rsa encrypt & decrypt, blind signatures, homomorphic multiplication

rsa/rsa.go

@@ -0,0 +1,98 @@
+package rsa
+
+import (
+	"bytes"
+	"math/big"
+	"math/rand"
+	"time"
+
+	prime "../prime"
+)
+
+const (
+	MaxPrime = 2000
+	MinPrime = 500
+)
+
+type PublicKey struct {
+	E *big.Int `json:"e"`
+	N *big.Int `json:"n"`
+}
+type PublicKeyString struct {
+	E string `json:"e"`
+	N string `json:"n"`
+}
+type PrivateKey struct {
+	D *big.Int `json:"d"`
+	N *big.Int `json:"n"`
+}
+
+type Key struct {
+	PubK  PublicKey
+	PrivK PrivateKey
+}
+
+func GenerateKeyPair() (key Key) {
+	rand.Seed(time.Now().Unix())
+	p := prime.RandPrime(MinPrime, MaxPrime)
+	q := prime.RandPrime(MinPrime, MaxPrime)
+
+	n := p * q
+	phi := (p - 1) * (q - 1)
+	e := 65537
+	var pubK PublicKey
+	pubK.E = big.NewInt(int64(e))
+	pubK.N = big.NewInt(int64(n))
+
+	d := new(big.Int).ModInverse(big.NewInt(int64(e)), big.NewInt(int64(phi)))
+
+	var privK PrivateKey
+	privK.D = d
+	privK.N = big.NewInt(int64(n))
+
+	key.PubK = pubK
+	key.PrivK = privK
+	return key
+}
+
+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)
+	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)
+	return m
+}
+
+func Blind(m *big.Int, r *big.Int, pubK PublicKey) *big.Int {
+	rE := new(big.Int).Exp(r, pubK.E, nil)
+	mrE := new(big.Int).Mul(m, rE)
+	mBlinded := new(big.Int).Mod(mrE, pubK.N)
+	return mBlinded
+}
+
+func BlindSign(m *big.Int, privK PrivateKey) *big.Int {
+	sigma := new(big.Int).Exp(m, privK.D, privK.N)
+	return sigma
+}
+func Unblind(sigma *big.Int, r *big.Int, pubK PublicKey) *big.Int {
+	r1 := new(big.Int).ModInverse(r, pubK.N)
+	bsr := new(big.Int).Mul(sigma, r1)
+	sig := new(big.Int).Mod(bsr, pubK.N)
+	return sig
+}
+func Verify(msg *big.Int, mSigned *big.Int, pubK PublicKey) bool {
+	//decrypt the mSigned with pubK
+	Cd := new(big.Int).Exp(mSigned, pubK.E, nil)
+	m := new(big.Int).Mod(Cd, pubK.N)
+	return bytes.Equal(msg.Bytes(), m.Bytes())
+}
+
+func HomomorphicMul(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
+}

rsa/rsa_test.go

@@ -0,0 +1,54 @@
+package rsa
+
+import (
+	"bytes"
+	"math/big"
+	"testing"
+)
+
+func TestEncryptDecrypt(t *testing.T) {
+	key := GenerateKeyPair()
+
+	mBytes := []byte("Hi")
+	m := new(big.Int).SetBytes(mBytes)
+	c := Encrypt(m, key.PubK)
+
+	d := Decrypt(c, key.PrivK)
+	if m == d {
+		t.Errorf("m not equal to decrypted")
+	}
+}
+func TestBlindSignature(t *testing.T) {
+	key := GenerateKeyPair()
+
+	mBytes := []byte("Hi")
+	m := new(big.Int).SetBytes(mBytes)
+	c := Encrypt(m, key.PubK)
+
+	d := Decrypt(c, key.PrivK)
+	if m == d {
+		t.Errorf("decrypted d not equal to original m")
+	}
+	rVal := big.NewInt(int64(101))
+	mBlinded := Blind(m, rVal, key.PubK)
+	sigma := BlindSign(mBlinded, key.PrivK)
+	mSigned := Unblind(sigma, rVal, key.PubK)
+	verified := Verify(m, mSigned, key.PubK)
+	if !verified {
+		t.Errorf("false, signature not verified")
+	}
+}
+
+func TestHomomorphiMultiplication(t *testing.T) {
+	key := GenerateKeyPair()
+
+	n1 := big.NewInt(int64(11))
+	n2 := big.NewInt(int64(15))
+	c1 := Encrypt(n1, key.PubK)
+	c2 := Encrypt(n2, key.PubK)
+	c3c4 := HomomorphicMul(c1, c2, key.PubK)
+	d := Decrypt(c3c4, key.PrivK)
+	if !bytes.Equal(new(big.Int).Mul(n1, n2).Bytes(), d.Bytes()) {
+		t.Errorf("decrypted result not equal to original result")
+	}
+}