From 7042a444c8454981f7020bc9db2402a935280ee0 Mon Sep 17 00:00:00 2001
From: MITSUNARI Shigeo <herumi@nifty.com>
Date: Tue, 13 Feb 2024 12:27:53 +0900
Subject: [PATCH] add conversion between Proj and Jacobi

---
 include/mcl/ec.hpp | 23 +++++++++++++++++++++++
 test/ec_test.cpp   | 24 ++++++++++++++++++++++++
 2 files changed, 47 insertions(+)

diff --git a/include/mcl/ec.hpp b/include/mcl/ec.hpp
index 2cd5a87a..4bba163b 100644
--- a/include/mcl/ec.hpp
+++ b/include/mcl/ec.hpp
@@ -226,6 +226,29 @@ void normalizeVecT(Eout& Q, Ein& P, size_t n, size_t N = 256)
 
 } // mcl::ec::local
 
+// [X:Y:Z] as Proj = (X/Z, Y/Z) as Affine = [XZ:YZ^2:Z] as Jacobi
+template<class E>
+void ProjToJacobi(E& Q, const E& P)
+{
+	typedef typename E::Fp F;
+	F::mul(Q.x, P.x, P.z);
+	F::mul(Q.y, P.y, P.z);
+	Q.y *= P.z;
+	Q.z = P.z;
+}
+
+// [X:Y:Z] as Jacobi = (X/Z^2, Y/Z^3) as Affine = [XZ:Y:Z^3] as Proj
+template<class E>
+void JacobiToProj(E& Q, const E& P)
+{
+	typedef typename E::Fp F;
+	F::mul(Q.x, P.x, P.z);
+	Q.y = P.y;
+	F t;
+	F::sqr(t, P.z);
+	F::mul(Q.z, P.z, t);
+}
+
 template<class E>
 void normalizeJacobi(E& P)
 {
diff --git a/test/ec_test.cpp b/test/ec_test.cpp
index c461b00f..160d0239 100644
--- a/test/ec_test.cpp
+++ b/test/ec_test.cpp
@@ -627,6 +627,29 @@ struct Test {
 		Ec::add(R, Zero, Zero);
 		CYBOZU_TEST_EQUAL(Q, R);
 	}
+	void ProjJacobi() const
+	{
+		if (Ec::getMode() == mcl::ec::Affine) return;
+		Fp x(para.gx);
+		Fp y(para.gy);
+		Ec P(x, y), Q, R;
+		P *= 123;
+		if (Ec::getMode() == mcl::ec::Proj) {
+			mcl::ec::ProjToJacobi(Q, P);
+			mcl::ec::normalizeJacobi(Q);
+			CYBOZU_TEST_EQUAL(Q, P);
+			mcl::ec::ProjToJacobi(Q, P);
+			mcl::ec::JacobiToProj(R, Q);
+			CYBOZU_TEST_EQUAL(R, P);
+		} else {
+			mcl::ec::JacobiToProj(Q, P);
+			mcl::ec::normalizeProj(Q);
+			CYBOZU_TEST_EQUAL(Q, P);
+			mcl::ec::JacobiToProj(Q, P);
+			mcl::ec::ProjToJacobi(R, Q);
+			CYBOZU_TEST_EQUAL(R, P);
+		}
+	}
 
 	template<class F>
 	void test(F f, const char *msg) const
@@ -672,6 +695,7 @@ mul 499.00usec
 		mulCT();
 		compare();
 		addCT();
+		ProjJacobi();
 	}
 private:
 	Test(const Test&);