G parameter removed from ThresholdKey

G _MUST_ be always n+1 to make the threshold encryption algorithm safe. We assume G=n+1 both for standard and threshold version.

paillier.go

@@ -37,6 +37,9 @@ func (pub *PublicKey) Encrypt(m *big.Int, random io.Reader) (*Cypher, error) {
 	}
 	nSquare := pub.GetNSquare()
 
+	// g is _always_ equal n+1
+	// Threshold encryption is safe only for g=n+1 choice.
+	// See [DJN 10], section 5.1
 	g := new(big.Int).Add(pub.N, big.NewInt(1))
 	gm := new(big.Int).Exp(g, m, nSquare)
 	rn := new(big.Int).Exp(r, pub.N, nSquare)

thresholdkey.go

@@ -14,7 +14,6 @@ type ThresholdKey struct {
 	Threshold                      int
 	V                              *big.Int
 	Vi                             []*big.Int
-	G                              *big.Int // usually G is set to N+1
 }
 
 // returns the value of (4*delta**2)** -1  mod n
@@ -165,7 +164,6 @@ func (this *ThresholdPrivateKey) GetThresholdKey() *ThresholdKey {
 	ret.V = new(big.Int).Add(this.V, big.NewInt(0))
 	ret.Vi = this.copyVi()
 	ret.N = new(big.Int).Add(this.N, big.NewInt(0))
-	ret.G = new(big.Int).Add(this.N, big.NewInt(1))
 	return ret
 }
 

thresholdkey_generator.go

@@ -219,7 +219,6 @@ func (this *ThresholdKeyGenerator) createViArray(shares []*big.Int) (viArray []*
 func (this *ThresholdKeyGenerator) createPrivateKey(i int, share *big.Int, viArray []*big.Int) *ThresholdPrivateKey {
 	ret := new(ThresholdPrivateKey)
 	ret.N = this.n
-	ret.G = new(big.Int).Add(ret.N, ONE)
 	ret.V = this.v
 
 	ret.TotalNumberOfDecryptionServers = this.TotalNumberOfDecryptionServers

thresholdkey_generator_test.go

@@ -207,7 +207,7 @@ func TestGenerate(t *testing.T) {
 		if len(tpk.Vi) != 10 {
 			t.Fail()
 		}
-		if tpk.G == nil || tpk.N == nil {
+		if tpk.N == nil {
 			t.Fail()
 		}
 		if tpk.Threshold != 6 || tpk.TotalNumberOfDecryptionServers != 10 {

thresholdkey_test.go

@@ -224,7 +224,6 @@ func TestDecryption(t *testing.T) {
 	tk.Threshold = 2
 	tk.TotalNumberOfDecryptionServers = 2
 	tk.N = b(637753)
-	tk.G = b(637754)
 	tk.V = b(70661107826)
 	if msg, err := tk.CombinePartialDecryptions([]*PartialDecryption{share1, share2}); err != nil {
 		t.Error(err)