add millerLoop2mixed for C

include/mcl/bn.h

@@ -308,6 +308,7 @@ MCLBN_DLL_API void mclBn_precomputeG2(uint64_t *Qbuf, const mclBnG2 *Q);
 
 MCLBN_DLL_API void mclBn_precomputedMillerLoop(mclBnGT *f, const mclBnG1 *P, const uint64_t *Qbuf);
 MCLBN_DLL_API void mclBn_precomputedMillerLoop2(mclBnGT *f, const mclBnG1 *P1, const uint64_t *Q1buf, const mclBnG1 *P2, const uint64_t *Q2buf);
+MCLBN_DLL_API void mclBn_precomputedMillerLoop2mixed(mclBnGT *f, const mclBnG1 *P1, const mclBnG2 *Q1, const mclBnG1 *P2, const uint64_t *Q2buf);
 
 /*
 	Lagrange interpolation

src/bn_c_impl.hpp

@@ -451,6 +451,11 @@ void mclBn_precomputedMillerLoop2(mclBnGT *f, const mclBnG1 *P1, const uint64_t
 	precomputedMillerLoop2(*cast(f), *cast(P1), cast(Q1buf), *cast(P2), cast(Q2buf));
 }
 
+void mclBn_precomputedMillerLoop2mixed(mclBnGT *f, const mclBnG1 *P1, const mclBnG2 *Q1, const mclBnG1 *P2, const uint64_t *Q2buf)
+{
+	precomputedMillerLoop2mixed(*cast(f), *cast(P1), *cast(Q1), *cast(P2), cast(Q2buf));
+}
+
 int mclBn_FrLagrangeInterpolation(mclBnFr *out, const mclBnFr *xVec, const mclBnFr *yVec, mclSize k)
 {
 	bool b;

test/bls12_test.cpp

@@ -231,6 +231,18 @@ void testMillerLoop2(const G1& P1, const G2& Q1)
 	CYBOZU_TEST_EQUAL(e2, e3);
 	finalExp(e2, e2);
 	CYBOZU_TEST_EQUAL(e1, e2);
+
+	// special value
+	G2 Z;
+	Z.clear();
+	Q2 += Q2;
+	precomputeG2(Q1coeff, Z);
+	precomputeG2(Q2coeff, Q2);
+	precomputedMillerLoop2(e2, P1, Q1coeff, P2, Q2coeff);
+	precomputedMillerLoop2mixed(e3, P1, Z, P2, Q2coeff);
+	finalExp(e2, e2);
+	finalExp(e3, e3);
+	CYBOZU_TEST_EQUAL(e2, e3);
 }
 
 void testPairing(const G1& P, const G2& Q, const char *eStr)

test/bn_c_test.hpp

@@ -334,7 +334,7 @@ CYBOZU_TEST_AUTO(precomputed)
 	mclBn_precomputeG2(Q1buf.data(), &Q1);
 	mclBn_precomputeG2(Q2buf.data(), &Q2);
 
-	mclBnGT e1, e2, f1, f2, f3;
+	mclBnGT e1, e2, f1, f2, f3, f4;
 	mclBn_pairing(&e1, &P1, &Q1);
 	mclBn_precomputedMillerLoop(&f1, &P1, Q1buf.data());
 	mclBn_finalExp(&f1, &f1);
@@ -346,6 +346,8 @@ CYBOZU_TEST_AUTO(precomputed)
 	CYBOZU_TEST_ASSERT(mclBnGT_isEqual(&e2, &f2));
 
 	mclBn_precomputedMillerLoop2(&f3, &P1, Q1buf.data(), &P2, Q2buf.data());
+	mclBn_precomputedMillerLoop2mixed(&f4, &P1, &Q1, &P2, Q2buf.data());
+	CYBOZU_TEST_ASSERT(mclBnGT_isEqual(&f3, &f4));
 	mclBn_finalExp(&f3, &f3);
 
 	mclBnGT_mul(&e1, &e1, &e2);

test/bn_test.cpp

@@ -232,6 +232,18 @@ void testMillerLoop2(const G1& P1, const G2& Q1)
 	CYBOZU_TEST_EQUAL(e2, e3);
 	finalExp(e2, e2);
 	CYBOZU_TEST_EQUAL(e1, e2);
+
+	// special value
+	G2 Z;
+	Z.clear();
+	Q2 += Q2;
+	precomputeG2(Q1coeff, Z);
+	precomputeG2(Q2coeff, Q2);
+	precomputedMillerLoop2(e2, P1, Q1coeff, P2, Q2coeff);
+	precomputedMillerLoop2mixed(e3, P1, Z, P2, Q2coeff);
+	finalExp(e2, e2);
+	finalExp(e3, e3);
+	CYBOZU_TEST_EQUAL(e2, e3);
 }
 
 void testPairing(const G1& P, const G2& Q, const char *eStr)