Explained how do we handle negative lambda parameter value

thresholdkey.go

@@ -97,8 +97,14 @@ func (tk *ThresholdPublicKey) updateCprime(cprime, lambda *big.Int, share *Parti
 	return new(big.Int).Mod(ret, tk.GetNSquare())
 }
 
+// We use `exp` from `updateCprime` to raise decryption share to the power of lambda
+// parameter. Since lambda can be a negative number and we do discrete math here,
+// we need to apply multiplicative inverse modulo in this case.
+//
+// For instance, for b = -18:
+// b^{−18} = (b^−1)^18, where b^{−1} is the multiplicative inverse modulo c.
 func (tk *ThresholdPublicKey) exp(a, b, c *big.Int) *big.Int {
-	if b.Cmp(ZERO) == -1 {
+	if b.Cmp(ZERO) == -1 { // b < 0 ?
 		ret := new(big.Int).Exp(a, new(big.Int).Neg(b), c)
 		return new(big.Int).ModInverse(ret, c)
 	}

thresholdkey_test.go

@@ -24,6 +24,22 @@ func TestDelta(t *testing.T) {
 	}
 }
 
+func TestExp(t *testing.T) {
+	tk := new(ThresholdPublicKey)
+
+	if exp := tk.exp(big.NewInt(720), big.NewInt(10), big.NewInt(49)); 43 != n(exp) {
+		t.Error("Unexpected exponent. Expected 43 but got", exp)
+	}
+
+	if exp := tk.exp(big.NewInt(720), big.NewInt(0), big.NewInt(49)); 1 != n(exp) {
+		t.Error("Unexpected exponent. Expected 0 but got", exp)
+	}
+
+	if exp := tk.exp(big.NewInt(720), big.NewInt(-10), big.NewInt(49)); 8 != n(exp) {
+		t.Error("Unexpected exponent. Expected 8 but got", exp)
+	}
+}
+
 func TestCombineSharesConstant(t *testing.T) {
 	tk := new(ThresholdPublicKey)
 	tk.N = big.NewInt(101 * 103)