reduced test time

Implement more agressive parallelism

.github/workflows/main.yml

@@ -18,10 +18,6 @@ jobs:
       uses: actions/setup-node@v1
       with:
         node-version: '10.x'
-    - name: Install circom
-      run: npm install -g circom
-    - name: Install snarkjs
-      run: npm install -g snarkjs
     - name: Checkout code
       uses: actions/checkout@v2
     - name: Compile circuits and execute Go tests

.gitignore

@@ -4,5 +4,6 @@ testdata/*/*.cpp
 testdata/*/*.sym
 testdata/*/*.r1cs
 testdata/*/*.sol
+testdata/*/*.bin
 !testdata/*/inputs.json
 cli/*.json

README.md

@@ -1,6 +1,6 @@
 # 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 implementation of the [Groth16 protocol](https://eprint.iacr.org/2016/260.pdf) zkSNARK prover & verifier compatible with [circom](https://github.com/iden3/circom).
 
 
 Using [bn256](https://github.com/ethereum/go-ethereum/tree/master/crypto/bn256/cloudflare) (used by [go-ethereum](https://github.com/ethereum/go-ethereum)) for the Pairing curve operations.
@@ -82,9 +82,9 @@ Usage of /tmp/go-build620318239/b001/exe/cli:
 
 - Prove
 ```
-> go run cli.go -prove -provingkey=../testdata/small/proving_key.json -witness=../testdata/small/witness.json
+> go run cli.go -prove -provingkey=../testdata/circuit5k/proving_key.json -witness=../testdata/circuit5k/witness.json
 ```
 - Verify
 ```
-> go run cli.go -verify -verificationkey=../testdata/small/verification_key.json
+> go run cli.go -verify -verificationkey=../testdata/circuit5k/verification_key.json
 ```

cli/cli.go

@@ -5,6 +5,7 @@ import (
 	"flag"
 	"fmt"
 	"io/ioutil"
+	"os"
 	"time"
 
 	"github.com/iden3/go-circom-prover-verifier/parsers"
@@ -34,15 +35,15 @@ func main() {
 		if err != nil {
 			fmt.Println("Error:", err)
 		}
-		return
+		os.Exit(0)
 	} else if *verify {
 		err := cmdVerify(*proofPath, *verificationKeyPath, *publicPath)
 		if err != nil {
 			fmt.Println("Error:", err)
 		}
-		return
+		os.Exit(0)
 	}
-	fmt.Println("use -help for the list of commands")
+	flag.PrintDefaults()
 }
 
 func cmdProve(provingKeyPath, witnessPath, proofPath, publicPath string) error {

parsers/parsers.go

@@ -1,11 +1,14 @@
 package parsers
 
 import (
+	"bufio"
 	"bytes"
 	"encoding/hex"
 	"encoding/json"
 	"fmt"
+	"io"
 	"math/big"
+	"os"
 	"strconv"
 	"strings"
 
@@ -496,3 +499,31 @@ func ProofToJson(p *types.Proof) ([]byte, error) {
 
 	return json.Marshal(ps)
 }
+
+// ParseWitness parses binary file representation of the Witness into the Witness struct
+func ParseWitnessBin(f *os.File) (types.Witness, error) {
+	var w types.Witness
+	r := bufio.NewReader(f)
+	for {
+		b := make([]byte, 32)
+		n, err := r.Read(b)
+		if err == io.EOF {
+			return w, nil
+		} else if err != nil {
+			return nil, err
+		}
+		if n != 32 {
+			return nil, fmt.Errorf("error on value format, expected 32 bytes, got %v", n)
+		}
+		w = append(w, new(big.Int).SetBytes(swapEndianness(b[0:32])))
+	}
+}
+
+// swapEndianness swaps the order of the bytes in the slice.
+func swapEndianness(b []byte) []byte {
+	o := make([]byte, len(b))
+	for i := range b {
+		o[len(b)-1-i] = b[i]
+	}
+	return o
+}

parsers/parsers_test.go

@@ -1,9 +1,12 @@
 package parsers
 
 import (
+	"io/ioutil"
+	"os"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
 func TestParseArrayG1(t *testing.T) {
@@ -143,3 +146,29 @@ func TestParseArrayG2(t *testing.T) {
 	assert.Equal(t, "bn256.G2((1922d70c934543aa655ec3277f7fa10a25ec973a4f001a7c54ce4954b4916f8c, 14865e836947c42cf35b47d30e06535fff9dab319c4296e28afde368960671d5), (2f50fbe77925b0a9d718c9ab38638bafa7c65f43f0d09035e518df97ad294847, 177dfa1a3b8627faf0425d9511bcb4c6ca986ea05e3803b5c643c35b94a7e6fe))", a[3].String())
 
 }
+
+func testCircuitParseWitnessBin(t *testing.T, circuit string) {
+	witnessBinFile, err := os.Open("../testdata/" + circuit + "/witness.bin")
+	require.Nil(t, err)
+	defer witnessBinFile.Close()
+	witness, err := ParseWitnessBin(witnessBinFile)
+	require.Nil(t, err)
+
+	witnessJson, err := ioutil.ReadFile("../testdata/" + circuit + "/witness.json")
+	require.Nil(t, err)
+	w, err := ParseWitness(witnessJson)
+	require.Nil(t, err)
+
+	assert.Equal(t, len(w), len(witness))
+	assert.Equal(t, w[0], witness[0])
+	assert.Equal(t, w[1], witness[1])
+	assert.Equal(t, w[10], witness[10])
+	assert.Equal(t, w[len(w)-3], witness[len(w)-3])
+	assert.Equal(t, w[len(w)-2], witness[len(w)-2])
+	assert.Equal(t, w[len(w)-1], witness[len(w)-1])
+}
+
+func TestParseWitnessBin(t *testing.T) {
+	testCircuitParseWitnessBin(t, "circuit1k")
+	testCircuitParseWitnessBin(t, "circuit5k")
+}

prover/arithmetic.go

@@ -4,28 +4,46 @@ import (
 	"bytes"
 	"math/big"
 
+	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
 	"github.com/iden3/go-circom-prover-verifier/types"
 	"github.com/iden3/go-iden3-crypto/ff"
 )
 
 func arrayOfZeroes(n int) []*big.Int {
-	var r []*big.Int
+	r := make([]*big.Int, n)
 	for i := 0; i < n; i++ {
-		r = append(r, new(big.Int).SetInt64(0))
+		r[i] = new(big.Int).SetInt64(0)
 	}
-	return r
+	return r[:]
 }
+
 func arrayOfZeroesE(n int) []*ff.Element {
-	var r []*ff.Element
+	r := make([]*ff.Element, n)
 	for i := 0; i < n; i++ {
-		r = append(r, ff.NewElement())
+		r[i] = ff.NewElement()
 	}
-	return r
+	return r[:]
+}
+
+func arrayOfZeroesG1(n int) []*bn256.G1 {
+	r := make([]*bn256.G1, n)
+	for i := 0; i < n; i++ {
+		r[i] = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
+	}
+	return r[:]
+}
+
+func arrayOfZeroesG2(n int) []*bn256.G2 {
+	r := make([]*bn256.G2, n)
+	for i := 0; i < n; i++ {
+		r[i] = new(bn256.G2).ScalarBaseMult(big.NewInt(0))
+	}
+	return r[:]
 }
 
 func fAdd(a, b *big.Int) *big.Int {
 	ab := new(big.Int).Add(a, b)
-	return new(big.Int).Mod(ab, types.R)
+	return ab.Mod(ab, types.R)
 }
 
 func fSub(a, b *big.Int) *big.Int {
@@ -35,7 +53,7 @@ func fSub(a, b *big.Int) *big.Int {
 
 func fMul(a, b *big.Int) *big.Int {
 	ab := new(big.Int).Mul(a, b)
-	return new(big.Int).Mod(ab, types.R)
+	return ab.Mod(ab, types.R)
 }
 
 func fDiv(a, b *big.Int) *big.Int {
@@ -62,7 +80,7 @@ func fExp(base *big.Int, e *big.Int) *big.Int {
 			res = fMul(res, exp)
 		}
 		exp = fMul(exp, exp)
-		rem = new(big.Int).Rsh(rem, 1)
+		rem.Rsh(rem, 1)
 	}
 	return res
 }

prover/gextra.go

@@ -0,0 +1,443 @@
+package prover
+
+import (
+        "math/big"
+	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+	cryptoConstants "github.com/iden3/go-iden3-crypto/constants"
+)
+
+type TableG1 struct{
+   data []*bn256.G1
+}
+
+
+func (t TableG1) GetData() []*bn256.G1 {
+  return t.data
+}
+
+
+// Compute table of gsize elements as ::
+//  Table[0] = Inf
+//  Table[1] = a[0]
+//  Table[2] = a[1]
+//  Table[3] = a[0]+a[1]
+//  .....
+//  Table[(1<<gsize)-1] = a[0]+a[1]+...+a[gsize-1]
+func (t *TableG1) NewTableG1(a []*bn256.G1, gsize int){
+   // EC table
+   table := make([]*bn256.G1, 0)
+
+   // We need at least gsize elements. If not enough, fill with 0
+   a_ext := make([]*bn256.G1, 0)
+   a_ext = append(a_ext, a...)
+
+   for i:=len(a); i<gsize; i++ {
+      a_ext = append(a_ext,new(bn256.G1).ScalarBaseMult(big.NewInt(0)))
+   }
+
+   elG1 := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
+   table = append(table,elG1)
+   last_pow2 := 1
+   nelems := 0
+   for i :=1; i< 1<<gsize; i++ {
+      elG1 := new(bn256.G1)
+      // if power of 2
+      if i & (i-1) == 0{
+        last_pow2 = i
+        elG1.Set(a_ext[nelems])
+        nelems++
+      } else {
+        elG1.Add(table[last_pow2], table[i-last_pow2])
+        // TODO bn256 doesn't export MakeAffine function. We need to fork repo
+        //table[i].MakeAffine()
+      }
+      table = append(table, elG1)
+  }
+  t.data = table
+}
+
+// Multiply scalar by precomputed table of G1 elements
+func (t *TableG1) MulTableG1(k []*big.Int, Q_prev *bn256.G1, gsize int) *bn256.G1 {
+   // We need at least gsize elements. If not enough, fill with 0
+   k_ext := make([]*big.Int, 0)
+   k_ext = append(k_ext, k...)
+
+   for i:=len(k); i < gsize; i++ {
+      k_ext = append(k_ext,new(big.Int).SetUint64(0))
+   }
+
+   Q := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
+
+   msb := getMsb(k_ext)
+
+   for i := msb-1; i >= 0; i-- {
+        // TODO. bn256 doesn't export double operation. We will need to fork repo and export it
+	Q = new(bn256.G1).Add(Q,Q)
+        b := getBit(k_ext,i)
+	if b != 0 {
+          // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+	  Q.Add(Q, t.data[b])
+	}
+   }
+   if Q_prev != nil {
+     return Q.Add(Q,Q_prev)
+   } else {
+     return Q
+   }
+}
+
+// Multiply scalar by precomputed table of G1 elements without intermediate doubling
+func MulTableNoDoubleG1(t []TableG1, k []*big.Int,  Q_prev *bn256.G1, gsize int) *bn256.G1 {
+   // We need at least gsize elements. If not enough, fill with 0
+   min_nelems := len(t) * gsize
+   k_ext := make([]*big.Int, 0)
+   k_ext = append(k_ext, k...)
+   for i := len(k); i <  min_nelems; i++ {
+      k_ext = append(k_ext,new(big.Int).SetUint64(0))
+   }
+   // Init Adders
+   nbitsQ := cryptoConstants.Q.BitLen()
+   Q := make([]*bn256.G1,nbitsQ)
+
+   for i:=0; i< nbitsQ; i++ {
+     Q[i] = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
+   }
+
+   // Perform bitwise addition
+   for j:=0; j < len(t); j++ {
+     msb := getMsb(k_ext[j*gsize:(j+1)*gsize])
+
+     for i := msb-1; i >= 0; i-- {
+        b := getBit(k_ext[j*gsize:(j+1)*gsize],i)
+	if b != 0 {
+          // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+	  Q[i].Add(Q[i], t[j].data[b])
+	}
+     }
+   }
+
+   // Consolidate Addition
+   R := new(bn256.G1).Set(Q[nbitsQ-1])
+   for i:=nbitsQ-1; i>0; i-- {
+      // TODO. bn256 doesn't export double operation. We will need to fork repo and export it
+      R = new(bn256.G1).Add(R,R)
+      R.Add(R,Q[i-1])
+   }
+
+   if Q_prev != nil {
+      return R.Add(R,Q_prev)
+   } else {
+      return R
+   }
+}
+
+// Compute tables within function. This solution should still be faster than std  multiplication
+// for gsize = 7
+func ScalarMultG1(a []*bn256.G1, k []*big.Int, Q_prev *bn256.G1, gsize int) *bn256.G1 {
+     ntables := int((len(a) + gsize - 1) / gsize)
+     table := TableG1{}
+     Q:= new(bn256.G1).ScalarBaseMult(new(big.Int))
+
+     for i:=0; i<ntables-1; i++ {
+       table.NewTableG1( a[i*gsize:(i+1)*gsize], gsize)
+       Q = table.MulTableG1(k[i*gsize:(i+1)*gsize], Q, gsize)
+     }
+     table.NewTableG1( a[(ntables-1)*gsize:], gsize)
+     Q = table.MulTableG1(k[(ntables-1)*gsize:], Q, gsize)
+
+     if Q_prev != nil {
+        return Q.Add(Q,Q_prev)
+     } else {
+        return Q
+     }
+}
+
+// Multiply scalar by precomputed table of G1 elements without intermediate doubling
+func ScalarMultNoDoubleG1(a []*bn256.G1, k []*big.Int, Q_prev *bn256.G1, gsize int) *bn256.G1 {
+   ntables := int((len(a) + gsize - 1) / gsize)
+   table := TableG1{}
+
+   // We need at least gsize elements. If not enough, fill with 0
+   min_nelems := ntables * gsize
+   k_ext := make([]*big.Int, 0)
+   k_ext = append(k_ext, k...)
+   for i := len(k); i <  min_nelems; i++ {
+      k_ext = append(k_ext,new(big.Int).SetUint64(0))
+   }
+   // Init Adders
+   nbitsQ := cryptoConstants.Q.BitLen()
+   Q := make([]*bn256.G1,nbitsQ)
+
+   for i:=0; i< nbitsQ; i++ {
+     Q[i] = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
+   }
+
+   // Perform bitwise addition
+   for j:=0; j < ntables-1; j++ {
+     table.NewTableG1( a[j*gsize:(j+1)*gsize], gsize)
+     msb := getMsb(k_ext[j*gsize:(j+1)*gsize])
+
+     for i := msb-1; i >= 0; i-- {
+        b := getBit(k_ext[j*gsize:(j+1)*gsize],i)
+	if b != 0 {
+          // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+	  Q[i].Add(Q[i], table.data[b])
+	}
+     }
+   }
+   table.NewTableG1( a[(ntables-1)*gsize:], gsize)
+   msb := getMsb(k_ext[(ntables-1)*gsize:])
+
+   for i := msb-1; i >= 0; i-- {
+     b := getBit(k_ext[(ntables-1)*gsize:],i)
+     if b != 0 {
+         // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+         Q[i].Add(Q[i], table.data[b])
+     }
+   }
+
+   // Consolidate Addition
+   R := new(bn256.G1).Set(Q[nbitsQ-1])
+   for i:=nbitsQ-1; i>0; i-- {
+      // TODO. bn256 doesn't export double operation. We will need to fork repo and export it
+      R = new(bn256.G1).Add(R,R)
+      R.Add(R,Q[i-1])
+   }
+   if Q_prev != nil {
+     return R.Add(R,Q_prev)
+   } else {
+     return R
+   }
+}
+
+/////
+
+// TODO - How can avoid replicating code in G2?
+//G2
+
+type TableG2 struct{
+   data []*bn256.G2
+}
+
+
+func (t TableG2) GetData() []*bn256.G2 {
+  return t.data
+}
+
+
+// Compute table of gsize elements as ::
+//  Table[0] = Inf
+//  Table[1] = a[0]
+//  Table[2] = a[1]
+//  Table[3] = a[0]+a[1]
+//  .....
+//  Table[(1<<gsize)-1] = a[0]+a[1]+...+a[gsize-1]
+func (t *TableG2) NewTableG2(a []*bn256.G2, gsize int){
+   // EC table
+   table := make([]*bn256.G2, 0)
+
+   // We need at least gsize elements. If not enough, fill with 0
+   a_ext := make([]*bn256.G2, 0)
+   a_ext = append(a_ext, a...)
+
+   for i:=len(a); i<gsize; i++ {
+      a_ext = append(a_ext,new(bn256.G2).ScalarBaseMult(big.NewInt(0)))
+   }
+
+   elG2 := new(bn256.G2).ScalarBaseMult(big.NewInt(0))
+   table = append(table,elG2)
+   last_pow2 := 1
+   nelems := 0
+   for i :=1; i< 1<<gsize; i++ {
+      elG2 := new(bn256.G2)
+      // if power of 2
+      if i & (i-1) == 0{
+        last_pow2 = i
+        elG2.Set(a_ext[nelems])
+        nelems++
+      } else {
+        elG2.Add(table[last_pow2], table[i-last_pow2])
+        // TODO bn256 doesn't export MakeAffine function. We need to fork repo
+        //table[i].MakeAffine()
+      }
+      table = append(table, elG2)
+  }
+  t.data = table
+}
+
+// Multiply scalar by precomputed table of G2 elements
+func (t *TableG2) MulTableG2(k []*big.Int, Q_prev *bn256.G2, gsize int) *bn256.G2 {
+   // We need at least gsize elements. If not enough, fill with 0
+   k_ext := make([]*big.Int, 0)
+   k_ext = append(k_ext, k...)
+
+   for i:=len(k); i < gsize; i++ {
+      k_ext = append(k_ext,new(big.Int).SetUint64(0))
+   }
+
+   Q := new(bn256.G2).ScalarBaseMult(big.NewInt(0))
+
+   msb := getMsb(k_ext)
+
+   for i := msb-1; i >= 0; i-- {
+        // TODO. bn256 doesn't export double operation. We will need to fork repo and export it
+	Q = new(bn256.G2).Add(Q,Q)
+        b := getBit(k_ext,i)
+	if b != 0 {
+          // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+	  Q.Add(Q, t.data[b])
+	}
+   }
+   if Q_prev != nil {
+     return Q.Add(Q, Q_prev)
+   } else {
+     return Q
+   }
+}
+
+// Multiply scalar by precomputed table of G2 elements without intermediate doubling
+func MulTableNoDoubleG2(t []TableG2, k []*big.Int, Q_prev *bn256.G2, gsize int) *bn256.G2 {
+   // We need at least gsize elements. If not enough, fill with 0
+   min_nelems := len(t) * gsize
+   k_ext := make([]*big.Int, 0)
+   k_ext = append(k_ext, k...)
+   for i := len(k); i <  min_nelems; i++ {
+      k_ext = append(k_ext,new(big.Int).SetUint64(0))
+   }
+   // Init Adders
+   nbitsQ := cryptoConstants.Q.BitLen()
+   Q := make([]*bn256.G2,nbitsQ)
+
+   for i:=0; i< nbitsQ; i++ {
+     Q[i] = new(bn256.G2).ScalarBaseMult(big.NewInt(0))
+   }
+
+   // Perform bitwise addition
+   for j:=0; j < len(t); j++ {
+     msb := getMsb(k_ext[j*gsize:(j+1)*gsize])
+
+     for i := msb-1; i >= 0; i-- {
+        b := getBit(k_ext[j*gsize:(j+1)*gsize],i)
+	if b != 0 {
+          // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+	  Q[i].Add(Q[i], t[j].data[b])
+	}
+     }
+   }
+
+   // Consolidate Addition
+   R := new(bn256.G2).Set(Q[nbitsQ-1])
+   for i:=nbitsQ-1; i>0; i-- {
+      // TODO. bn256 doesn't export double operation. We will need to fork repo and export it
+      R = new(bn256.G2).Add(R,R)
+      R.Add(R,Q[i-1])
+   }
+   if Q_prev != nil {
+     return R.Add(R,Q_prev)
+   } else {
+     return R
+   }
+}
+
+// Compute tables within function. This solution should still be faster than std  multiplication
+// for gsize = 7
+func ScalarMultG2(a []*bn256.G2, k []*big.Int, Q_prev *bn256.G2, gsize int) *bn256.G2 {
+     ntables := int((len(a) + gsize - 1) / gsize)
+     table := TableG2{}
+     Q:= new(bn256.G2).ScalarBaseMult(new(big.Int))
+
+     for i:=0; i<ntables-1; i++ {
+       table.NewTableG2( a[i*gsize:(i+1)*gsize], gsize)
+       Q = table.MulTableG2(k[i*gsize:(i+1)*gsize], Q, gsize)
+     }
+     table.NewTableG2( a[(ntables-1)*gsize:], gsize)
+     Q = table.MulTableG2(k[(ntables-1)*gsize:], Q, gsize)
+
+     if Q_prev != nil {
+       return Q.Add(Q,Q_prev)
+     } else {
+       return Q
+     }
+}
+
+// Multiply scalar by precomputed table of G2 elements without intermediate doubling
+func ScalarMultNoDoubleG2(a []*bn256.G2, k []*big.Int, Q_prev *bn256.G2, gsize int) *bn256.G2 {
+   ntables := int((len(a) + gsize - 1) / gsize)
+   table := TableG2{}
+
+   // We need at least gsize elements. If not enough, fill with 0
+   min_nelems := ntables * gsize
+   k_ext := make([]*big.Int, 0)
+   k_ext = append(k_ext, k...)
+   for i := len(k); i <  min_nelems; i++ {
+      k_ext = append(k_ext,new(big.Int).SetUint64(0))
+   }
+   // Init Adders
+   nbitsQ := cryptoConstants.Q.BitLen()
+   Q := make([]*bn256.G2,nbitsQ)
+
+   for i:=0; i< nbitsQ; i++ {
+     Q[i] = new(bn256.G2).ScalarBaseMult(big.NewInt(0))
+   }
+
+   // Perform bitwise addition
+   for j:=0; j < ntables-1; j++ {
+     table.NewTableG2( a[j*gsize:(j+1)*gsize], gsize)
+     msb := getMsb(k_ext[j*gsize:(j+1)*gsize])
+
+     for i := msb-1; i >= 0; i-- {
+        b := getBit(k_ext[j*gsize:(j+1)*gsize],i)
+	if b != 0 {
+          // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+	  Q[i].Add(Q[i], table.data[b])
+	}
+     }
+   }
+   table.NewTableG2( a[(ntables-1)*gsize:], gsize)
+   msb := getMsb(k_ext[(ntables-1)*gsize:])
+
+   for i := msb-1; i >= 0; i-- {
+     b := getBit(k_ext[(ntables-1)*gsize:],i)
+     if b != 0 {
+         // TODO. bn256 doesn't export mixed addition (Jacobian + Affine), which is more efficient.
+         Q[i].Add(Q[i], table.data[b])
+     }
+   }
+
+   // Consolidate Addition
+   R := new(bn256.G2).Set(Q[nbitsQ-1])
+   for i:=nbitsQ-1; i>0; i-- {
+      // TODO. bn256 doesn't export double operation. We will need to fork repo and export it
+      R = new(bn256.G2).Add(R,R)
+      R.Add(R,Q[i-1])
+   }
+   if Q_prev != nil {
+     return R.Add(R,Q_prev)
+   } else {
+     return R
+   }
+}
+
+// Return most significant bit position in a group of Big Integers
+func getMsb(k []*big.Int) int{
+  msb := 0
+
+  for _, el := range(k){
+     tmp_msb := el.BitLen()
+     if tmp_msb > msb {
+        msb = tmp_msb
+     }
+  }
+  return msb
+}
+
+// Return ith bit in group of Big Integers
+func getBit(k []*big.Int, i int) uint {
+   table_idx := uint(0)
+
+   for idx, el := range(k){
+     b := el.Bit(i)
+     table_idx += (b << idx)
+   }
+   return table_idx
+}

prover/gextra_test.go

@@ -0,0 +1,166 @@
+package prover
+
+import (
+	"crypto/rand"
+	"math/big"
+	"testing"
+	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+        "time"
+        "bytes"
+        "fmt"
+)
+
+const (
+       N1 = 5000
+       N2 = 5000
+)
+
+func randomBigIntArray(n int) []*big.Int{
+	var p []*big.Int
+	for i := 0; i < n; i++ {
+		pi := randBI()
+		p = append(p, pi)
+	}
+
+        return p
+}
+
+func randomG1Array(n int) []*bn256.G1 {
+     arrayG1 := make([]*bn256.G1, n)
+
+     for i:=0; i<n; i++ {
+       _, arrayG1[i], _ = bn256.RandomG1(rand.Reader)
+     }
+     return arrayG1
+}
+
+func randomG2Array(n int) []*bn256.G2 {
+     arrayG2 := make([]*bn256.G2, n)
+
+     for i:=0; i<n; i++ {
+       _, arrayG2[i], _ = bn256.RandomG2(rand.Reader)
+     }
+     return arrayG2
+}
+
+
+
+func TestTableG1(t *testing.T){
+     n     := N1
+
+     // init scalar
+     var arrayW = randomBigIntArray(n)
+     // init G1 array
+     var arrayG1 = randomG1Array(n)
+
+     beforeT := time.Now()
+     Q1 := new(bn256.G1).ScalarBaseMult(new(big.Int))
+     for i:=0; i < n; i++ {
+         Q1.Add(Q1, new(bn256.G1).ScalarMult(arrayG1[i], arrayW[i]))
+     }
+     fmt.Println("Std. Mult. time elapsed:", time.Since(beforeT))
+
+     for gsize:=2; gsize < 10; gsize++ {
+        ntables := int((n + gsize - 1) / gsize)
+        table := make([]TableG1, ntables)
+
+        for i:=0; i<ntables-1; i++ {
+          table[i].NewTableG1( arrayG1[i*gsize:(i+1)*gsize], gsize)
+        }
+        table[ntables-1].NewTableG1( arrayG1[(ntables-1)*gsize:], gsize)
+
+        beforeT = time.Now()
+        Q2:= new(bn256.G1).ScalarBaseMult(new(big.Int))
+        for i:=0; i<ntables-1; i++ {
+           Q2 = table[i].MulTableG1(arrayW[i*gsize:(i+1)*gsize], Q2, gsize)
+        }
+        Q2 = table[ntables-1].MulTableG1(arrayW[(ntables-1)*gsize:], Q2, gsize)
+        fmt.Printf("Gsize : %d, TMult time elapsed: %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q3 := ScalarMultG1(arrayG1, arrayW, nil, gsize)
+        fmt.Printf("Gsize : %d, TMult time elapsed (inc table comp): %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q4 := MulTableNoDoubleG1(table, arrayW, nil, gsize)
+        fmt.Printf("Gsize : %d, TMultNoDouble time elapsed: %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q5 := ScalarMultNoDoubleG1(arrayG1, arrayW, nil, gsize)
+        fmt.Printf("Gsize : %d, TMultNoDouble time elapsed (inc table comp): %s\n", gsize,time.Since(beforeT))
+
+
+        if bytes.Compare(Q1.Marshal(),Q2.Marshal()) != 0 {
+            t.Error("Error in TMult")
+        }
+        if bytes.Compare(Q1.Marshal(),Q3.Marshal()) != 0 {
+            t.Error("Error in  TMult with table comp")
+        }
+        if bytes.Compare(Q1.Marshal(),Q4.Marshal()) != 0 {
+            t.Error("Error in  TMultNoDouble")
+        }
+        if bytes.Compare(Q1.Marshal(),Q5.Marshal()) != 0 {
+            t.Error("Error in  TMultNoDoublee with table comp")
+        }
+    }
+}
+
+func TestTableG2(t *testing.T){
+     n     := N2
+
+     // init scalar
+     var arrayW = randomBigIntArray(n)
+     // init G2 array
+     var arrayG2 = randomG2Array(n)
+
+     beforeT := time.Now()
+     Q1 := new(bn256.G2).ScalarBaseMult(new(big.Int))
+     for i:=0; i < n; i++ {
+         Q1.Add(Q1, new(bn256.G2).ScalarMult(arrayG2[i], arrayW[i]))
+     }
+     fmt.Println("Std. Mult. time elapsed:", time.Since(beforeT))
+
+     for gsize:=2; gsize < 10; gsize++ {
+        ntables := int((n + gsize - 1) / gsize)
+        table := make([]TableG2, ntables)
+
+        for i:=0; i<ntables-1; i++ {
+          table[i].NewTableG2( arrayG2[i*gsize:(i+1)*gsize], gsize)
+        }
+        table[ntables-1].NewTableG2( arrayG2[(ntables-1)*gsize:], gsize)
+
+        beforeT = time.Now()
+        Q2:= new(bn256.G2).ScalarBaseMult(new(big.Int))
+        for i:=0; i<ntables-1; i++ {
+           Q2 =table[i].MulTableG2(arrayW[i*gsize:(i+1)*gsize], Q2, gsize)
+        }
+        Q2 = table[ntables-1].MulTableG2(arrayW[(ntables-1)*gsize:], Q2, gsize)
+        fmt.Printf("Gsize : %d, TMult time elapsed: %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q3 := ScalarMultG2(arrayG2, arrayW, nil, gsize)
+        fmt.Printf("Gsize : %d, TMult time elapsed (inc table comp): %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q4 := MulTableNoDoubleG2(table, arrayW, nil, gsize)
+        fmt.Printf("Gsize : %d, TMultNoDouble time elapsed: %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q5 := ScalarMultNoDoubleG2(arrayG2, arrayW, nil, gsize)
+        fmt.Printf("Gsize : %d, TMultNoDouble time elapsed (inc table comp): %s\n", gsize,time.Since(beforeT))
+
+
+        if bytes.Compare(Q1.Marshal(),Q2.Marshal()) != 0 {
+            t.Error("Error in TMult")
+        }
+        if bytes.Compare(Q1.Marshal(),Q3.Marshal()) != 0 {
+            t.Error("Error in  TMult with table comp")
+        }
+        if bytes.Compare(Q1.Marshal(),Q4.Marshal()) != 0 {
+            t.Error("Error in  TMultNoDouble")
+        }
+        if bytes.Compare(Q1.Marshal(),Q5.Marshal()) != 0 {
+            t.Error("Error in  TMultNoDoublee with table comp")
+        }
+    }
+}

prover/prover.go

@@ -4,12 +4,13 @@ import (
 	"crypto/rand"
 	"math"
 	"math/big"
+	"runtime"
 	"sync"
 
 	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
 	"github.com/iden3/go-circom-prover-verifier/types"
-	"github.com/iden3/go-iden3-crypto/ff"
 	"github.com/iden3/go-iden3-crypto/utils"
+        //"fmt"
 )
 
 // Proof is the data structure of the Groth16 zkSNARK proof
@@ -42,6 +43,11 @@ type Pk struct {
 // Witness contains the witness
 type Witness []*big.Int
 
+// Group Size
+const (
+    GSIZE = 6
+)
+
 func randBigInt() (*big.Int, error) {
 	maxbits := types.R.BitLen()
 	b := make([]byte, (maxbits/8)-1)
@@ -68,66 +74,92 @@ func GenerateProof(pk *types.Pk, w types.Witness) (*types.Proof, []*big.Int, err
 		return nil, nil, err
 	}
 
-	proof.A = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
+	// BEGIN PAR
-	proof.B = new(bn256.G2).ScalarBaseMult(big.NewInt(0))
+	numcpu := runtime.NumCPU()
-	proof.C = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
-	proofBG1 := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
 
-	var wg sync.WaitGroup
+	proofA := arrayOfZeroesG1(numcpu)
-	wg.Add(4)
+	proofB := arrayOfZeroesG2(numcpu)
-	go func() {
+	proofC := arrayOfZeroesG1(numcpu)
-		for i := 0; i < pk.NVars; i++ {
+	proofBG1 := arrayOfZeroesG1(numcpu)
-			proof.A = new(bn256.G1).Add(proof.A, new(bn256.G1).ScalarMult(pk.A[i], w[i]))
+        gsize := GSIZE
+	var wg1 sync.WaitGroup
+	wg1.Add(numcpu)
+	for _cpu, _ranges := range ranges(pk.NVars, numcpu) {
+		// split 1
+		go func(cpu int, ranges [2]int) {
+                        proofA[cpu] = ScalarMultNoDoubleG1(pk.A[ranges[0]:ranges[1]],
+                                                           w[ranges[0]:ranges[1]],
+                                                           proofA[cpu],
+                                                           gsize)
+                        proofB[cpu] = ScalarMultNoDoubleG2(pk.B2[ranges[0]:ranges[1]],
+                                                           w[ranges[0]:ranges[1]],
+                                                           proofB[cpu],
+                                                           gsize)
+                        proofBG1[cpu] = ScalarMultNoDoubleG1(pk.B1[ranges[0]:ranges[1]],
+                                                           w[ranges[0]:ranges[1]],
+                                                           proofBG1[cpu],
+                                                           gsize)
+                        min_lim := pk.NPublic+1
+                        if ranges[0] > pk.NPublic+1 {
+                           min_lim = ranges[0]
                         }
-		wg.Done()
+                        if ranges[1] > pk.NPublic + 1 {
-	}()
+                            proofC[cpu] = ScalarMultNoDoubleG1(pk.C[min_lim:ranges[1]],
-	go func() {
+                                                           w[min_lim:ranges[1]],
-		for i := 0; i < pk.NVars; i++ {
+                                                           proofC[cpu],
-			proof.B = new(bn256.G2).Add(proof.B, new(bn256.G2).ScalarMult(pk.B2[i], w[i]))
+                                                           gsize)
                         }
-		wg.Done()
+			wg1.Done()
-	}()
+		}(_cpu, _ranges)
-	go func() {
-		for i := 0; i < pk.NVars; i++ {
-			proofBG1 = new(bn256.G1).Add(proofBG1, new(bn256.G1).ScalarMult(pk.B1[i], w[i]))
 	}
-		wg.Done()
+	wg1.Wait()
-	}()
+	// join 1
-	go func() {
+	for cpu := 1; cpu < numcpu; cpu++ {
-		for i := pk.NPublic + 1; i < pk.NVars; i++ {
+		proofA[0].Add(proofA[0], proofA[cpu])
-			proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(pk.C[i], w[i]))
+		proofB[0].Add(proofB[0], proofB[cpu])
+		proofC[0].Add(proofC[0], proofC[cpu])
+		proofBG1[0].Add(proofBG1[0], proofBG1[cpu])
 	}
-		wg.Done()
+	proof.A = proofA[0]
-	}()
+	proof.B = proofB[0]
-	wg.Wait()
+	proof.C = proofC[0]
+	// END PAR
 
 	h := calculateH(pk, w)
 
+	proof.A.Add(proof.A, pk.VkAlpha1)
+	proof.A.Add(proof.A, new(bn256.G1).ScalarMult(pk.VkDelta1, r))
+
+	proof.B.Add(proof.B, pk.VkBeta2)
+	proof.B.Add(proof.B, new(bn256.G2).ScalarMult(pk.VkDelta2, s))
+
+	proofBG1[0].Add(proofBG1[0], pk.VkBeta1)
+	proofBG1[0].Add(proofBG1[0], new(bn256.G1).ScalarMult(pk.VkDelta1, s))
+
+	proofC = arrayOfZeroesG1(numcpu)
 	var wg2 sync.WaitGroup
-	wg2.Add(2)
+	wg2.Add(numcpu)
-	go func() {
+	for _cpu, _ranges := range ranges(len(h), numcpu) {
-		proof.A = new(bn256.G1).Add(proof.A, pk.VkAlpha1)
+		// split 2
-		proof.A = new(bn256.G1).Add(proof.A, new(bn256.G1).ScalarMult(pk.VkDelta1, r))
+		go func(cpu int, ranges [2]int) {
-
+                        proofC[cpu] = ScalarMultNoDoubleG1(pk.HExps[ranges[0]:ranges[1]],
-		proof.B = new(bn256.G2).Add(proof.B, pk.VkBeta2)
+                                                           h[ranges[0]:ranges[1]],
-		proof.B = new(bn256.G2).Add(proof.B, new(bn256.G2).ScalarMult(pk.VkDelta2, s))
+                                                           proofC[cpu],
-
+                                                           gsize)
-		proofBG1 = new(bn256.G1).Add(proofBG1, pk.VkBeta1)
-		proofBG1 = new(bn256.G1).Add(proofBG1, new(bn256.G1).ScalarMult(pk.VkDelta1, s))
 			wg2.Done()
-	}()
+		}(_cpu, _ranges)
-	go func() {
-		for i := 0; i < len(h); i++ {
-			proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(pk.HExps[i], h[i]))
 	}
-		wg2.Done()
-	}()
 	wg2.Wait()
+	// join 2
+	for cpu := 1; cpu < numcpu; cpu++ {
+		proofC[0].Add(proofC[0], proofC[cpu])
+	}
+	proof.C.Add(proof.C, proofC[0])
 
-	proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(proof.A, s))
+	proof.C.Add(proof.C, new(bn256.G1).ScalarMult(proof.A, s))
-	proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(proofBG1, r))
+	proof.C.Add(proof.C, new(bn256.G1).ScalarMult(proofBG1[0], r))
-	rsneg := new(big.Int).Mod(new(big.Int).Neg(new(big.Int).Mul(r, s)), types.R) // fAdd & fMul
+	rsneg := new(big.Int).Mod(new(big.Int).Neg(new(big.Int).Mul(r, s)), types.R)
-	proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(pk.VkDelta1, rsneg))
+	proof.C.Add(proof.C, new(bn256.G1).ScalarMult(pk.VkDelta1, rsneg))
 
 	pubSignals := w[1 : pk.NPublic+1]
 
@@ -139,14 +171,27 @@ func calculateH(pk *types.Pk, w types.Witness) []*big.Int {
 	polAT := arrayOfZeroes(m)
 	polBT := arrayOfZeroes(m)
 
+	numcpu := runtime.NumCPU()
+
+	var wg1 sync.WaitGroup
+	wg1.Add(2)
+	go func() {
 		for i := 0; i < pk.NVars; i++ {
 			for j := range pk.PolsA[i] {
 				polAT[j] = fAdd(polAT[j], fMul(w[i], pk.PolsA[i][j]))
 			}
+		}
+		wg1.Done()
+	}()
+	go func() {
+		for i := 0; i < pk.NVars; i++ {
 			for j := range pk.PolsB[i] {
 				polBT[j] = fAdd(polBT[j], fMul(w[i], pk.PolsB[i][j]))
 			}
 		}
+		wg1.Done()
+	}()
+	wg1.Wait()
 	polATe := utils.BigIntArrayToElementArray(polAT)
 	polBTe := utils.BigIntArrayToElementArray(polBT)
 
@@ -156,22 +201,49 @@ func calculateH(pk *types.Pk, w types.Witness) []*big.Int {
 	r := int(math.Log2(float64(m))) + 1
 	roots := newRootsT()
 	roots.setRoots(r)
-	for i := 0; i < len(polASe); i++ {
+
-		polASe[i] = ff.NewElement().Mul(polASe[i], roots.roots[r][i])
+	var wg2 sync.WaitGroup
-		polBSe[i] = ff.NewElement().Mul(polBSe[i], roots.roots[r][i])
+	wg2.Add(numcpu)
+	for _cpu, _ranges := range ranges(len(polASe), numcpu) {
+		go func(cpu int, ranges [2]int) {
+			for i := ranges[0]; i < ranges[1]; i++ {
+				polASe[i].Mul(polASe[i], roots.roots[r][i])
+				polBSe[i].Mul(polBSe[i], roots.roots[r][i])
 			}
+			wg2.Done()
+		}(_cpu, _ranges)
+	}
+	wg2.Wait()
 
 	polATodd := fft(polASe)
 	polBTodd := fft(polBSe)
 
 	polABT := arrayOfZeroesE(len(polASe) * 2)
-	for i := 0; i < len(polASe); i++ {
+	var wg3 sync.WaitGroup
-		polABT[2*i] = ff.NewElement().Mul(polATe[i], polBTe[i])
+	wg3.Add(numcpu)
-		polABT[2*i+1] = ff.NewElement().Mul(polATodd[i], polBTodd[i])
+	for _cpu, _ranges := range ranges(len(polASe), numcpu) {
+		go func(cpu int, ranges [2]int) {
+			for i := ranges[0]; i < ranges[1]; i++ {
+				polABT[2*i].Mul(polATe[i], polBTe[i])
+				polABT[2*i+1].Mul(polATodd[i], polBTodd[i])
 			}
+			wg3.Done()
+		}(_cpu, _ranges)
+	}
+	wg3.Wait()
 
 	hSeFull := ifft(polABT)
 
 	hSe := hSeFull[m:]
 	return utils.ElementArrayToBigIntArray(hSe)
 }
+
+func ranges(n, parts int) [][2]int {
+	s := make([][2]int, parts)
+	p := float64(n) / float64(parts)
+	for i := 0; i < parts; i++ {
+		a, b := int(float64(i)*p), int(float64(i+1)*p)
+		s[i] = [2]int{a, b}
+	}
+	return s
+}

prover/prover_test.go

@@ -16,8 +16,8 @@ import (
 func TestCircuitsGenerateProof(t *testing.T) {
 	testCircuitGenerateProof(t, "circuit1k") // 1000 constraints
 	testCircuitGenerateProof(t, "circuit5k") // 5000 constraints
-	// testCircuitGenerateProof(t, "circuit10k") // 10000 constraints
+        //testCircuitGenerateProof(t, "circuit10k") // 10000 constraints
-	// testCircuitGenerateProof(t, "circuit20k") // 20000 constraints
+        //testCircuitGenerateProof(t, "circuit20k") // 20000 constraints
 }
 
 func testCircuitGenerateProof(t *testing.T, circuit string) {
@@ -61,12 +61,12 @@ func testCircuitGenerateProof(t *testing.T, circuit string) {
 
 func BenchmarkGenerateProof(b *testing.B) {
 	// benchmark with a circuit of 10000 constraints
-	provingKeyJson, err := ioutil.ReadFile("../testdata/circuit1/proving_key.json")
+	provingKeyJson, err := ioutil.ReadFile("../testdata/circuit5k/proving_key.json")
 	require.Nil(b, err)
 	pk, err := parsers.ParsePk(provingKeyJson)
 	require.Nil(b, err)
 
-	witnessJson, err := ioutil.ReadFile("../testdata/circuit1/witness.json")
+	witnessJson, err := ioutil.ReadFile("../testdata/circuit5k/witness.json")
 	require.Nil(b, err)
 	w, err := parsers.ParseWitness(witnessJson)
 	require.Nil(b, err)

prover/tables.md

@@ -0,0 +1,49 @@
+# Tables Pre-calculation
+The most time consuming part of a ZKSnark proof calculation is the scalar multiplication of elliptic curve points. Direct mechanism accumulates each multiplication. However, prover only needs the total accumulation.
+
+There are two potential improvements to the naive approach:
+
+1. Apply Strauss-Shamir method (https://stackoverflow.com/questions/50993471/ec-scalar-multiplication-with-strauss-shamir-method).
+2. Leave the doubling operation for the last step
+
+Both options can be combined. 
+
+In the following table, we show the results of using the naive method, Srauss-Shamir and Strauss-Shamir + No doubling. These last two options are repeated for different table grouping order.
+
+There are 50000 G1 Elliptical Curve Points, and the scalars are 254 bits (BN256 curve). 
+
+There may be some concern on the additional size of the tables since they need to be loaded into a smartphone during the proof, and the time required to load these tables may exceed the benefits. If this is a problem, another althernative is to compute the tables during the proof itself. Depending on the Group Size, timing may be better than the naive approach.
+
+
+| Algorithm (G1) | GS 2 | GS 3 | GS 4 | GS 5 | GS 6 | GS 7 | GS 8 | GS 9 | 
+|---|---|---|---|---|---|---|---|---|
+| Naive | 6.63s | - | - | - | - | - |  - | - |
+| Strauss |  13.16s | 9.03s | 6.95s | 5.61s | 4.91s | 4.26s | 3.88s | 3.54 s |
+| Strauss + Table Computation | 16.13s | 11.32s | 8.47s | 7.10s | 6.2s | 5.94s | 6.01s | 6.69s |
+| No Doubling | 3.74s | 3.00s | 2.38s | 1.96s | 1.79s | 1.54s | 1.50s | 1.44s|
+| No Doubling + Table Computation  | 6.83s | 5.1s | 4.16s | 3.52s| 3.22s | 3.21s | 3.57s | 4.56s |
+
+There are 5000 G2 Elliptical Curve Points, and the scalars are 254 bits (BN256 curve). 
+
+| Algorithm (G2) | GS 2 | GS 3 | GS 4 | GS 5 | GS 6 | GS 7 | GS 8 | GS 9 | 
+|---|---|---|---|---|---|---|---|---|
+| Naive | 3.55s | | | | | | | |
+| Strauss |  3.55s | 2.54s | 1.96s | 1.58s |  1.38s | 1.20s | 1.03s | 937ms |
+| Strauss + Table Computation | 3.59s | 2.58s | 2.04s | 1.71s | 1.51s | 1.46s | 1.51s | 1.82s |
+| No Doubling | 1.49s | 1.16s | 952ms | 719ms | 661ms | 548ms | 506ms| 444ms |
+| No Doubling + Table Computation  | 1.55s |  1.21s | 984ms | 841ms | 826ms | 847ms | 1.03s | 1.39s |
+
+| GS | Extra Disk Space per Constraint (G1)|
+|----|--------|
+| 2  |  64 B  |
+| 3  |  106 B |
+| 4  |  192 B |
+| 5  |  346 B |
+| 6  |  618 B |
+| 7  |  1106 B |
+| 8  |  1984 B |
+| 9  |  3577 B |
+| N  |  2^(N+6)/N - 64 B |
+
+Extra disk space per constraint in G2 is twice the requirements for G1
+

tables.md

@@ -0,0 +1,25 @@
+# Tables Pre-calculation
+The most time consuming part of a ZKSnark proof calculation is the scalar multiplication of elliptic curve points. Direct mechanism accumulates each multiplication. However, prover only needs the total accumulation.
+
+There are two potential improvements to the naive approach:
+
+1. Apply Strauss-Shamir method (https://stackoverflow.com/questions/50993471/ec-scalar-multiplication-with-strauss-shamir-method).
+2. Leave the doubling operation for the last step
+
+Both options can be combined. 
+
+In the following table, we show the results of using the naive method, Srauss-Shamir and Strauss-Shamir + No doubling. These last two options are repeated for different table grouping order.
+
+There are 5000 G1 Elliptical Curve Points, and the scalars are 254 bits (BN256 curve). 
+
+There may be some concern on the additional size of the tables since they need to be loaded into a smartphone during the proof, and the time required to load these tables may exceed the benefits. If this is a problem, another althernative is to compute the tables during the proof itself. Depending on the Group Size, timing may be better than the naive approach.
+
+
+| Algorithm | GS / Time |
+|---|---|---|
+| Naive | 6.63s | | | | | | | |
+| Strauss |  13.16s | 9.033s | 6.95s | 5.61s | 4.91s | 4.26s | 3.88s | 3.54 s | 1.44 s |
+| Strauss + Table Computation | 16.13s | 11.32s | 8.47s | 7.10s | 6.2s | 5.94s | 6.01s | 6.69s |
+| No Doubling | 3.74s | 3.00s | 2.38s | 1.96s | 1.79s | 1.54s | 1.50s | 1.44s|
+| No Doubling + Table Computation  | 6.83s | 5.1s | 4.16s | 3.52s| 3.22s | 3.21s | 3.57s | 4.56s |
+

testdata/.gitignore

@@ -0,0 +1 @@
+node_modules

testdata/compile-circuits.sh

@@ -1,29 +1,31 @@
 #!/bin/sh
 
+npm install
+
 compile_and_ts_and_witness() {
   echo $(date +"%T") "circom circuit.circom --r1cs --wasm --sym"
   itime="$(date -u +%s)"
-  circom circuit.circom --r1cs --wasm --sym
+  ../node_modules/.bin/circom circuit.circom --r1cs --wasm --sym
   ftime="$(date -u +%s)"
   echo "	($(($(date -u +%s)-$itime))s)"
 
   echo $(date +"%T") "snarkjs info -r circuit.r1cs"
-  snarkjs info -r circuit.r1cs
+  ../node_modules/.bin/snarkjs info -r circuit.r1cs
 
   echo $(date +"%T") "snarkjs setup"
   itime="$(date -u +%s)"
-  snarkjs setup
+  ../node_modules/.bin/snarkjs setup
   echo "	($(($(date -u +%s)-$itime))s)"
   echo $(date +"%T") "trusted setup generated"
 
   sed -i 's/null/["0","0","0"]/g' proving_key.json
 
   echo "calculating witness"
-  snarkjs calculatewitness --wasm circuit.wasm --input inputs.json --witness witness.json
+  ../node_modules/.bin/snarkjs calculatewitness --wasm circuit.wasm --input inputs.json --witness witness.json
 
   echo $(date +"%T") "snarkjs generateverifier"
   itime="$(date -u +%s)"
-  snarkjs generateverifier
+  ../node_modules/.bin/snarkjs generateverifier
   echo "	($(($(date -u +%s)-$itime))s)"
   echo $(date +"%T") "generateverifier generated"
 }
@@ -40,3 +42,22 @@ compile_and_ts_and_witness
 # echo "compile & trustesetup for circuit20k"
 # cd ../circuit20k
 # compile_and_ts_and_witness
+
+cd ../
+
+echo "convert witness & pk of circuit1k to bin"
+node node_modules/wasmsnark/tools/buildwitness.js -i circuit1k/witness.json -o circuit1k/witness.bin
+node node_modules/wasmsnark/tools/buildpkey.js -i circuit1k/proving_key.json -o circuit1k/proving_key.bin
+
+echo "convert witness & pk of circuit5k to bin"
+node node_modules/wasmsnark/tools/buildwitness.js -i circuit5k/witness.json -o circuit5k/witness.bin
+node node_modules/wasmsnark/tools/buildpkey.js -i circuit5k/proving_key.json -o circuit5k/proving_key.bin
+
+# echo "convert witness & pk of circuit10k to bin"
+# node node_modules/wasmsnark/tools/buildwitness.js -i circuit10k/witness.json -o circuit10k/witness.bin
+# node node_modules/wasmsnark/tools/buildpkey.js -i circuit10k/proving_key.json -o circuit10k/proving_key.bin
+# 
+# echo "convert witness & pk of circuit20k to bin"
+# node node_modules/wasmsnark/tools/buildwitness.js -i circuit20k/witness.json -o circuit20k/witness.bin
+# node node_modules/wasmsnark/tools/buildpkey.js -i circuit20k/proving_key.json -o circuit20k/proving_key.bin
+

testdata/package-lock.json

@@ -0,0 +1,923 @@
+{
+  "name": "binformat",
+  "version": "0.0.1",
+  "lockfileVersion": 1,
+  "requires": true,
+  "dependencies": {
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+    },
+    "ansi-regex": {
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+      "resolved": "https://registry.npmjs.org/ansi-regex/-/ansi-regex-5.0.0.tgz",
+      "integrity": "sha512-bY6fj56OUQ0hU1KjFNDQuJFezqKdrAyFdIevADiqrWHwSlbmBNMHp5ak2f40Pm8JTFyM2mqxkG6ngkHO11f/lg=="
+    },
+    "ansi-styles": {
+      "version": "3.2.1",
+      "resolved": "https://registry.npmjs.org/ansi-styles/-/ansi-styles-3.2.1.tgz",
+      "integrity": "sha512-VT0ZI6kZRdTh8YyJw3SMbYm/u+NqfsAxEpWO0Pf9sq8/e94WxxOpPKx9FR1FlyCtOVDNOQ+8ntlqFxiRc+r5qA==",
+      "requires": {
+        "color-convert": "^1.9.0"
+      }
+    },
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+    },
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+      "version": "0.9.2",
+      "resolved": "https://registry.npmjs.org/async/-/async-0.9.2.tgz",
+      "integrity": "sha1-rqdNXmHB+JlhO/ZL2mbUx48v0X0="
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+        "get-caller-file": "^2.0.1",
+        "require-directory": "^2.1.1",
+        "require-main-filename": "^2.0.0",
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+        "string-width": "^4.2.0",
+        "which-module": "^2.0.0",
+        "y18n": "^4.0.0",
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+      "requires": {
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+        "decamelize": "^1.2.0"
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+  }
+}

testdata/package.json

@@ -0,0 +1,16 @@
+{
+  "name": "binformat",
+  "version": "0.0.1",
+  "description": "",
+  "main": "index.js",
+  "scripts": {
+    "test": "echo \"Error: no test specified\" && exit 1"
+  },
+  "author": "",
+  "license": "GPL-3.0",
+  "dependencies": {
+    "wasmsnark": "0.0.10",
+    "circom": "^0.5.11",
+    "snarkjs": "^0.1.31"
+  }
+}

verifier/verifier.go

@@ -17,6 +17,7 @@ type Vk struct {
 	IC    []*bn256.G1
 }
 
+// Verify verifies the Groth16 zkSNARK proof
 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)")