Merge pull request #7 from keep-network/master

Added EncryptWithR allowing to specify the randomness

paillier.go

@@ -14,6 +14,31 @@ func (pk *PublicKey) GetNSquare() *big.Int {
 	return new(big.Int).Mul(pk.N, pk.N)
 }
 
+// EncryptWithR encrypts a plaintext into a cypher one with random `r` specified
+// in the argument. The plain text must be smaller that N and bigger or equal
+// than zero. `r` is the randomness used to encrypt the plaintext. `r` must be
+// a random element from a multiplicative group of integers modulo N.
+//
+// If you don't need to use the specific `r`, you should use the `Encrypt`
+// function instead.
+//
+// m - plaintext to encrypt
+// r - randomness used for encryption
+// E(m, r) = [(1 + N) r^N] mod N^2
+//
+// See [KL 08] construction 11.32, page 414.
+func (pk *PublicKey) EncryptWithR(m *big.Int, r *big.Int) (*Cypher, error) {
+	nSquare := pk.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(pk.N, big.NewInt(1))
+	gm := new(big.Int).Exp(g, m, nSquare)
+	rn := new(big.Int).Exp(r, pk.N, nSquare)
+	return &Cypher{new(big.Int).Mod(new(big.Int).Mul(rn, gm), nSquare)}, nil
+}
+
 // Encrypt a plaintext into a cypher one. The plain text must be smaller that
 // N and bigger or equal than zero. random is usually rand.Reader from the
 // package crypto/rand.
@@ -29,15 +54,8 @@ func (pk *PublicKey) Encrypt(m *big.Int, random io.Reader) (*Cypher, error) {
 	if err != nil {
 		return nil, err
 	}
-	nSquare := pk.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(pk.N, big.NewInt(1))
-	gm := new(big.Int).Exp(g, m, nSquare)
-	rn := new(big.Int).Exp(r, pk.N, nSquare)
-	return &Cypher{new(big.Int).Mod(new(big.Int).Mul(rn, gm), nSquare)}, nil
+	return pk.EncryptWithR(m, r)
 }
 
 // Add takes an arbitrary number of cyphertexts and returns one that encodes