affine zero point for short-weierstrass added

example/curves.cpp

@@ -41,13 +41,27 @@
 //#include <nil/crypto3/algebra/curves/wei25519.hpp>
 #include <nil/crypto3/algebra/curves/secp_k1.hpp>
 #include <nil/crypto3/algebra/curves/pallas.hpp>
+#include <nil/crypto3/algebra/curves/vesta.hpp>
 #include <nil/crypto3/algebra/curves/secp_r1.hpp>
 
 using namespace nil::crypto3::algebra;
 
+template<typename FpCurveGroupElement>
+void print_affine_fp_curve_group_element(FpCurveGroupElement e) {
+    if (e.is_zero()) {
+        std::cout << "zero\n";
+    } else {
+        std::cout << e.X.data << " " << e.Y.data << std::endl;
+    }
+}
+
 template<typename FpCurveGroupElement>
 void print_fp_curve_group_element(FpCurveGroupElement e) {
-    std::cout << e.X.data << " " << e.Y.data << " " << e.Z.data << std::endl;
+    if (e.is_zero()) {
+        std::cout << "zero\n";
+    } else {
+        std::cout << e.X.data << " " << e.Y.data << " " << e.Z.data << std::endl;
+    }
 }
 
 template<typename Fp2CurveGroupElement>
@@ -65,12 +79,45 @@ void print_fp3_curve_group_element(Fp3CurveGroupElement e) {
 
 // print dunctions can be made using arity in fields
 
+template<typename FpCurveGroup>
+void fp_curve_group_affine_math_examples() {
+    typedef typename FpCurveGroup::value_type group_value_type;
+    typedef typename FpCurveGroup::field_type::value_type field_value_type;
+
+    field_value_type e1 = field_value_type(2), e2(5);
+    group_value_type c1 = group_value_type::zero();
+    group_value_type c2(e1, e2);
+
+    std::cout << "Curve element values: " << std::endl;
+    std::cout << "c1 value: ";
+    print_affine_fp_curve_group_element(c1);
+
+    std::cout << "c2 value: ";
+    print_affine_fp_curve_group_element(c2);
+
+    std::cout << "c1 + c2 value: ";
+    print_affine_fp_curve_group_element(c1 + c2);
+
+    std::cout << "c1 - c2 value: ";
+    print_affine_fp_curve_group_element(c1 - c2);
+
+    std::cout << "Doubled c1 value: ";
+    print_affine_fp_curve_group_element(c1.doubled());
+
+    group_value_type cd = c1.doubled();
+
+    // group_value_type cn = c1.normalize();
+
+    // std::cout << "c1 normalized value: ";
+    // print_fp_curve_group_element(cn);
+}
+
 template<typename FpCurveGroup>
 void fp_curve_group_basic_math_examples() {
     typedef typename FpCurveGroup::value_type group_value_type;
     typedef typename FpCurveGroup::field_type::value_type field_value_type;
 
-    field_value_type e1 = field_value_type(2), e2(3), e3(5), e4(3), e5(5), e6(7);
+    field_value_type e1 = field_value_type(0), e2(1), e3(0), e4(3), e5(5), e6(7);
     group_value_type c1(e1, e2, e3), c2(e4, e5, e6);
 
     std::cout << "Curve element values: " << std::endl;
@@ -246,5 +293,15 @@ int main() {
 
      std::cout << "----------------------------" << std::endl;
 
+    std::cout << "Pallas curve g1 group affine math:" << std::endl;
+    fp_curve_group_affine_math_examples<curves::pallas::g1_type<curves::coordinates::affine>>();
+
+     std::cout << "----------------------------" << std::endl;
+
+    std::cout << "Vesta curve g1 group affine math:" << std::endl;
+    fp_curve_group_affine_math_examples<curves::vesta::g1_type<curves::coordinates::affine>>();
+
+     std::cout << "----------------------------" << std::endl;
+
     return 0;
 }

include/nil/crypto3/algebra/curves/detail/forms/short_weierstrass/element_g1_affine.hpp

@@ -67,6 +67,7 @@ namespace nil {
 
                         field_value_type X;
                         field_value_type Y;
+                        bool is_zero_flag;
 
                         /*************************  Constructors and zero/one  ***********************************/
 
@@ -75,7 +76,7 @@ namespace nil {
                          *
                          */
                         constexpr curve_element() :
-                            curve_element(params_type::zero_fill[0], params_type::zero_fill[1]) {};
+                            is_zero_flag(true) {};
 
                         /** @brief
                          *    @return the selected point $(X:Y)$ in the affine coordinates
@@ -84,6 +85,7 @@ namespace nil {
                         constexpr curve_element(field_value_type in_X, field_value_type in_Y) {
                             this->X = in_X;
                             this->Y = in_Y;
+                            is_zero_flag = false;
                         };
 
                         /** @brief Get the point at infinity
@@ -133,7 +135,7 @@ namespace nil {
                          * @return true if element from group G1 is the point at infinity
                          */
                         constexpr bool is_zero() const {
-                            return X == params_type::zero_fill[0] && Y == params_type::zero_fill[1];
+                            return is_zero_flag;
                         }
 
                         /*************************  Reducing operations  ***********************************/