cha2 curve check

src/math/ecc.rs

@@ -56,7 +56,8 @@ impl EllipticCurve {
             F(X, Y) = Y² - X³ - {a}X - {b}")
         }
 
-        // check diskriminante
+        // check if the curve is valid
+        if field.cha > 2 {
             let d = 4*a.pow(3) + 27*b.pow(2);
             if field.reduce::<_, u128>(d) == 0 {
                 if verbose {
@@ -69,6 +70,23 @@ impl EllipticCurve {
                 println!("4*{a}³ + 27*{b}² = {d} = {} != 0\n\
                     Check for Diskriminante passed", field.reduce::<_, u128>(d));
             }
+        }
+        else {
+            let valid: bool = field.reduce::<_, i128>(b) == 0;
+            
+            if verbose {
+                if valid {
+                    println!("b = {b} != 0 => Curve valid");
+                }
+                else {
+                    println!("b = {b} == 0 => Curve invalid")
+                }
+            }
+
+            if !valid {
+                return Err(String::from("b == 0 => Curve invalid"));
+            }
+        }
 
         let mut infty = EllipticCurvePoint::new(0, 0);
         infty.is_infinity_point = true;
@@ -121,7 +139,9 @@ impl EllipticCurve {
 
     pub fn check_point(&self, p: EllipticCurvePoint, verbose: bool) -> bool {
         if p.is_infinity_point {
+            if self.verbose {
                 println!("p is infinity: {p}");
+            }
             return true;
         }
         let mut valid = true;
@@ -310,8 +330,11 @@ impl EllipticCurve {
 
     /// get negative of a point
     pub fn neg(&self, p: EllipticCurvePoint) -> EllipticCurvePoint {
-        self.new_point(p.r, self.field.reduce::<_, u128>(-(p.s as i128))).expect("negation of \
-        point is not on field, math error")
+        if p.is_infinity_point {
+            return p;
+        }
+        self.new_point(p.r, self.field.reduce(-(p.s as i128))).expect(format!("negation of \
+        point is not on field, math error: {}", p).as_str())
     }
 
     /// multip.s a point by an integer
@@ -327,7 +350,7 @@ impl EllipticCurve {
         }
         let t: usize = num::cast(t).unwrap();
         if t < 1 {
-            return Err(String::from("point multiplication works only if t > 0"));
+            return Ok(self.INFINITY_POINT);
         }
         if self.verbose {
             println!("h = t * g = {t} * {g}\n\
@@ -453,8 +476,19 @@ impl EllipticCurve {
 
 impl std::fmt::Display for EllipticCurve{
     fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+        if self.field.prime_base {
             write!(f, "F(X, Y) = Y² - X³ -{}X - {}", self.a, self.b)
         }
+        else if self.field.cha == 2 {
+            write!(f, "F(X, Y) = Y² + XY + X³ + ({}) * X² + ({})", 
+                   self.field.display(self.a),
+                   self.field.display(self.b),
+                   )
+        }
+        else {
+            write!(f, "ERROR")
+        }
+    }
 }
 
 #[pyclass]