From f5d913b6a74c3e955f084c2695de0b31a7243091 Mon Sep 17 00:00:00 2001
From: arnaucube <arnaucube@gmail.com>
Date: Tue, 11 Dec 2018 00:19:54 +0100
Subject: [PATCH] bls: doing aggregated signatures

---
 bls/README.md   |  2 +-
 bls/bls.go      | 64 +++++++++++++++++++++++++++++++++++++++++--------
 bls/bls_test.go | 39 +++++++++++++++++++++++-------
 3 files changed, 86 insertions(+), 19 deletions(-)

diff --git a/bls/README.md b/bls/README.md
index f50eb03..959a445 100644
--- a/bls/README.md
+++ b/bls/README.md
@@ -2,7 +2,7 @@
 Boneh–Lynn–Shacham (BLS) signature scheme implemented in Go.
 https://en.wikipedia.org/wiki/Boneh%E2%80%93Lynn%E2%80%93Shacham
 
-This package uses the BN128 Go implementation from https://github.com/arnaucube/go-snark/tree/master/bn128
+This package uses the BN128 Pairing Go implementation from https://github.com/arnaucube/go-snark/tree/master/bn128
 
 ### Usage
 ```go
diff --git a/bls/bls.go b/bls/bls.go
index c5df6bd..2ab8eb9 100644
--- a/bls/bls.go
+++ b/bls/bls.go
@@ -3,6 +3,7 @@ package bls
 import (
 	"crypto/rand"
 	"crypto/sha256"
+	"fmt"
 	"math/big"
 
 	"github.com/arnaucube/go-snark/bn128"
@@ -14,27 +15,36 @@ const bits = 2048
 
 // BLS is the data structure of the BLS signature scheme, including the BN128 pairing curve
 type BLS struct {
-	Bn    bn128.Bn128
+	Bn bn128.Bn128
+}
+type BLSKeys struct {
 	PrivK *big.Int
 	PubK  [3]*big.Int
 }
 
-// NewKeys generate new Private Key and Public Key
-func NewKeys() (BLS, error) {
+// NewBLS generates a new BLS scheme
+func NewBLS() (BLS, error) {
 	bn, err := bn128.NewBn128()
 	if err != nil {
 		return BLS{}, err
 	}
 	bls := BLS{}
 	bls.Bn = bn
-	bls.PrivK, err = rand.Prime(rand.Reader, bits)
+	return bls, nil
+}
+
+// NewKeys generate new Private Key and Public Key
+func (bls BLS) NewKeys() (BLSKeys, error) {
+	var err error
+	k := BLSKeys{}
+	k.PrivK, err = rand.Prime(rand.Reader, bits)
 	if err != nil {
-		return BLS{}, err
+		return BLSKeys{}, err
 	}
 
 	// pubK = pk * G
-	bls.PubK = bls.Bn.G1.MulScalar(bls.Bn.G1.G, bls.PrivK)
-	return bls, nil
+	k.PubK = bls.Bn.G1.MulScalar(bls.Bn.G1.G, k.PrivK)
+	return k, nil
 }
 
 // Hash hashes a message m
@@ -49,17 +59,17 @@ func (bls BLS) Hash(m []byte) [3][2]*big.Int {
 }
 
 // Sign performs the BLS signature of a message m
-func (bls BLS) Sign(m []byte) [3][2]*big.Int {
+func (bls BLS) Sign(privK *big.Int, m []byte) [3][2]*big.Int {
 	// s = pk * H(m)
 	h := bls.Hash(m)
-	sig := bls.Bn.G2.MulScalar(h, bls.PrivK)
+	sig := bls.Bn.G2.MulScalar(h, privK)
 	return sig
 }
 
 // Verify checks the signature of a message m with the given Public Key
 func (bls BLS) Verify(m []byte, sig [3][2]*big.Int, pubK [3]*big.Int) bool {
 	// checks e(P, G) == e(G, s)
-	p1, err := bls.Bn.Pairing(bls.PubK, bls.Hash(m))
+	p1, err := bls.Bn.Pairing(pubK, bls.Hash(m))
 	if err != nil {
 		return false
 	}
@@ -70,3 +80,37 @@ func (bls BLS) Verify(m []byte, sig [3][2]*big.Int, pubK [3]*big.Int) bool {
 
 	return bls.Bn.Fq12.Equal(p1, p2)
 }
+
+func (bls BLS) AggregateSignatures(signatures ...[3][2]*big.Int) [3][2]*big.Int {
+	aggr := signatures[0]
+	for _, sig := range signatures {
+		aggr = bls.Bn.G2.Add(aggr, sig)
+	}
+	return aggr
+}
+func (bls BLS) VerifyAggregatedSignatures(aggrsig [3][2]*big.Int, pubKArray [][3]*big.Int, mArray [][]byte) bool {
+	if len(pubKArray) != len(mArray) {
+		fmt.Println("pubK array and msg array not with the same number of elements")
+		return false
+	}
+	pairingGS, err := bls.Bn.Pairing(bls.Bn.G1.G, aggrsig)
+	if err != nil {
+		return false
+	}
+	pairingsMul, err := bls.Bn.Pairing(pubKArray[0], bls.Hash(mArray[0]))
+	if err != nil {
+		return false
+	}
+
+	for i := 1; i < len(pubKArray); i++ {
+		e, err := bls.Bn.Pairing(pubKArray[i], bls.Hash(mArray[i]))
+		if err != nil {
+			return false
+		}
+		pairingsMul = bls.Bn.Fq12.Mul(pairingsMul, e)
+	}
+	if !bls.Bn.Fq12.Equal(pairingGS, pairingsMul) {
+		return false
+	}
+	return true
+}
diff --git a/bls/bls_test.go b/bls/bls_test.go
index e94a0f3..af9ec1b 100644
--- a/bls/bls_test.go
+++ b/bls/bls_test.go
@@ -2,23 +2,46 @@ package bls
 
 import (
 	"fmt"
+	"math/big"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
 )
 
 func TestBls(t *testing.T) {
-	bls, err := NewKeys()
+	bls, err := NewBLS()
+	assert.Nil(t, err)
+	keys0, err := bls.NewKeys()
 	assert.Nil(t, err)
 
-	fmt.Println("privK:", bls.PrivK)
-	fmt.Println("pubK:", bls.PubK)
+	fmt.Println("privK:", keys0.PrivK)
+	fmt.Println("pubK:", keys0.PubK)
 
-	m := []byte("test")
-	sig := bls.Sign(m)
-	fmt.Println("signature:", sig)
+	m0 := []byte("message0")
+	sig0 := bls.Sign(keys0.PrivK, m0)
+	fmt.Println("signature:", sig0)
 
-	verified := bls.Verify(m, sig, bls.PubK)
-	fmt.Println("verified:", verified)
+	verified := bls.Verify(m0, sig0, keys0.PubK)
+	fmt.Println("one signature verified:", verified)
 	assert.True(t, verified)
+
+	// signature aggregation
+	keys1, err := bls.NewKeys()
+	assert.Nil(t, err)
+	m1 := []byte("message1")
+	sig1 := bls.Sign(keys1.PrivK, m1)
+
+	keys2, err := bls.NewKeys()
+	assert.Nil(t, err)
+	m2 := []byte("message2")
+	sig2 := bls.Sign(keys2.PrivK, m2)
+
+	aggr := bls.AggregateSignatures(sig0, sig1, sig2)
+
+	pubKArray := [][3]*big.Int{keys0.PubK, keys1.PubK, keys2.PubK}
+	mArray := [][]byte{m0, m1, m2}
+	verified = bls.VerifyAggregatedSignatures(aggr, pubKArray, mArray)
+	fmt.Println("signature aggregation verified:", verified)
+	assert.True(t, verified)
+
 }