pairing(P, zero) should be 1

include/mcl/bn.hpp

@@ -1178,6 +1178,10 @@ struct BNT {
 		G2 Q(Q_);
 		P.normalize();
 		Q.normalize();
+		if (Q.isZero()) {
+			f = 1;
+			return;
+		}
 		G2 T = Q;
 		G2 negQ;
 		if (param.useNAF) {
@@ -1241,6 +1245,12 @@ struct BNT {
 		size_t idx = 0;
 		G2 Q(Q_);
 		Q.normalize();
+		if (Q.isZero()) {
+			for (size_t i = 0; i < param.precomputedQcoeffSize; i++) {
+				Qcoeff[i] = 1;
+			}
+			return;
+		}
 		G2 T = Q;
 		G2 negQ;
 		if (param.useNAF) {

test/bn_test.cpp

@@ -250,6 +250,30 @@ void testPairing(const G1& P, const G2& Q, const char *eStr)
 #endif
 }
 
+void testTrivial(const G1& P, const G2& Q)
+{
+	G1 Z1; Z1.clear();
+	G2 Z2; Z2.clear();
+	Fp12 e;
+	BN::pairing(e, Z1, Q);
+	CYBOZU_TEST_EQUAL(e, 1);
+	BN::pairing(e, P, Z2);
+	CYBOZU_TEST_EQUAL(e, 1);
+	BN::pairing(e, Z1, Z2);
+	CYBOZU_TEST_EQUAL(e, 1);
+
+	std::vector<Fp6> Qcoeff;
+	BN::precomputeG2(Qcoeff, Z2);
+	BN::precomputedMillerLoop(e, P, Qcoeff);
+	BN::finalExp(e, e);
+	CYBOZU_TEST_EQUAL(e, 1);
+
+	BN::precomputeG2(Qcoeff, Q);
+	BN::precomputedMillerLoop(e, Z1, Qcoeff);
+	BN::finalExp(e, e);
+	CYBOZU_TEST_EQUAL(e, 1);
+}
+
 CYBOZU_TEST_AUTO(naive)
 {
 	for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(g_testSetTbl); i++) {
@@ -259,6 +283,7 @@ CYBOZU_TEST_AUTO(naive)
 		G1 P(ts.g1.a, ts.g1.b);
 		G2 Q(Fp2(ts.g2.aa, ts.g2.ab), Fp2(ts.g2.ba, ts.g2.bb));
 //G1::mul(P, P, Fr::getOp().mp - 1);exit(0);
+		testTrivial(P, Q);
 		testSetStr(Q);
 		testMapToG1();
 		testMapToG2();