diff --git a/include/mcl/ec.hpp b/include/mcl/ec.hpp
index e1db56d..d8a0fc1 100644
--- a/include/mcl/ec.hpp
+++ b/include/mcl/ec.hpp
@@ -424,6 +424,55 @@ void addJacobi(E& R, const E& P, const E& Q)
 	F::sub(R.y, U1, H3);
 }
 
+/*
+	accept P == Q
+	https://github.com/apache/incubator-milagro-crypto-c/blob/fa0a45a3/src/ecp.c.in#L767-L976
+	(x, y, z) is zero <=> x = 0, y = 1, z = 0
+*/
+template<class E>
+void addCTProj(E& R, const E& P, const E& Q)
+{
+	typedef typename E::Fp F;
+	assert(E::a_ == 0);
+	F b3;
+	F::add(b3, E::b_, E::b_);
+	b3 += E::b_;
+	F t0, t1, t2, t3, t4, x3, y3, z3;
+	F::mul(t0, P.x, Q.x);
+	F::mul(t1, P.y, Q.y);
+	F::mul(t2, P.z, Q.z);
+	F::add(t3, P.x, P.y);
+	F::add(t4, Q.x, Q.y);
+	F::mul(t3, t3, t4);
+	F::add(t4, t0, t1);
+	F::sub(t3, t3, t4);
+	F::add(t4, P.y, P.z);
+	F::add(x3, Q.y, Q.z);
+	F::mul(t4, t4, x3);
+	F::add(x3, t1, t2);
+	F::sub(t4, t4, x3);
+	F::add(x3, P.x, P.z);
+	F::add(y3, Q.x, Q.z);
+	F::mul(x3, x3, y3);
+	F::add(y3, t0, t2);
+	F::sub(y3, x3, y3);
+	F::add(x3, t0, t0);
+	F::add(t0, t0, x3);
+	t2 *= b3;
+	F::add(z3, t1, t2);
+	F::sub(t1, t1, t2);
+	y3 *= b3;
+	F::mul(x3, y3, t4);
+	F::mul(t2, t3, t1);
+	F::sub(R.x, t2, x3);
+	F::mul(y3, y3, t0);
+	F::mul(t1, t1, z3);
+	F::add(R.y, y3, t1);
+	F::mul(t0, t0, t3);
+	F::mul(z3, z3, t4);
+	F::add(R.z, z3, t0);
+}
+
 template<class E>
 void normalizeProj(E& P)
 {
diff --git a/include/mcl/util.hpp b/include/mcl/util.hpp
index 0132405..8915c88 100644
--- a/include/mcl/util.hpp
+++ b/include/mcl/util.hpp
@@ -328,6 +328,7 @@ bool mulSmallUnit(T& z, const T& x, U y)
 	case 9: { T t; T::add(t, x, x); T::add(t, t, t); T::add(t, t, t); T::add(z, t, x); break; }
 	case 10: { T t; T::add(t, x, x); T::add(t, t, t); T::add(t, t, x); T::add(z, t, t); break; }
 	case 11: { T t; T::add(t, x, x); T::add(t, t, x); T::add(t, t, t); T::add(t, t, t); T::sub(z, t, x); break; }
+	case 12: { T t; T::add(t, x, x); T::add(t, t, t); T::add(z, t, t); T::add(z, z, t); break; }
 	default:
 		return false;
 	}
diff --git a/readme.md b/readme.md
index d99acba..d1c5619 100644
--- a/readme.md
+++ b/readme.md
@@ -102,7 +102,7 @@ env MCL_PROF=2 bin/bls12_test.exe
 
 ## How to build on 32-bit x86 Linux
 
-Build GMP and for 32-bit mode and install `<lib32>` at yourself.
+Build GMP for 32-bit mode (`env ABI=32 ./configure --enable-cxx ...`) and install `<lib32>` at yourself.
 
 ```
 make ARCH=x86 CFLAGS_USER="-I <lib32>/include" LDFLAGS_USER="-L <lib32>/lib -Wl,-rpath,<lib32>/lib"
diff --git a/test/ec_test.cpp b/test/ec_test.cpp
index 855ceba..f544714 100644
--- a/test/ec_test.cpp
+++ b/test/ec_test.cpp
@@ -491,6 +491,31 @@ struct Test {
 		CYBOZU_TEST_ASSERT(!(P1 < P1));
 		CYBOZU_TEST_ASSERT((P1 <= P1));
 	}
+	void addCT() const
+	{
+		if (Ec::getMode() != mcl::ec::Proj) return;
+		if (Ec::a_ != 0) return;
+		Fp x(para.gx);
+		Fp y(para.gy);
+		Ec P(x, y), Q, R, Zero;
+		Zero.clear();
+		Zero.y = 1;
+		mcl::ec::addCTProj(Q, P, P);
+		Ec::add(R, P, P);
+		CYBOZU_TEST_EQUAL(Q, R);
+		mcl::ec::addCTProj(Q, Q, P);
+		Ec::add(R, R, P);
+		CYBOZU_TEST_EQUAL(Q, R);
+		mcl::ec::addCTProj(Q, Q, Zero);
+		Ec::add(R, R, Zero);
+		CYBOZU_TEST_EQUAL(Q, R);
+		mcl::ec::addCTProj(Q, Zero, Q);
+		Ec::add(R, Zero, R);
+		CYBOZU_TEST_EQUAL(Q, R);
+		mcl::ec::addCTProj(Q, Zero, Zero);
+		Ec::add(R, Zero, Zero);
+		CYBOZU_TEST_EQUAL(Q, R);
+	}
 
 	template<class F>
 	void test(F f, const char *msg) const
@@ -532,6 +557,7 @@ mul 499.00usec
 		ioMode();
 		mulCT();
 		compare();
+		addCT();
 	}
 private:
 	Test(const Test&);