover
+package prover
 
 import (
 	"crypto/rand"
 	"math/big"
 
 	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+	"github.com/iden3/go-circom-prover-verifier/types"
 )
 
 // Proof is the data structure of the Groth16 zkSNARK proof
@@ -54,8 +55,8 @@ func randBigInt() (*big.Int, error) {
 }
 
 // GenerateProof generates the Groth16 zkSNARK proof
-func GenerateProof(pk *Pk, w Witness) (*Proof, []*big.Int, error) {
+func GenerateProof(pk *types.Pk, w types.Witness) (*types.Proof, []*big.Int, error) {
-	var proof Proof
+	var proof types.Proof
 
 	r, err := randBigInt()
 	if err != nil {
@@ -105,7 +106,7 @@ func GenerateProof(pk *Pk, w Witness) (*Proof, []*big.Int, error) {
 	return &proof, pubSignals, nil
 }
 
-func calculateH(pk *Pk, w Witness) []*big.Int {
+func calculateH(pk *types.Pk, w types.Witness) []*big.Int {
 	m := pk.DomainSize
 	polAT := arrayOfZeroes(m)
 	polBT := arrayOfZeroes(m)

prover/prover_test.go

@@ -0,0 +1,106 @@
+package prover
+
+import (
+	"encoding/json"
+	"io/ioutil"
+	"math/big"
+	"testing"
+
+	"github.com/iden3/go-circom-prover-verifier/parsers"
+	"github.com/iden3/go-circom-prover-verifier/types"
+	"github.com/iden3/go-circom-prover-verifier/verifier"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestSmallCircuitGenerateProf(t *testing.T) {
+	provingKeyJson, err := ioutil.ReadFile("../testdata/small/proving_key.json")
+	require.Nil(t, err)
+	pk, err := parsers.ParsePk(provingKeyJson)
+	require.Nil(t, err)
+
+	witnessJson, err := ioutil.ReadFile("../testdata/small/witness.json")
+	require.Nil(t, err)
+	w, err := parsers.ParseWitness(witnessJson)
+	require.Nil(t, err)
+
+	assert.Equal(t, types.Witness{big.NewInt(1), big.NewInt(33), big.NewInt(3), big.NewInt(11)}, w)
+
+	proof, pubSignals, err := GenerateProof(pk, w)
+	assert.Nil(t, err)
+
+	proofStr, err := parsers.ProofToJson(proof)
+	assert.Nil(t, err)
+
+	err = ioutil.WriteFile("../testdata/small/proof.json", proofStr, 0644)
+	assert.Nil(t, err)
+	publicStr, err := json.Marshal(parsers.ArrayBigIntToString(pubSignals))
+	assert.Nil(t, err)
+	err = ioutil.WriteFile("../testdata/small/public.json", publicStr, 0644)
+	assert.Nil(t, err)
+
+	// verify the proof
+	vkJson, err := ioutil.ReadFile("../testdata/small/verification_key.json")
+	require.Nil(t, err)
+	vk, err := parsers.ParseVk(vkJson)
+	require.Nil(t, err)
+
+	v := verifier.Verify(vk, proof, pubSignals)
+	assert.True(t, v)
+
+	// to verify the proof with snarkjs:
+	// snarkjs verify --vk testdata/small/verification_key.json -p testdata/small/proof.json --pub testdata/small/public.json
+}
+
+func TestBigCircuitGenerateProf(t *testing.T) {
+	provingKeyJson, err := ioutil.ReadFile("../testdata/big/proving_key.json")
+	require.Nil(t, err)
+	pk, err := parsers.ParsePk(provingKeyJson)
+	require.Nil(t, err)
+
+	witnessJson, err := ioutil.ReadFile("../testdata/big/witness.json")
+	require.Nil(t, err)
+	w, err := parsers.ParseWitness(witnessJson)
+	require.Nil(t, err)
+
+	proof, pubSignals, err := GenerateProof(pk, w)
+	assert.Nil(t, err)
+
+	proofStr, err := parsers.ProofToJson(proof)
+	assert.Nil(t, err)
+
+	err = ioutil.WriteFile("../testdata/big/proof.json", proofStr, 0644)
+	assert.Nil(t, err)
+	publicStr, err := json.Marshal(parsers.ArrayBigIntToString(pubSignals))
+	assert.Nil(t, err)
+	err = ioutil.WriteFile("../testdata/big/public.json", publicStr, 0644)
+	assert.Nil(t, err)
+
+	// verify the proof
+	vkJson, err := ioutil.ReadFile("../testdata/big/verification_key.json")
+	require.Nil(t, err)
+	vk, err := parsers.ParseVk(vkJson)
+	require.Nil(t, err)
+
+	v := verifier.Verify(vk, proof, pubSignals)
+	assert.True(t, v)
+
+	// to verify the proof with snarkjs:
+	// snarkjs verify --vk testdata/big/verification_key.json -p testdata/big/proof.json --pub testdata/big/public.json
+}
+
+func BenchmarkGenerateProof(b *testing.B) {
+	provingKeyJson, err := ioutil.ReadFile("../testdata/big/proving_key.json")
+	require.Nil(b, err)
+	pk, err := parsers.ParsePk(provingKeyJson)
+	require.Nil(b, err)
+
+	witnessJson, err := ioutil.ReadFile("../testdata/big/witness.json")
+	require.Nil(b, err)
+	w, err := parsers.ParseWitness(witnessJson)
+	require.Nil(b, err)
+
+	for i := 0; i < b.N; i++ {
+		GenerateProof(pk, w)
+	}
+}

prover_test.go

@@ -1,103 +0,0 @@
-package gocircomprover
-
-import (
-	"encoding/json"
-	"io/ioutil"
-	"math/big"
-	"testing"
-
-	"github.com/stretchr/testify/assert"
-	"github.com/stretchr/testify/require"
-)
-
-func TestSmallCircuitGenerateProf(t *testing.T) {
-	provingKeyJson, err := ioutil.ReadFile("testdata/small/proving_key.json")
-	require.Nil(t, err)
-	pk, err := ParsePk(provingKeyJson)
-	require.Nil(t, err)
-
-	witnessJson, err := ioutil.ReadFile("testdata/small/witness.json")
-	require.Nil(t, err)
-	w, err := ParseWitness(witnessJson)
-	require.Nil(t, err)
-
-	assert.Equal(t, Witness{big.NewInt(1), big.NewInt(33), big.NewInt(3), big.NewInt(11)}, w)
-
-	proof, pubSignals, err := GenerateProof(pk, w)
-	assert.Nil(t, err)
-
-	proofStr, err := ProofToJson(proof)
-	assert.Nil(t, err)
-
-	err = ioutil.WriteFile("testdata/small/proof.json", proofStr, 0644)
-	assert.Nil(t, err)
-	publicStr, err := json.Marshal(ArrayBigIntToString(pubSignals))
-	assert.Nil(t, err)
-	err = ioutil.WriteFile("testdata/small/public.json", publicStr, 0644)
-	assert.Nil(t, err)
-
-	// verify the proof
-	vkJson, err := ioutil.ReadFile("testdata/small/verification_key.json")
-	require.Nil(t, err)
-	vk, err := ParseVk(vkJson)
-	require.Nil(t, err)
-
-	v := Verify(vk, proof, pubSignals)
-	assert.True(t, v)
-
-	// to verify the proof with snarkjs:
-	// snarkjs verify --vk testdata/small/verification_key.json -p testdata/small/proof.json --pub testdata/small/public.json
-}
-
-func TestBigCircuitGenerateProf(t *testing.T) {
-	provingKeyJson, err := ioutil.ReadFile("testdata/big/proving_key.json")
-	require.Nil(t, err)
-	pk, err := ParsePk(provingKeyJson)
-	require.Nil(t, err)
-
-	witnessJson, err := ioutil.ReadFile("testdata/big/witness.json")
-	require.Nil(t, err)
-	w, err := ParseWitness(witnessJson)
-	require.Nil(t, err)
-
-	proof, pubSignals, err := GenerateProof(pk, w)
-	assert.Nil(t, err)
-
-	proofStr, err := ProofToJson(proof)
-	assert.Nil(t, err)
-
-	err = ioutil.WriteFile("testdata/big/proof.json", proofStr, 0644)
-	assert.Nil(t, err)
-	publicStr, err := json.Marshal(ArrayBigIntToString(pubSignals))
-	assert.Nil(t, err)
-	err = ioutil.WriteFile("testdata/big/public.json", publicStr, 0644)
-	assert.Nil(t, err)
-
-	// verify the proof
-	vkJson, err := ioutil.ReadFile("testdata/big/verification_key.json")
-	require.Nil(t, err)
-	vk, err := ParseVk(vkJson)
-	require.Nil(t, err)
-
-	v := Verify(vk, proof, pubSignals)
-	assert.True(t, v)
-
-	// to verify the proof with snarkjs:
-	// snarkjs verify --vk testdata/big/verification_key.json -p testdata/big/proof.json --pub testdata/big/public.json
-}
-
-func BenchmarkGenerateProof(b *testing.B) {
-	provingKeyJson, err := ioutil.ReadFile("testdata/big/proving_key.json")
-	require.Nil(b, err)
-	pk, err := ParsePk(provingKeyJson)
-	require.Nil(b, err)
-
-	witnessJson, err := ioutil.ReadFile("testdata/big/witness.json")
-	require.Nil(b, err)
-	w, err := ParseWitness(witnessJson)
-	require.Nil(b, err)
-
-	for i := 0; i < b.N; i++ {
-		GenerateProof(pk, w)
-	}
-}

types/types.go

@@ -0,0 +1,46 @@
+package types
+
+import (
+	"math/big"
+
+	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+)
+
+// Proof is the data structure of the Groth16 zkSNARK proof
+type Proof struct {
+	A *bn256.G1
+	B *bn256.G2
+	C *bn256.G1
+}
+
+// Pk holds the data structure of the ProvingKey
+type Pk struct {
+	A          []*bn256.G1
+	B2         []*bn256.G2
+	B1         []*bn256.G1
+	C          []*bn256.G1
+	NVars      int
+	NPublic    int
+	VkAlpha1   *bn256.G1
+	VkDelta1   *bn256.G1
+	VkBeta1    *bn256.G1
+	VkBeta2    *bn256.G2
+	VkDelta2   *bn256.G2
+	HExps      []*bn256.G1
+	DomainSize int
+	PolsA      []map[int]*big.Int
+	PolsB      []map[int]*big.Int
+	PolsC      []map[int]*big.Int
+}
+
+// Witness contains the witness
+type Witness []*big.Int
+
+// Vk is the Verification Key data structure
+type Vk struct {
+	Alpha *bn256.G1
+	Beta  *bn256.G2
+	Gamma *bn256.G2
+	Delta *bn256.G2
+	IC    []*bn256.G1
+}

verifier/verifier.go

@@ -1,10 +1,12 @@
-package gocircomprover
+package verifier
 
 import (
 	"fmt"
 	"math/big"
 
 	"github.com/ethereum/go-ethereum/crypto/bn256"
+	"github.com/iden3/go-circom-prover-verifier/prover"
+	"github.com/iden3/go-circom-prover-verifier/types"
 )
 
 // Vk is the Verification Key data structure
@@ -16,7 +18,7 @@ type Vk struct {
 	IC    []*bn256.G1
 }
 
-func Verify(vk *Vk, proof *Proof, inputs []*big.Int) bool {
+func Verify(vk *types.Vk, proof *types.Proof, inputs []*big.Int) bool {
 	if len(inputs)+1 != len(vk.IC) {
 		fmt.Println("len(inputs)+1 != len(vk.IC)")
 		return false
@@ -24,7 +26,7 @@ func Verify(vk *Vk, proof *Proof, inputs []*big.Int) bool {
 	vkX := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
 	for i := 0; i < len(inputs); i++ {
 		// check input inside field
-		if inputs[0].Cmp(R) != -1 {
+		if inputs[0].Cmp(prover.R) != -1 {
 			return false
 		}
 		vkX = new(bn256.G1).Add(vkX, new(bn256.G1).ScalarMult(vk.IC[i+1], inputs[i]))

verifier/verifier_test.go

@@ -0,0 +1,50 @@
+package verifier
+
+import (
+	"io/ioutil"
+	"testing"
+
+	"github.com/iden3/go-circom-prover-verifier/parsers"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestVerify1(t *testing.T) {
+	proofJson, err := ioutil.ReadFile("../testdata/big/proof.json")
+	require.Nil(t, err)
+	vkJson, err := ioutil.ReadFile("../testdata/big/verification_key.json")
+	require.Nil(t, err)
+	publicJson, err := ioutil.ReadFile("../testdata/big/public.json")
+	require.Nil(t, err)
+
+	public, err := parsers.ParsePublicSignals(publicJson)
+	require.Nil(t, err)
+	proof, err := parsers.ParseProof(proofJson)
+	require.Nil(t, err)
+	vk, err := parsers.ParseVk(vkJson)
+	require.Nil(t, err)
+
+	v := Verify(vk, proof, public)
+	assert.True(t, v)
+}
+
+func BenchmarkVerify(b *testing.B) {
+	proofJson, err := ioutil.ReadFile("../testdata/big/proof.json")
+	require.Nil(b, err)
+	vkJson, err := ioutil.ReadFile("../testdata/big/verification_key.json")
+	require.Nil(b, err)
+	publicJson, err := ioutil.ReadFile("../testdata/big/public.json")
+	require.Nil(b, err)
+
+	public, err := parsers.ParsePublicSignals(publicJson)
+	require.Nil(b, err)
+	proof, err := parsers.ParseProof(proofJson)
+	require.Nil(b, err)
+	vk, err := parsers.ParseVk(vkJson)
+	require.Nil(b, err)
+
+	for i := 0; i < b.N; i++ {
+		Verify(vk, proof, public)
+	}
+}

verifier_test.go

@@ -1,48 +0,0 @@
-package gocircomprover
-
-import (
-	"io/ioutil"
-	"testing"
-
-	"github.com/stretchr/testify/assert"
-	"github.com/stretchr/testify/require"
-)
-
-func TestVerify1(t *testing.T) {
-	proofJson, err := ioutil.ReadFile("testdata/big/proof.json")
-	require.Nil(t, err)
-	vkJson, err := ioutil.ReadFile("testdata/big/verification_key.json")
-	require.Nil(t, err)
-	publicJson, err := ioutil.ReadFile("testdata/big/public.json")
-	require.Nil(t, err)
-
-	public, err := ParsePublicSignals(publicJson)
-	require.Nil(t, err)
-	proof, err := ParseProof(proofJson)
-	require.Nil(t, err)
-	vk, err := ParseVk(vkJson)
-	require.Nil(t, err)
-
-	v := Verify(vk, proof, public)
-	assert.True(t, v)
-}
-
-func BenchmarkVerify(b *testing.B) {
-	proofJson, err := ioutil.ReadFile("testdata/big/proof.json")
-	require.Nil(b, err)
-	vkJson, err := ioutil.ReadFile("testdata/big/verification_key.json")
-	require.Nil(b, err)
-	publicJson, err := ioutil.ReadFile("testdata/big/public.json")
-	require.Nil(b, err)
-
-	public, err := ParsePublicSignals(publicJson)
-	require.Nil(b, err)
-	proof, err := ParseProof(proofJson)
-	require.Nil(b, err)
-	vk, err := ParseVk(vkJson)
-	require.Nil(b, err)
-
-	for i := 0; i < b.N; i++ {
-		Verify(vk, proof, public)
-	}
-}