Added support for a Cypher multiplication

It's now possible to multiply Cypher by an integer.

Paillier is a homomorphic encryption scheme, where an encrypted
plaintext `m` raised to an integer `k` will decrypt to the product of
the plaintext `m` and `k`.

paillier.go

@@ -63,6 +63,19 @@ func (pk *PublicKey) Add(cypher ...*Cypher) *Cypher {
 	}
 }
 
+// Mul returns a product of `cypher` and `scalar` without decrypting `cypher`.
+//
+// It's possible because Paillier is a homomorphic encryption scheme, where
+// an encrypted plaintext `m` raised to an integer `k` will decrypt to the
+// product of the plaintext `m` and `k`:
+//
+// D( E(m)^k mod N^2 ) = km mod N
+func (pk *PublicKey) Mul(cypher *Cypher, scalar *big.Int) *Cypher {
+	return &Cypher{
+		C: new(big.Int).Exp(cypher.C, scalar, pk.GetNSquare()),
+	}
+}
+
 type PrivateKey struct {
 	PublicKey
 	Lambda *big.Int

paillier_test.go

@@ -92,3 +92,36 @@ func TestAddCypherWithSmallKeyModulus(t *testing.T) {
 		t.Errorf("Unexpected decrypted value [%v]", m)
 	}
 }
+
+func TestMulCypher(t *testing.T) {
+	privateKey := CreatePrivateKey(big.NewInt(17), big.NewInt(13))
+
+	cypher, err := privateKey.Encrypt(big.NewInt(3), rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	cypherMultiple := privateKey.Mul(cypher, big.NewInt(7))
+	multiple := privateKey.Decrypt(cypherMultiple)
+
+	if !reflect.DeepEqual(multiple, big.NewInt(21)) {
+		t.Errorf("Unexpected decrypted value [%v]", multiple)
+	}
+}
+
+func TestMulCypherWithSmallKeyModulus(t *testing.T) {
+	privateKey := CreatePrivateKey(big.NewInt(7), big.NewInt(5))
+
+	cypher, err := privateKey.Encrypt(big.NewInt(30), rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	cypherMultiple := privateKey.Mul(cypher, big.NewInt(93))
+	multiple := privateKey.Decrypt(cypherMultiple)
+
+	// (30*93) mod (7*5) = 25
+	if !reflect.DeepEqual(multiple, big.NewInt(25)) {
+		t.Errorf("Unexpected decrypted value [%v]", multiple)
+	}
+}