From ae5b3a733010bddda8074c8fc8f49f19ee2f6647 Mon Sep 17 00:00:00 2001
From: MITSUNARI Shigeo <herumi@nifty.com>
Date: Tue, 16 Feb 2021 16:29:53 +0900
Subject: [PATCH] _

---
 include/mcl/bn.hpp       |  1 +
 include/mcl/fp_tower.hpp | 57 +++++++++-------------------------------
 test/common_test.hpp     | 11 ++------
 3 files changed, 16 insertions(+), 53 deletions(-)

diff --git a/include/mcl/bn.hpp b/include/mcl/bn.hpp
index 0c514de..c8255aa 100644
--- a/include/mcl/bn.hpp
+++ b/include/mcl/bn.hpp
@@ -57,6 +57,7 @@ typedef Fp12 GT;
 
 typedef mcl::FpDblT<Fp> FpDbl;
 typedef mcl::Fp2DblT<Fp> Fp2Dbl;
+typedef mcl::Fp6DblT<Fp> Fp6Dbl;
 
 inline void Frobenius(Fp2& y, const Fp2& x)
 {
diff --git a/include/mcl/fp_tower.hpp b/include/mcl/fp_tower.hpp
index 1f3ec7e..55a2bbe 100644
--- a/include/mcl/fp_tower.hpp
+++ b/include/mcl/fp_tower.hpp
@@ -995,7 +995,11 @@ struct Fp6DblT {
 		Fp2Dbl::sub(z.b, x.b, y.b);
 		Fp2Dbl::sub(z.c, x.c, y.c);
 	}
-	static void sub2(Fp2Dbl& y, const Fp2Dbl& x)
+	/*
+		imaginary part of Fp2Dbl::mul uses only add,
+		so it does not require mod.
+	*/
+	static void specialSub(Fp2Dbl& y, const Fp2Dbl& x)
 	{
 		FpDbl::sub(y.a, y.a, x.a);
 		FpDbl::subPre(y.b, y.b, x.b);
@@ -1006,6 +1010,8 @@ struct Fp6DblT {
 		bf + ce = (b + c)(e + f) - be - cf
 		ae + bd = (a + b)(e + d) - ad - be
 		af + cd = (a + c)(d + f) - ad - cf
+		assum p < W/4 where W = 1 << (sizeof(Unit) * 8 * N)
+		then (b + c)(e + f) < 4p^2 < pW
 	*/
 	static void mulPre(Fp6DblT& z, const Fp6& x, const Fp6& y)
 	{
@@ -1016,7 +1022,6 @@ struct Fp6DblT {
 		const Fp2& d = y.a;
 		const Fp2& e = y.b;
 		const Fp2& f = y.c;
-#if 1
 		Fp2Dbl& ZA = z.a;
 		Fp2Dbl& ZB = z.b;
 		Fp2Dbl& ZC = z.c;
@@ -1034,53 +1039,17 @@ struct Fp6DblT {
 		Fp2Dbl::mulPre(BE, b, e);
 		Fp2Dbl::mulPre(CF, c, f);
 		Fp2Dbl::mulPre(AD, a, d);
-		sub2(ZA, BE);
-		sub2(ZA, CF);
-		sub2(ZB, AD);
-		sub2(ZB, BE);
-		sub2(ZC, AD);
-		sub2(ZC, CF);
+		specialSub(ZA, BE);
+		specialSub(ZA, CF);
+		specialSub(ZB, AD);
+		specialSub(ZB, BE);
+		specialSub(ZC, AD);
+		specialSub(ZC, CF);
 		Fp2Dbl::mul_xi(ZA, ZA);
 		Fp2Dbl::add(ZA, ZA, AD);
 		Fp2Dbl::mul_xi(CF, CF);
 		Fp2Dbl::add(ZB, ZB, CF);
 		Fp2Dbl::add(ZC, ZC, BE);
-#else
-		Fp2Dbl& za = z.a;
-		Fp2Dbl& zb = z.b;
-		Fp2Dbl& zc = z.c;
-		Fp2Dbl BE;
-		Fp2Dbl::mulPre(za, a, d);
-		Fp2Dbl::mulPre(BE, b, e);
-		Fp2Dbl::mulPre(zb, c, f);
-
-		Fp2 t1, t2;
-		Fp2::add(t1, b, c);
-		Fp2::add(t2, e, f);
-		Fp2Dbl T1;
-		Fp2Dbl::mulPre(T1, t1, t2);
-		Fp2Dbl::sub(T1, T1, BE);
-		Fp2Dbl::sub(T1, T1, zb);
-		Fp2Dbl::mul_xi(T1, T1);
-
-		Fp2::add(t1, a, b);
-		Fp2::add(t2, e, d);
-		Fp2Dbl T2;
-		Fp2Dbl::mulPre(T2, t1, t2);
-		Fp2Dbl::sub(T2, T2, za);
-		Fp2Dbl::sub(T2, T2, BE);
-
-		Fp2::add(t1, a, c);
-		Fp2::add(t2, d, f);
-		Fp2Dbl::mulPre(zc, t1, t2);
-		Fp2Dbl::sub(zc, zc, za);
-		Fp2Dbl::sub(zc, zc, zb);
-
-		Fp2Dbl::add(za, za, T1);
-		Fp2Dbl::mul_xi(zb, zb);
-		Fp2Dbl::add(zb, zb, T2);
-		Fp2Dbl::add(zc, zc, BE);
-#endif
 //clk.end();
 	}
 	static void mod(Fp6& y, const Fp6Dbl& x)
diff --git a/test/common_test.hpp b/test/common_test.hpp
index ba990f1..afe23ee 100644
--- a/test/common_test.hpp
+++ b/test/common_test.hpp
@@ -135,15 +135,8 @@ void testABCDsub(const Fp2& a, const Fp2& b, const Fp2& c, const Fp2& d)
 	Fp2Dbl::mulPre(T1, t1, t2);
 	Fp2Dbl::mulPre(AC, a, c);
 	Fp2Dbl::mulPre(BD, b, d);
-#if 0
-	Fp2Dbl::sub(T1, T1, AC);
-	Fp2Dbl::sub(T1, T1, BD);
-#else
-	FpDbl::sub(T1.a, T1.a, AC.a);
-	FpDbl::subPre(T1.b, T1.b, AC.b);
-	FpDbl::sub(T1.a, T1.a, BD.a);
-	FpDbl::subPre(T1.b, T1.b, BD.b);
-#endif
+	Fp6Dbl::specialSub(T1, AC);
+	Fp6Dbl::specialSub(T1, BD);
 	Fp2Dbl::mod(t1, T1);
 	CYBOZU_TEST_EQUAL(t1, a * d + b * c);
 }