fixed poly

src/math/ecc.rs

@@ -1,8 +1,10 @@
 #![allow(dead_code)]
-/// eliptic curve cryptography
+use std::{ops::{Mul, Neg}, fmt::Debug};
+
+/// eliptic curve cryptograp.s
 ///
-/// This module implements structs and functionalities used for eliptic curve cryptography (ECC).
+/// This module implements structs and functionalities used for eliptic curve cryptograp.s (ECC).
-/// Do not expect it to actually be secure, I made this for cryptography lectures.
+/// Do not expect it to actually be secure, I made this for cryptograp.s lectures.
 ///
 /// Author:     Christoph J. Scherr <software@cscherr.de>
 /// License:    MIT
@@ -10,19 +12,11 @@
 
 use super::gallois::GalloisField;
 
+use num::Integer;
 use pyo3::prelude::*;
 
-/// This is a very special math point, it does not really exist but is useful.
-pub const INFINITY_POINT: ElipticCurvePoint = ElipticCurvePoint {
-    x: 0,
-    y: 0,
-    is_infinity_point: true,
-    verbose: false
-};
-
 #[derive(Debug, Clone)]
 #[allow(non_snake_case)]
-#[pyclass]
 /// represent a specific eliptic curve
 ///
 /// real curves not supported, only in Gallois Fields
@@ -32,36 +26,56 @@ pub struct ElipticCurve {
     b: i128,
     points: Vec<ElipticCurvePoint>,
     verbose: bool,
-    INFINITY_POINT: ElipticCurvePoint,
+    INFINITY_POINT: Option<ElipticCurvePoint>
 }
 
 impl ElipticCurve {
     pub fn new(f: GalloisField, a: i128, b: i128, verbose: bool) -> Self {
-        let e = ElipticCurve {
+        let mut e = ElipticCurve {
             f,
             a,
             b,
             points: Vec::new(),
             verbose,
-            INFINITY_POINT
+            INFINITY_POINT: None
         };
+        let infty = ElipticCurvePoint::new(0, 0, e.f);
+        e.INFINITY_POINT = Some(infty);
         return e;
     }
 
-    /// calculate a point for coordinates
+    /// calculate a value for coordinates
-    pub fn poly(&self, x: i128, y: i128) -> i128 {
+    pub fn poly<T>(&self, r: T, s: T) -> i128 
-        return y.pow(2) - x.pow(3) - (self.a * x) - self.b;
+    where
+    T: Integer,
+    T: Mul,
+    T: Debug,
+    T: num::cast::AsPrimitive<i128>,
+    T: Neg
+    {
+        dbg!(&r);
+        dbg!(&s);
+        let r: i128 = num::cast::AsPrimitive::as_(r);
+        let s: i128 = num::cast::AsPrimitive::as_(s);
+        let res =  s.pow(2) - r.pow(3) - (self.a * r) - self.b;
+        let res1 = self.f.reduce(res);
+        if self.verbose {
+            println!("F({}, {}) = {}² - {}³ - {} * {} - {} = {res} = {res1}",
+                r, s, s, r, self.a, r, self.b
+            );
+        }
+        return res1 as i128;
     }
 
     pub fn check_point(self, p: ElipticCurvePoint) -> bool {
         let mut valid = true;
-        let r =  self.f.reduce(self.poly(p.x, p.y));
+        let res =  self.f.reduce(self.poly(p.r, p.s));
         if self.verbose {
-            println!("F({}, {}) = {}² - {}³ - {} * {} - {} = {r}",
+            println!("F({}, {}) = {}² - {}³ - {} * {} - {} = {res}",
-                p.x, p.y, p.y, p.x, self.a, p.x, self.b
+                p.r, p.s, p.s, p.r, self.a, p.r, self.b
             )
         }
-        valid &= r == 0;
+        valid &= res == 0;
         return valid;
     }
 }
@@ -72,15 +86,15 @@ fn test_check_point() {
     let ec = ElipticCurve::new(f, 1, 679, true);
     // real points
     let p = vec![
-        ElipticCurvePoint::new(298, 531),
+        ElipticCurvePoint::new(298, 531, f),
-        ElipticCurvePoint::new(600, 127),
+        ElipticCurvePoint::new(600, 127, f),
-        ElipticCurvePoint::new(846, 176),
+        ElipticCurvePoint::new(846, 176, f),
     ];
-    // random values, not part of the ec.
+    // random values, not part of the e, fc.
     let np = vec![
-        ElipticCurvePoint::new(198, 331),
+        ElipticCurvePoint::new(198, 331, f),
-        ElipticCurvePoint::new(100, 927),
+        ElipticCurvePoint::new(100, 927, f),
-        ElipticCurvePoint::new(446, 876),
+        ElipticCurvePoint::new(446, 876, f),
     ];
     for i in p {
         dbg!(&i);
@@ -94,43 +108,72 @@ fn test_check_point() {
 
 
 #[derive(Debug, Clone, Copy)]
-#[pyclass]
 /// represent a specific eliptic curves point
 pub struct ElipticCurvePoint {
-    x: i128,
+    r: i128,
-    y: i128,
+    s: i128,
     is_infinity_point: bool,
-    verbose: bool
+    field: GalloisField
 }
 
 impl ElipticCurvePoint {
-    pub fn new(x: i128, y: i128) -> Self {
+    pub fn new(r: i128, s: i128, field: GalloisField) -> ElipticCurvePoint {
         ElipticCurvePoint {
-            x,
+            r,
-            y,
+            s,
             is_infinity_point: false,
-            verbose: false
+            field
         }
     }
     
-    pub fn get_infinity_point() -> Self {
-        return INFINITY_POINT;
-    }
-
     /// add two points
-    pub fn add(a: Self, b: Self) -> Self {
+    pub fn add(self, point: Self) -> Result<Self, String> {
-        // TODO
+        if self.field.cha != point.field.cha {
+            return Err(String::from("Points are not on the same field"));
+        }
+        if self.field.prime_base {
+            // case 1 both infty
+            if self.is_infinity_point && point.is_infinity_point {
+                return Ok(point);
+            }
+            // case 2 one is infty
+            else if self.is_infinity_point && !point.is_infinity_point {
+                return Ok(point);
+            }
+            else if !self.is_infinity_point && point.is_infinity_point {
+                return Ok(self);
+            }
+            // case 3 r_1 != r_2
+            else if self.r != point.r {
                 panic!("TODO");
             }
+            // case 4 r_1 = r_2; s_1 = -s_2
+            else if self.r == point.r && self.s == point.neg().s {
+                return Ok(Self::new(0, 0, self.field));
+            }
+
+            // how do we get here?
+            // this should never occur
+            else {
+                panic!("we dont know what to do in this case?")
+            }
+        }
+        else {
+            return Err(String::from("Only prime fields are supported currently"));
+        }
+    }
 
     /// get negative of a point
-    pub fn neg(p: Self) -> Self {
+    pub fn neg(self) -> Self {
-        // TODO
+        return ElipticCurvePoint::new(
-        panic!("TODO");
+            self.r, 
+            self.field.reduce(-(self.s as i128)) as i128, 
+            self.field
+            );
     }
 
-    /// multiply a point by an integer
+    /// multip.s a point by an integer
-    pub fn mul(n: u128, a: Self) -> Self {
+    pub fn mul(self, n: u128) -> Self {
         // TODO
         panic!("TODO");
     }