paillier encrypt & decrypt, homomorphic addition

README.md

@@ -14,5 +14,10 @@ Crypto algorithms from scratch. Academic purposes only.
 - [x] Homomorphic Multiplication
 
 ## Paillier
+- [x] GenerateKeyPair
+- [x] Encrypt
+- [x] Decrypt
+- [x] Homomorphic Addition
+
 ## ECC
 ## Shamir Secret Sharing

paillier/paillier.go

@@ -0,0 +1,111 @@
+package paillier
+
+import (
+	"crypto/rand"
+	"errors"
+	"math/big"
+
+	prime "../prime"
+)
+
+const (
+	bits = 16
+)
+
+type PublicKey struct {
+	N *big.Int `json:"n"`
+	G *big.Int `json:"g"`
+}
+type PrivateKey struct {
+	Lambda *big.Int `json:"lambda"`
+	Mu     *big.Int `json:"mu"`
+}
+
+type Key struct {
+	PubK  PublicKey
+	PrivK PrivateKey
+}
+
+func GenerateKeyPair() (key Key, err error) {
+	p, err := rand.Prime(rand.Reader, bits/2)
+	if err != nil {
+		return key, err
+	}
+	q, err := rand.Prime(rand.Reader, bits/2)
+	if err != nil {
+		return key, err
+	}
+
+	pq := new(big.Int).Mul(p, q)
+	p1q1 := big.NewInt((p.Int64() - 1) * (q.Int64() - 1))
+	gcd := new(big.Int).GCD(nil, nil, pq, p1q1)
+	if gcd.Int64() != int64(1) {
+		return key, errors.New("gcd comprovation failed")
+	}
+
+	n := new(big.Int).Mul(p, q)
+	lambda := big.NewInt(int64(Lcm(float64(p.Int64())-1, float64(q.Int64())-1)))
+
+	//g generation
+	alpha := big.NewInt(int64(prime.RandInt(0, int(n.Int64()))))
+	beta := big.NewInt(int64(prime.RandInt(0, int(n.Int64()))))
+	alphan := new(big.Int).Mul(alpha, n)
+	alphan1 := new(big.Int).Add(alphan, big.NewInt(1))
+	betaN := new(big.Int).Exp(beta, n, nil)
+	ab := new(big.Int).Mul(alphan1, betaN)
+	n2 := new(big.Int).Mul(n, n)
+	g := new(big.Int).Mod(ab, n2)
+	//in some Paillier implementations use this:
+	// g = new(big.Int).Add(n, big.NewInt(1))
+
+	key.PubK.N = n
+	key.PubK.G = g
+
+	//mu generation
+	Glambda := new(big.Int).Exp(g, lambda, nil)
+	u := new(big.Int).Mod(Glambda, n2)
+	L := L(u, n)
+	mu := new(big.Int).ModInverse(L, n)
+
+	key.PrivK.Lambda = lambda
+	key.PrivK.Mu = mu
+
+	return key, nil
+}
+
+func Lcm(a, b float64) float64 {
+	r := (a * b) / float64(prime.Gcd(int(a), int(b)))
+	return r
+
+}
+func L(u *big.Int, n *big.Int) *big.Int {
+	u1 := new(big.Int).Sub(u, big.NewInt(1))
+	L := new(big.Int).Div(u1, n)
+	return L
+}
+
+func Encrypt(m *big.Int, pubK PublicKey) *big.Int {
+	gM := new(big.Int).Exp(pubK.G, m, nil)
+	r := big.NewInt(int64(prime.RandInt(0, int(pubK.N.Int64()))))
+	rN := new(big.Int).Exp(r, pubK.N, nil)
+	gMrN := new(big.Int).Mul(gM, rN)
+	n2 := new(big.Int).Mul(pubK.N, pubK.N)
+	c := new(big.Int).Mod(gMrN, n2)
+	return c
+}
+func Decrypt(c *big.Int, pubK PublicKey, privK PrivateKey) *big.Int {
+	cLambda := new(big.Int).Exp(c, privK.Lambda, nil)
+	n2 := new(big.Int).Mul(pubK.N, pubK.N)
+	u := new(big.Int).Mod(cLambda, n2)
+	L := L(u, pubK.N)
+	LMu := new(big.Int).Mul(L, privK.Mu)
+	m := new(big.Int).Mod(LMu, pubK.N)
+	return m
+}
+
+func HomomorphicAddition(c1 *big.Int, c2 *big.Int, pubK PublicKey) *big.Int {
+	c1c2 := new(big.Int).Mul(c1, c2)
+	n2 := new(big.Int).Mul(pubK.N, pubK.N)
+	d := new(big.Int).Mod(c1c2, n2)
+	return d
+}

paillier/paillier_test.go

@@ -0,0 +1,41 @@
+package paillier
+
+import (
+	"bytes"
+	"fmt"
+	"math/big"
+	"testing"
+)
+
+func TestEncryptDecrypt(t *testing.T) {
+	key, err := GenerateKeyPair()
+	if err != nil {
+		t.Errorf(err.Error())
+	}
+	fmt.Println(key)
+	mBytes := []byte("Hi")
+	m := new(big.Int).SetBytes(mBytes)
+	c := Encrypt(m, key.PubK)
+	d := Decrypt(c, key.PubK, key.PrivK)
+	if m == d {
+		fmt.Println(key)
+		t.Errorf("m not equal to decrypted")
+	}
+}
+
+func TestHomomorphicAddition(t *testing.T) {
+	key, err := GenerateKeyPair()
+	if err != nil {
+		t.Errorf(err.Error())
+	}
+	n1 := big.NewInt(int64(110))
+	n2 := big.NewInt(int64(150))
+	c1 := Encrypt(n1, key.PubK)
+	c2 := Encrypt(n2, key.PubK)
+	c3c4 := HomomorphicAddition(c1, c2, key.PubK)
+	d := Decrypt(c3c4, key.PubK, key.PrivK)
+	if !bytes.Equal(new(big.Int).Add(n1, n2).Bytes(), d.Bytes()) {
+		fmt.Println(key)
+		t.Errorf("decrypted result not equal to original result")
+	}
+}

prime/prime.go

@@ -2,6 +2,11 @@ package prime
 
 import "math/rand"
 
+const (
+	MaxPrime = 2000
+	MinPrime = 500
+)
+
 func RandInt(min int, max int) int {
 	r := rand.Intn(max-min) + min
 	return r

rsa/rsa.go

@@ -2,18 +2,16 @@ package rsa
 
 import (
 	"bytes"
+	"crypto/rand"
 	"math/big"
-	"math/rand"
-	"time"
-
-	prime "../prime"
 )
 
 const (
-	MaxPrime = 2000
-	MinPrime = 500
+	bits = 512 // 2048
 )
 
+var bigOne = big.NewInt(int64(1))
+
 type PublicKey struct {
 	E *big.Int `json:"e"`
 	N *big.Int `json:"n"`
@@ -32,37 +30,42 @@ type Key struct {
 	PrivK PrivateKey
 }
 
-func GenerateKeyPair() (key Key) {
-	rand.Seed(time.Now().Unix())
-	p := prime.RandPrime(MinPrime, MaxPrime)
-	q := prime.RandPrime(MinPrime, MaxPrime)
+func GenerateKeyPair() (key Key, err error) {
+	p, err := rand.Prime(rand.Reader, bits/2)
+	if err != nil {
+		return key, err
+	}
+	q, err := rand.Prime(rand.Reader, bits/2)
+	if err != nil {
+		return key, err
+	}
 
-	n := p * q
-	phi := (p - 1) * (q - 1)
+	n := new(big.Int).Mul(p, q)
+	p_1 := new(big.Int).Sub(p, bigOne)
+	q_1 := new(big.Int).Sub(q, bigOne)
+	phi := new(big.Int).Mul(p_1, q_1)
 	e := 65537
 	var pubK PublicKey
 	pubK.E = big.NewInt(int64(e))
-	pubK.N = big.NewInt(int64(n))
+	pubK.N = n
 
-	d := new(big.Int).ModInverse(big.NewInt(int64(e)), big.NewInt(int64(phi)))
+	d := new(big.Int).ModInverse(big.NewInt(int64(e)), phi)
 
 	var privK PrivateKey
 	privK.D = d
-	privK.N = big.NewInt(int64(n))
+	privK.N = n
 
 	key.PubK = pubK
 	key.PrivK = privK
-	return key
+	return key, nil
 }
 
 func Encrypt(m *big.Int, pubK PublicKey) *big.Int {
-	Me := new(big.Int).Exp(m, pubK.E, nil)
-	c := new(big.Int).Mod(Me, pubK.N)
+	c := new(big.Int).Exp(m, pubK.E, pubK.N)
 	return c
 }
 func Decrypt(c *big.Int, privK PrivateKey) *big.Int {
-	Cd := new(big.Int).Exp(c, privK.D, nil)
-	m := new(big.Int).Mod(Cd, privK.N)
+	m := new(big.Int).Exp(c, privK.D, privK.N)
 	return m
 }
 

rsa/rsa_test.go

@@ -2,13 +2,17 @@ package rsa
 
 import (
 	"bytes"
+	"fmt"
 	"math/big"
 	"testing"
 )
 
 func TestEncryptDecrypt(t *testing.T) {
-	key := GenerateKeyPair()
-
+	key, err := GenerateKeyPair()
+	if err != nil {
+		t.Errorf(err.Error())
+	}
+	fmt.Println(key)
 	mBytes := []byte("Hi")
 	m := new(big.Int).SetBytes(mBytes)
 	c := Encrypt(m, key.PubK)
@@ -19,7 +23,10 @@ func TestEncryptDecrypt(t *testing.T) {
 	}
 }
 func TestBlindSignature(t *testing.T) {
-	key := GenerateKeyPair()
+	key, err := GenerateKeyPair()
+	if err != nil {
+		t.Errorf(err.Error())
+	}
 
 	mBytes := []byte("Hi")
 	m := new(big.Int).SetBytes(mBytes)
@@ -39,8 +46,11 @@ func TestBlindSignature(t *testing.T) {
 	}
 }
 
-func TestHomomorphiMultiplication(t *testing.T) {
-	key := GenerateKeyPair()
+func TestHomomorphicMultiplication(t *testing.T) {
+	key, err := GenerateKeyPair()
+	if err != nil {
+		t.Errorf(err.Error())
+	}
 
 	n1 := big.NewInt(int64(11))
 	n2 := big.NewInt(int64(15))