G1 Functionality to precomput G1 tables

prover/gextra.go

@@ -0,0 +1,218 @@
+package prover
+
+import (
+        "math/big"
+	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+	cryptoConstants "github.com/iden3/go-iden3-crypto/constants"
+        //"fmt"
+)
+
+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, 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])
+	} 
+   }
+   return Q
+}
+
+// Multiply scalar by precomputed table of G1 elements without intermediate doubling
+func MulTableNoDoubleG1(t []TableG1, k []*big.Int, 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])
+   }
+   return R
+}
+
+// Compute tables within function. This solution should still be faster than std  multiplication
+// for gsize = 7
+func ScalarMult(a []*bn256.G1, k []*big.Int, 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.Add(Q,table.MulTableG1(k[i*gsize:(i+1)*gsize], gsize))
+     }
+     table.NewTableG1( a[(ntables-1)*gsize:], gsize)
+     Q.Add(Q,table.MulTableG1(k[(ntables-1)*gsize:], gsize))
+
+     return Q
+}
+
+// Multiply scalar by precomputed table of G1 elements without intermediate doubling
+func ScalarMultNoDoubleG1(a []*bn256.G1, k []*big.Int, 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])
+   }
+   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 +1,96 @@
+package prover
+
+import (
+	"crypto/rand"
+	"math/big"
+	"testing"
+	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
+        "time"
+        "bytes"
+        "fmt"
+)
+
+const (
+       N = 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 TestTable(t *testing.T){
+     n     := N
+
+     // 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.Add(Q2,table[i].MulTableG1(arrayW[i*gsize:(i+1)*gsize], gsize))
+        }
+        Q2.Add(Q2,table[ntables-1].MulTableG1(arrayW[(ntables-1)*gsize:], gsize))
+        fmt.Printf("Gsize : %d, TMult time elapsed: %s\n", gsize,time.Since(beforeT))
+   
+        beforeT = time.Now()
+        Q3 := ScalarMult(arrayG1, arrayW, gsize)
+        fmt.Printf("Gsize : %d, TMult time elapsed (inc table comp): %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q4 := MulTableNoDoubleG1(table, arrayW, gsize)
+        fmt.Printf("Gsize : %d, TMultNoDouble time elapsed: %s\n", gsize,time.Since(beforeT))
+
+        beforeT = time.Now()
+        Q5 := ScalarMultNoDoubleG1(arrayG1, arrayW, 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")
+        }
+    }
+}