add EcT::normalize(EcT&, const EcT&)

include/mcl/ec.hpp

@@ -155,6 +155,11 @@ public:
 		}
 #endif
 	}
+	static void normalize(EcT& y, const EcT& x)
+	{
+		y = x;
+		y.normalize();
+	}
 	static inline void init(const Fp& a, const Fp& b, int mode = ec::Jacobi)
 	{
 		a_ = a;
@@ -835,7 +840,7 @@ public:
 			px = &tmp;
 		}
 		z.clear();
-		fp::powGeneric(z, *px, y, yn, EcT::add, EcT::dbl, constTime);
+		fp::powGeneric(z, *px, y, yn, EcT::add, EcT::dbl, EcT::normalize, constTime);
 		if (isNegative) {
 			neg(z, z);
 		}

include/mcl/fp.hpp

@@ -455,7 +455,6 @@ public:
 	{
 		return fp::isLessArray(v_, rhs.v_, op_.N);
 	}
-	void normalize() const {} // dummy method
 	/*
 		set IoMode for operator<<(), or operator>>()
 	*/

include/mcl/fp_tower.hpp

@@ -180,7 +180,6 @@ public:
 	bool isOne() const { return a.isOne() && b.isZero(); }
 	bool operator==(const Fp2T& rhs) const { return a == rhs.a && b == rhs.b; }
 	bool operator!=(const Fp2T& rhs) const { return !operator==(rhs); }
-	void normalize() const {} // dummy method
 	/*
 		return true is a is odd (do not consider b)
 		this function is for only compressed reprezentation of EC
@@ -782,7 +781,6 @@ struct Fp6T : public fp::Operator<Fp6T<Fp> > {
 		Fp2::mul(y.b, p.b, q);
 		Fp2::mul(y.c, p.c, q);
 	}
-	void normalize() const {} // dummy
 };
 
 /*
@@ -926,7 +924,6 @@ struct Fp12T : public fp::Operator<Fp12T<Fp> > {
 	{
 		return a.getStr(ioMode) + fp::getIoSeparator(ioMode) + b.getStr(ioMode);
 	}
-	void normalize() const {} // dummy
 };
 
 } // mcl

include/mcl/operator.hpp

@@ -66,7 +66,7 @@ private:
 			px = &tmp;
 		}
 		z = 1;
-		fp::powGeneric(z, *px, y, yn, T::mul, T::sqr);
+		fp::powGeneric(z, *px, y, yn, T::mul, T::sqr, (void (*)(T&, const T&))0);
 		if (isNegative) {
 			T::inv(z, z);
 		}

include/mcl/util.hpp

@@ -196,7 +196,7 @@ void getRandVal(T *out, RG& rg, const T *in, size_t bitSize)
 	@note &out != x and out = the unit element of G
 */
 template<class G, class T>
-void powGeneric(G& out, const G& x, const T *y, size_t n, void mul(G&, const G&, const G&) , void sqr(G&, const G&), bool constTime = false)
+void powGeneric(G& out, const G& x, const T *y, size_t n, void mul(G&, const G&, const G&) , void sqr(G&, const G&), void normalize(G&, const G&), bool constTime = false)
 {
 	assert(&out != &x);
 	while (n > 0) {
@@ -223,11 +223,16 @@ void powGeneric(G& out, const G& x, const T *y, size_t n, void mul(G&, const G&,
 		}
 	}
 	G tbl[4]; // tbl = { discard, x, x^2, x^3 }
-	x.normalize();
+	if (normalize) {
-	tbl[0] = x;
+		normalize(tbl[0], x);
-	tbl[1] = x;
+	} else {
-	sqr(tbl[2], tbl[1]); tbl[2].normalize();
+		tbl[0] = x;
-	mul(tbl[3], tbl[2], x); tbl[3].normalize();
+	}
+	tbl[1] = tbl[0];
+	sqr(tbl[2], tbl[1]);
+	if (normalize) { normalize(tbl[2], tbl[2]); }
+	mul(tbl[3], tbl[2], x);
+	if (normalize) { normalize(tbl[3], tbl[3]); }
 	T v = y[n - 1];
 	int m = cybozu::bsr<T>(v);
 	if (m & 1) {