BLS signatures

.gitignore

@@ -1,3 +1,4 @@
 fmt
 schnorr.goBACKUP
 notes.md
+rsa-rs

README.md

@@ -12,7 +12,8 @@ Crypto algorithms from scratch. Academic purposes only.
 - [ECC ElGamal](#ecc-elgamal)
 - [ECC ECDSA](#ecc-ecdsa)
 - [Schnorr signature](#schnorr-signature)
-- [Bn128](#bn128)
+- [Bn128 pairing](#bn128)
+- [BLS signature](#bls)
 
 ---
 
@@ -420,7 +421,37 @@ if verified {
 
 ## Bn128
 Implementation of the bn128 pairing.
-Code moved to https://github.com/arnaucube/bn128
+Code moved to https://github.com/arnaucube/go-snark/tree/master/bn128
+
+
+## BLS
+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
+
+### Usage
+```go
+bls, err := NewKeys()
+assert.Nil(t, err)
+
+fmt.Println("privK:", bls.PrivK)
+fmt.Println("pubK:", bls.PubK)
+
+m := []byte("test")
+sig := bls.Sign(m)
+fmt.Println("signature:", sig)
+
+verified := bls.Verify(m, sig, bls.PubK)
+assert.True(t, verified)
+
+/* out:
+privK: 28151522174243194157727175362620544050084772361374505986857263387912025505082855947281432752362814690196305655335201716186584298643231993241609823412370437094839017595372164876997343464950463323765646363122343203470911131219733598647659483557447955173651057370197665461325593653581904430885385707255151472097067657072671643359241937143381958053903725229458882818033464163487351806079175441316235756460455300637131488613568714712448336232283394011955460567718918055245116200622473324300828876609569556897836255866438665750954410544846238847540023603735360532628141508114304504053826700874403280496870140784630677100277
+pubK: [528167154220154970470523315181365784447502116458960328551053767278433374201 18282159022449399855128689249640771309991127595389457870089153259100566421596 19728585501269572907574045312283749798205079570296187960832716959652451330253]
+signature: [[12832528436266902887734423636380781315321578271441494003771296275495461508593 6964131770814642748778827029569297554111206304527781019989920684169107205085] [6508357389516441729339280841134358160957092583050390612877406497974519092306 12073245715182483402311045895787625736998570529454024932833669602347318770866] [13520730275909614846121720877644124261162513989808465368770765804305866618385 19571107788574492009101590535904131414163790958090376021518899789800327786039]]
+verified: true
+*/
+```
 
 
 ---

bls/README.md

@@ -0,0 +1,28 @@
+# BLS [![GoDoc](https://godoc.org/github.com/arnaucube/cryptofun/bls?status.svg)](https://godoc.org/github.com/arnaucube/cryptofun/bls)
+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
+
+### Usage
+```go
+bls, err := NewKeys()
+assert.Nil(t, err)
+
+fmt.Println("privK:", bls.PrivK)
+fmt.Println("pubK:", bls.PubK)
+
+m := []byte("test")
+sig := bls.Sign(m)
+fmt.Println("signature:", sig)
+
+verified := bls.Verify(m, sig, bls.PubK)
+assert.True(t, verified)
+
+/* out:
+privK: 28151522174243194157727175362620544050084772361374505986857263387912025505082855947281432752362814690196305655335201716186584298643231993241609823412370437094839017595372164876997343464950463323765646363122343203470911131219733598647659483557447955173651057370197665461325593653581904430885385707255151472097067657072671643359241937143381958053903725229458882818033464163487351806079175441316235756460455300637131488613568714712448336232283394011955460567718918055245116200622473324300828876609569556897836255866438665750954410544846238847540023603735360532628141508114304504053826700874403280496870140784630677100277
+pubK: [528167154220154970470523315181365784447502116458960328551053767278433374201 18282159022449399855128689249640771309991127595389457870089153259100566421596 19728585501269572907574045312283749798205079570296187960832716959652451330253]
+signature: [[12832528436266902887734423636380781315321578271441494003771296275495461508593 6964131770814642748778827029569297554111206304527781019989920684169107205085] [6508357389516441729339280841134358160957092583050390612877406497974519092306 12073245715182483402311045895787625736998570529454024932833669602347318770866] [13520730275909614846121720877644124261162513989808465368770765804305866618385 19571107788574492009101590535904131414163790958090376021518899789800327786039]]
+verified: true
+*/
+```

bls/bls.go

@@ -0,0 +1,72 @@
+package bls
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"math/big"
+
+	"github.com/arnaucube/go-snark/bn128"
+)
+
+// this BLS implementation uses the Go implementation of the BN128 pairing github.com/arnaucube/go-snark/bn128
+
+const bits = 2048
+
+// BLS is the data structure of the BLS signature scheme, including the BN128 pairing curve
+type BLS struct {
+	Bn    bn128.Bn128
+	PrivK *big.Int
+	PubK  [3]*big.Int
+}
+
+// NewKeys generate new Private Key and Public Key
+func NewKeys() (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)
+	if err != nil {
+		return BLS{}, err
+	}
+
+	// pubK = pk * G
+	bls.PubK = bls.Bn.G1.MulScalar(bls.Bn.G1.G, bls.PrivK)
+	return bls, nil
+}
+
+// Hash hashes a message m
+func (bls BLS) Hash(m []byte) [3][2]*big.Int {
+	h := sha256.New()
+	h.Write(m)
+	hash := h.Sum(nil)
+	r := new(big.Int).SetBytes(hash)
+	// get point over the curve
+	point := bls.Bn.G2.MulScalar(bls.Bn.G2.G, r)
+	return point
+}
+
+// Sign performs the BLS signature of a message m
+func (bls BLS) Sign(m []byte) [3][2]*big.Int {
+	// s = pk * H(m)
+	h := bls.Hash(m)
+	sig := bls.Bn.G2.MulScalar(h, bls.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))
+	if err != nil {
+		return false
+	}
+	p2, err := bls.Bn.Pairing(bls.Bn.G1.G, sig)
+	if err != nil {
+		return false
+	}
+
+	return bls.Bn.Fq12.Equal(p1, p2)
+}

bls/bls_test.go

@@ -0,0 +1,24 @@
+package bls
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestBls(t *testing.T) {
+	bls, err := NewKeys()
+	assert.Nil(t, err)
+
+	fmt.Println("privK:", bls.PrivK)
+	fmt.Println("pubK:", bls.PubK)
+
+	m := []byte("test")
+	sig := bls.Sign(m)
+	fmt.Println("signature:", sig)
+
+	verified := bls.Verify(m, sig, bls.PubK)
+	fmt.Println("verified:", verified)
+	assert.True(t, verified)
+}

bn128/README.md

@@ -1,3 +1,3 @@
 ## Bn128
 Implementation of the bn128 pairing.
-Code moved to https://github.com/arnaucube/bn128
+Code moved to https://github.com/arnaucube/go-snark/tree/master/bn128

go.mod

@@ -1,7 +1,7 @@
 module github.com/arnaucube/cryptofun
 
 require (
-	github.com/davecgh/go-spew v1.1.1 // indirect
-	github.com/pmezard/go-difflib v1.0.0 // indirect
+	github.com/arnaucube/bn128 v0.0.0-20181124004642-3bb6b68ddbe4
+	github.com/arnaucube/go-snark v0.0.0-20181207210027-19f7216d0e3d
 	github.com/stretchr/testify v1.2.2
 )

go.sum

@@ -1,3 +1,9 @@
+github.com/arnaucube/bn128 v0.0.0-20181124004642-3bb6b68ddbe4 h1:Fy/hr/PH/8LIs8+a0oHQdAcI1mntdsM6Ndb0ZWLUtN0=
+github.com/arnaucube/bn128 v0.0.0-20181124004642-3bb6b68ddbe4/go.mod h1:bIKGJe1ZaHy7HYQML7Me4q38pOpggn3JO1VPPyMe3zI=
+github.com/arnaucube/cryptofun v0.0.0-20181124001128-d55d875d7a54/go.mod h1:PZE8kKpHPD1UMrS3mTfAMmEEinGtijSwjxLRqRcD64A=
+github.com/arnaucube/cryptofun v0.0.0-20181124004321-9b11ae8280bd/go.mod h1:PZE8kKpHPD1UMrS3mTfAMmEEinGtijSwjxLRqRcD64A=
+github.com/arnaucube/go-snark v0.0.0-20181207210027-19f7216d0e3d h1:fLsNI9g3nTSqXStD2dtkr86MMFicst28uREsXUd6jr0=
+github.com/arnaucube/go-snark v0.0.0-20181207210027-19f7216d0e3d/go.mod h1:gLycS/B43DufBaH0jH8kqiE4A7w5FdOM8I9S416xh2Y=
 github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
 github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
 github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=